From 37795d9f90a78966bf12218d5881dc8b488c39cc Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 10:24:54 +0000
Subject: [PATCH 01/58] Cut screw holes and counterbores no narrower than the
 size asked

A plate's screw counterbore is 14-sided and its shank 12-sided, and both had their
corners on the size typed, so across their flats they were narrower than it at every
size: the default 6 mm counterbore was 5.85 mm and the 3 mm hole 2.90. Now their
corners go out until the flats stand on the size, as #61 did for the magnet pocket. No
allowance on top: a screw head drops into its counterbore rather than being pressed in.

The limits measure the pocket as it is now cut, so each screw size is the room times
cos(pi/12) for the hole and cos(pi/14) for the head. At 42 mm the widest hole goes from
8.3 to 8 mm and the widest head from 14 to 13.6; the cap between a cell's four pockets
from 25 to 24.3 (head) and 24.1 (hole); the default 3 mm hole now needs a 36.81 mm
pitch rather than 36.7, and the 6 mm head 34.16 rather than 34. Designs without screws
are unchanged.

The plate audit's pinned digest for magnets and screws moves with the pocket, and the
22.2 mm shank row keeps the pocket it was written about (22.2 mm across its corners).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md                    | 16 +++++++++++---
 src/core.js                       | 35 ++++++++++++++++++++-----------
 test/plate-audit.js               | 22 ++++++++++++-------
 test/ui/plates-robustness.spec.js | 19 +++++++++--------
 4 files changed, 60 insertions(+), 32 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index 0b03935..bdc4885 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -692,6 +692,15 @@ currently installed):
   thick walls, scoops, shelves and notes, holes, removable plates and half sizes, it
   came to 0.998 to 1.001, the lowest those whose shelf has a note raised on it, whose
   letters it leaves out.
+- **A mounting pocket's size is the size across its flats.** Every bore is a polygon, 14
+  sides for a magnet and a counterbore and 12 for a shank, and one with its corners on
+  the size asked is narrower than that across its flats: the default 6 mm counterbore was
+  5.85 mm, the 3 mm shank 2.90, a 10 mm magnet's pocket 9.94 even with its 0.1 mm press
+  fit at the corners. So `fastenerCutter` stands the corners 1/cos(π/n) of the radius out
+  and the flats on it, and the magnet keeps its 0.1 at the corners where that is further,
+  up to 7.77 mm. A screw gets no allowance on top: its head drops into the counterbore,
+  which the field already sizes with room round it. `mountLimits` measures every room to
+  the corners, so the largest size it takes is that room times cos(π/n).
 - **The socket's corner clearance is not uniform.** Known, documented, deliberately not
   fixed — see [socket-clearance.md](socket-clearance.md).
 - **The plate's outer corner radius has a ceiling, and it is the socket's.** Both the
@@ -799,9 +808,10 @@ currently installed):
   the cell's side where it crosses it, and that side stands on the same plane as the
   neighbour's, so a split that lands on a corner of the neighbour's region is that
   corner's edge in both shells (a 21.7 mm magnet from beneath at 55 mm, 0.03 microns off;
-  a 22.2 mm screw shank at 56.5 mm, on main too). With pockets on the piece, every cell
-  and margin is checked against the shells built beside it (`settle`), and the pockets of
-  one or the other are cut again moved 1.7 microns, turned a 28th of a turn, or both. The
+  a screw shank 22.2 mm across its corners at 56.5 mm, on main too). With pockets on the
+  piece, every cell and margin is checked against the shells built beside it (`settle`),
+  and the pockets of one or the other are cut again moved 1.7 microns, turned a 28th of a
+  turn, or both. The
   cut kept is the one that shares the fewest edges with every shell beside it: keeping one
   that touched fewer shells, as `settle` first did, left a cell built later sharing an edge
   nothing cleared (10.1 to 11.1 mm magnets at 47.91 to 50.05 mm, clean on main). And once
diff --git a/src/core.js b/src/core.js
index 36e5684..3e2f8d7 100644
--- a/src/core.js
+++ b/src/core.js
@@ -846,10 +846,18 @@ function fastenerCutter(cfg, magZ0, magZ1, shankTop) {
     add(cfg.magnetSide === 'top'
       ? cylinder(0, 0, magnetR, magZ0, magZ1, 14)
       : cylinder(0, 0, magnetR, -0.5, cfg.magnetH, 14));
+  /* A screw's two bores had their corners on the size asked, so their flats came inside
+     it at every size: the 14-sided counterbore cos(π/14) of the head and the 12-sided
+     shank cos(π/12) of the hole, 5.85 mm across the flats for the default 6 mm head and
+     2.90 for the 3 mm shank. Their corners go out the same way, so the flats stand on the
+     radius and neither bore is narrower anywhere than the size typed. And no more than
+     that: the magnet's 0.1 is a press fit, and a screw head is not pressed in. It drops
+     into its counterbore, which the field already sizes with room round it (6 mm for an
+     M3's 5.5 mm head), and the shank is a clearance hole. */
   if (cfg.screws) {
     if (cfg.screwHeadD > cfg.screwHoleD)
-      add(cylinder(0, 0, cfg.screwHeadD/2, -0.5, cfg.screwHeadDepth, 14));
-    add(cylinder(0, 0, cfg.screwHoleD/2, -0.5, shankTop, 12));
+      add(cylinder(0, 0, cfg.screwHeadD/2 / Math.cos(Math.PI/14), -0.5, cfg.screwHeadDepth, 14));
+    add(cylinder(0, 0, cfg.screwHoleD/2 / Math.cos(Math.PI/12), -0.5, shankTop, 12));
   }
   return cut;
 }
@@ -865,13 +873,15 @@ function movePolys(polys, dx, dy) {
   }));
 }
 
-// counterbore: hole cylinder full height + wider recess from chosen face
+// counterbore: hole cylinder full height + wider recess from chosen face, each with its
+// flats on its size as fastenerCutter cuts them
 function screwCutter(cx, cy, holeD, headD, z0, z1, headDepth, fromTop) {
-  let polys = cylinder(cx, cy, holeD/2, z0 - 0.5, z1 + 0.5, 12);
+  let polys = cylinder(cx, cy, holeD/2 / Math.cos(Math.PI/12), z0 - 0.5, z1 + 0.5, 12);
   if (headD > holeD) {
+    const headR = headD/2 / Math.cos(Math.PI/14);
     const rec = fromTop
-      ? cylinder(cx, cy, headD/2, z1 - headDepth, z1 + 0.5, 14)
-      : cylinder(cx, cy, headD/2, z0 - 0.5, z0 + headDepth, 14);
+      ? cylinder(cx, cy, headR, z1 - headDepth, z1 + 0.5, 14)
+      : cylinder(cx, cy, headR, z0 - 0.5, z0 + headDepth, 14);
     polys = csgUnion(polys, rec);
   }
   return polys;
@@ -2483,9 +2493,10 @@ function mountLimits(cfg, layout) {
     // a magnet pocket's corners are 0.1 mm over the magnet's radius, or out to where its
     // flats stand on that radius if that is further (fastenerCutter)
     magnetD: r10(2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14))),
-    // a screw's bores have their corners on its size
-    screwHoleD: r10(2 * Math.min(fit(top), below)),
-    screwHeadD: r10(2 * Math.min(fit(under), below)),
+    // a screw's bores have their flats on its size, so their corners stand 1/cos(π/n) of
+    // it out: the shank's 12 sides and the counterbore's 14 (fastenerCutter)
+    screwHoleD: r10(2 * Math.min(fit(top), below) * Math.cos(Math.PI / 12)),
+    screwHeadD: r10(2 * Math.min(fit(under), below) * Math.cos(Math.PI / 14)),
     // in the solid floor the pad grows to suit, so only a boss caps the depth
     depth: bosses ? r10(BOSS_H - MOUNT_SKIN) : Infinity,
     // which of the sizes the cut beside it stops, rather than the floor, cell or boss
@@ -3111,9 +3122,9 @@ function buildPiece(cfg, layout, piece, onStatus) {
    * A 21.7 mm magnet from beneath at a 55 mm pitch did it: a flat of the pocket in the
    * cell at the back left, on the magnet's radius, crosses that cell's front side 0.03
    * microns from the corner of the cell at the back right. A 22.2 mm screw shank at 56.5
-   * mm did it twice over, from the cell at the back right as well, on main too. Each shell
-   * is closed on its own, so the pockets' own retries never see it, and it comes and goes
-   * with the size and the pitch.
+   * mm (22.2 across its corners, as shanks were cut then) did it twice over, from the cell
+   * at the back right as well, on main too. Each shell is closed on its own, so the
+   * pockets' own retries never see it, and it comes and goes with the size and the pitch.
    *
    * So with mounting pockets on the piece, every shell the cells and margins make is
    * checked against those built before it beside it, as jointed cells are above. One that
diff --git a/test/plate-audit.js b/test/plate-audit.js
index 18eb9bb..c7fdcf5 100644
--- a/test/plate-audit.js
+++ b/test/plate-audit.js
@@ -1945,12 +1945,14 @@ console.log('\nthe other limits, built at their ends:');
      half a MOUNT_WALL short of the line halfway to the one beside it, so its corners stop
      at holeOffset less 0.5 and the wall between two pockets is at least 1 mm. A magnet
      pocket's corners are at the larger of 0.1 over the magnet's radius and
-     the radius over cos(π/14) (its flats on the magnet); a screw's bores have their corners
-     on its size. At 55 and 60 mm, each way in: the widest the page takes has to build
-     watertight, and the first tenth past the rule has to be refused. */
+     the radius over cos(π/14) (its flats on the magnet); a screw's bores have their flats
+     on its size too, so their corners are its radius over cos(π/12) for the 12-sided shank
+     and cos(π/14) for the 14-sided head. At 55 and 60 mm, each way in: the widest the page
+     takes has to build watertight, and the first tenth past the rule has to be refused. */
   const reach = G.DEFAULTS.holeOffset - 0.5;
   const corner = { magnetD: (d) => Math.max(d / 2 + 0.1, d / 2 / Math.cos(Math.PI / 14)),
-                   screwHoleD: (d) => d / 2, screwHeadD: (d) => d / 2 };
+                   screwHoleD: (d) => d / 2 / Math.cos(Math.PI / 12),
+                   screwHeadD: (d) => d / 2 / Math.cos(Math.PI / 14) };
   const firstPast = (f) => { let d = 1; while (corner[f](d) <= reach + 1e-9) d = Math.round(d * 10 + 1) / 10; return d; };
   const WIDE = [
     ['magnet from below', { magnets: true }, 'magnetD'],
@@ -1988,9 +1990,12 @@ console.log('\nthe other limits, built at their ends:');
      sliver of the socket floor by a corner 4.7 microns from one of the floor's spokes:
      11.1 mm at 48.55, 24 open edges on d9442d4. Main's pocket has a corner 1.0 micron
      from the same spoke and none open, so it is how the cut falls, not how near. A cell
-     open at the floor's height has its floor fanned again (fanCentre). */
+     open at the floor's height has its floor fanned again (fanCentre).
+     The shank is the pocket it was then, 22.2 mm across its corners: since a screw's
+     bores stand their flats on the size asked, that is the shank a 21.44 mm hole cuts. */
+  const shank222 = 22.2 * Math.cos(Math.PI / 12);
   for (const [nm, o] of [['21.7 mm magnet at 55 mm', { pitch: 55, magnets: true, magnetD: 21.7 }],
-                         ['22.2 mm screw shank at 56.5', { pitch: 56.5, screws: true, screwHoleD: 22.2, screwHeadD: 22.2 }],
+                         ['22.2 mm screw shank at 56.5', { pitch: 56.5, screws: true, screwHoleD: shank222, screwHeadD: shank222 }],
                          ['10.1 mm magnet above, 47.91', { pitch: 47.91, magnets: true, magnetD: 10.1, magnetSide: 'top' }],
                          ['10.6 mm magnet below, 48.98', { pitch: 48.98, magnets: true, magnetD: 10.6 }],
                          ['11.1 mm magnet above, 48.55', { pitch: 48.55, magnets: true, magnetD: 11.1, magnetSide: 'top' }]]) {
@@ -2468,9 +2473,10 @@ console.log('\nplates without half cells build the same bytes:');
       alignX: 'end', alignY: 'end', connector: 'none' }, '37b5f305cc4da6dd'],
     // fanCentre moved four of its nine cells' bottom caps off a spoke a few thousandths from
     // a cutter's corner: the same bottom face fanned from another point, its area and the
-    // volume unchanged
+    // volume unchanged. Then the screw's bores went out until their flats stood on the
+    // sizes asked, the counterbore and the shank wider by design
     ['126 x 126, magnets and screws', { drawerW: 126, drawerD: 126, marginMode: 'custom',
-      mLeft: 0, mRight: 0, mFront: 0, mBack: 0, magnets: true, screws: true }, '5b339b75bd8c513e'],
+      mLeft: 0, mRight: 0, mFront: 0, mBack: 0, magnets: true, screws: true }, '7eaec017027d5a46'],
     ['140 x 140, corner pockets', { drawerW: 140, drawerD: 140, marginMode: 'auto',
       magnets: true, baseMode: 'bosses' }, '7088f24def428095'],
     ['168 x 180, skeleton', { drawerW: 168, drawerD: 180, marginMode: 'auto',
diff --git a/test/ui/plates-robustness.spec.js b/test/ui/plates-robustness.spec.js
index db5c058..ef96ee4 100644
--- a/test/ui/plates-robustness.spec.js
+++ b/test/ui/plates-robustness.spec.js
@@ -97,10 +97,10 @@ test.describe('ranges on the geometry fields', () => {
     ['#pi=55&w=110&d=110&mm=custom&ml=0&mr=0&mf=0&mb=0&bw=400&bd=400&mg=1&md=25.4', 'errMagnet',
       /Magnet Ø must be 24\.3 mm or less at a 55 mm pitch — mounting holes sit 13 mm from each cell centre, where the Gridfinity spec puts them, and a cell's four holes have to stay clear of each other/],
     ['#pi=60&w=120&d=120&mm=custom&ml=0&mr=0&mf=0&mb=0&bw=400&bd=400&sc=1&sd=26', 'errScrew',
-      /Screw head Ø must be 25 mm or less at a 60 mm pitch — .* a cell's four holes have to stay clear of each other/],
+      /Screw head Ø must be 24\.3 mm or less at a 60 mm pitch — .* a cell's four holes have to stay clear of each other/],
     ['#mg=1&bm=bosses&mh=3', 'errMagnet', /Magnet depth must be 2\.4 mm or less with corner pockets/],
-    ['#sc=1&sh=20', 'errScrew', /Screw hole Ø must be 8\.3 mm or less/],
-    ['#cn=none&sc=1&sd=30', 'errScrew', /Screw head Ø must be 14 mm or less/],
+    ['#sc=1&sh=20', 'errScrew', /Screw hole Ø must be 8 mm or less/],
+    ['#cn=none&sc=1&sd=30', 'errScrew', /Screw head Ø must be 13\.6 mm or less/],
     ['#sc=1&se=50', 'errScrew', /Screw head depth must be 10 mm or less/],
     ['#cl=1', 'errConnClr', /Fit clearance must be 0\.3 mm or less — any looser and a dovetail pocket/],
     ['#cn=bowtie&cl=5', 'errConnClr', /Fit clearance must be 1 mm or less — check the figure is in millimetres/],
@@ -114,7 +114,7 @@ test.describe('ranges on the geometry fields', () => {
     [`${BOWTIE_42}&mg=1&ms=top&md=8`, 'errMagnet',
       /Magnet Ø must be 7\.6 mm or less at a 42 mm pitch — .* the recesses the bowtie keys fit into/],
     [`${BOWTIE_42.replace('cn=bowtie', 'cn=snap')}&sc=1&sd=10`, 'errScrew',
-      /Screw head Ø must be 7\.8 mm or less at a 42 mm pitch — .* the recesses the snap clips fit into/],
+      /Screw head Ø must be 7\.6 mm or less at a 42 mm pitch — .* the recesses the snap clips fit into/],
     ['#mg=1&md=20', 'errMagnet',
       /Magnet Ø must be 12\.3 mm or less at a 42 mm pitch — .* the notches the dovetail tabs fit into/],
   ];
@@ -385,12 +385,13 @@ test.describe('limits no tighter than the geometry', () => {
     expect(s.built).toBeCloseTo(7.05, 9);
   });
 
-  /* The 34 mm case takes no joint: the default dovetail's notches hold its 6 mm screw head
-     to 3.8 mm there, which is a field error of its own. The puzzle tabs' are what leave
-     a magnet no room at 36 mm, where the cell alone would take 7.7. */
+  /* The 34.5 mm case takes no joint: the default dovetail's notches hold its 6 mm screw
+     head to 4.1 mm there, which is a field error of its own. Nor 34 mm, where the head's
+     flats on its size leave the cell room for 5.8. The puzzle tabs' are what leave a
+     magnet no room at 36 mm, where the cell alone would take 7.7. */
   for (const [hash, id, errId, carried, msg] of [
-    ['#cn=none&sc=1&pi=34', 'screwHoleD', 'errScrew', 3,
-     /Screw hole Ø: there is no room for one at a 34 mm pitch.*Use a larger pitch, or turn off screw holes\./],
+    ['#cn=none&sc=1&pi=34.5', 'screwHoleD', 'errScrew', 3,
+     /Screw hole Ø: there is no room for one at a 34\.5 mm pitch.*Use a larger pitch, or turn off screw holes\./],
     ['#mg=1&pi=20', 'magnetD', 'errMagnet', 6,
      /Magnet Ø: there is no room for one at a 20 mm pitch.*Use a larger pitch, or turn off magnet pockets\./],
     ['#cn=puzzle&mg=1&pi=36', 'magnetD', 'errMagnet', 6,

From 7007724f3dab285fb6b2e42112fcd287a9552b05 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 10:41:44 +0000
Subject: [PATCH 02/58] Decide each mounting bore's shape in one place, for the
 cutters and the limits alike

MOUNT_BORE holds each bore's sides, how far its corners stand for a size, and the largest
size whose corners fit a room. fastenerCutter and screwCutter cut what it says, and
mountLimits reads its sizes back from it, so a pocket and its limit cannot drift apart.
Nothing built changes: the same bytes for the plates tried, and the same limits over
19,404 configurations.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md | 12 ++++----
 src/core.js    | 80 +++++++++++++++++++++++++++++---------------------
 2 files changed, 54 insertions(+), 38 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index bdc4885..13397bb 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -696,11 +696,13 @@ currently installed):
   sides for a magnet and a counterbore and 12 for a shank, and one with its corners on
   the size asked is narrower than that across its flats: the default 6 mm counterbore was
   5.85 mm, the 3 mm shank 2.90, a 10 mm magnet's pocket 9.94 even with its 0.1 mm press
-  fit at the corners. So `fastenerCutter` stands the corners 1/cos(π/n) of the radius out
-  and the flats on it, and the magnet keeps its 0.1 at the corners where that is further,
-  up to 7.77 mm. A screw gets no allowance on top: its head drops into the counterbore,
-  which the field already sizes with room round it. `mountLimits` measures every room to
-  the corners, so the largest size it takes is that room times cos(π/n).
+  fit at the corners. So every bore stands its corners 1/cos(π/n) of the radius out and
+  its flats on it, and the magnet keeps its 0.1 at the corners where that is further, up
+  to 7.77 mm. A screw gets no allowance on top: its head drops into the counterbore,
+  which the field already sizes with room round it. `MOUNT_BORE` says each bore's sides
+  and corner radius, and the largest size whose corners fit a room; `fastenerCutter` cuts
+  what it says, and `mountLimits`, which measures every room to the corners, reads its
+  sizes back from it, so the shape is decided in one place.
 - **The socket's corner clearance is not uniform.** Known, documented, deliberately not
   fixed — see [socket-clearance.md](socket-clearance.md).
 - **The plate's outer corner radius has a ceiling, and it is the socket's.** Both the
diff --git a/src/core.js b/src/core.js
index 3e2f8d7..2bf36e8 100644
--- a/src/core.js
+++ b/src/core.js
@@ -813,6 +813,36 @@ function cylinder(cx, cy, r, z0, z1, seg) {
   return polys;
 }
 
+/* The polygon each mounting bore is cut as: how many sides, and how far out its corners
+ * stand for a size typed (`r`), and back the other way, the largest size whose corners
+ * stay inside a room (`fits`). fastenerCutter and screwCutter cut these and mountLimits
+ * holds the sizes to them, so a bore's shape is decided here and nowhere else. Each is
+ * cylinder's polygon about the site, a corner at every 2πk/sides from +x.
+ *
+ * Every bore stands its flats on the size asked, so its corners are 1/cos(π/sides) of the
+ * radius out and it is no narrower anywhere than the size typed.
+ *   - magnet: 14 sides, cut 0.1 mm over the magnet's radius at its corners: 0.2 over the
+ *     diameter, the press fit bins/bin.js keeps as well ("the plate's rule"). Its flats
+ *     are cos(π/14) of that, and past a 7.78 mm magnet they came inside the magnet
+ *     itself: 4.972 mm for a 10 mm one, a pocket narrower than what goes in it, where
+ *     bins/bin.js's 16 sides keep their flats outside every magnet its field takes. So
+ *     the corners go out as far as it takes for the flats to stand on the magnet's
+ *     radius. For a magnet up to 7.77 mm, the 6 mm default among them, nothing moves.
+ *   - head, the counterbore: 14 sides, and hole, the shank: 12. Both had their corners on
+ *     the size asked, so their flats came inside it at every size, 5.85 mm across for the
+ *     default 6 mm head and 2.90 for the 3 mm hole. Now their corners go out the same
+ *     way, and no further: the magnet's 0.1 is a press fit, and a screw head is not
+ *     pressed in. It drops into its counterbore, which the field already sizes with room
+ *     round it (6 mm for an M3's 5.5 mm head), and the shank is a clearance hole. */
+const MOUNT_BORE = {
+  magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
+            fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },
+  head: { sides: 14, r: (d) => d/2 / Math.cos(Math.PI/14),
+          fits: (room) => 2 * room * Math.cos(Math.PI / 14) },
+  hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
+          fits: (room) => 2 * room * Math.cos(Math.PI / 12) },
+};
+
 /* Everything removed at one mounting site, as ONE solid.
  *
  * Up to three cylinders share this axis: a magnet pocket, a screw shank, and the head's
@@ -834,30 +864,17 @@ function cylinder(cx, cy, r, z0, z1, seg) {
 function fastenerCutter(cfg, magZ0, magZ1, shankTop) {
   let cut = null;
   const add = (c) => { cut = cut ? csgUnion(cut, c) : c; };
-  /* A magnet's pocket is 14-sided, cut 0.1 mm over the magnet's radius at its corners:
-     0.2 over the diameter, the press fit bins/bin.js keeps as well ("the plate's rule").
-     Its flats are cos(π/14) of that, and past a 7.78 mm magnet they came inside the
-     magnet itself: 4.972 mm for a 10 mm one, a pocket narrower than what goes in it,
-     where bins/bin.js's 16 sides keep their flats outside every magnet its field takes.
-     So the corners go out as far as it takes for the flats to stand on the magnet's
-     radius. For a magnet up to 7.77 mm, the 6 mm default among them, nothing moves. */
-  const magnetR = Math.max(cfg.magnetD/2 + 0.1, cfg.magnetD/2 / Math.cos(Math.PI/14));
+  // each bore as MOUNT_BORE shapes it
+  const { magnet, head, hole } = MOUNT_BORE;
+  const magnetR = magnet.r(cfg.magnetD);
   if (cfg.magnets)
     add(cfg.magnetSide === 'top'
-      ? cylinder(0, 0, magnetR, magZ0, magZ1, 14)
-      : cylinder(0, 0, magnetR, -0.5, cfg.magnetH, 14));
-  /* A screw's two bores had their corners on the size asked, so their flats came inside
-     it at every size: the 14-sided counterbore cos(π/14) of the head and the 12-sided
-     shank cos(π/12) of the hole, 5.85 mm across the flats for the default 6 mm head and
-     2.90 for the 3 mm shank. Their corners go out the same way, so the flats stand on the
-     radius and neither bore is narrower anywhere than the size typed. And no more than
-     that: the magnet's 0.1 is a press fit, and a screw head is not pressed in. It drops
-     into its counterbore, which the field already sizes with room round it (6 mm for an
-     M3's 5.5 mm head), and the shank is a clearance hole. */
+      ? cylinder(0, 0, magnetR, magZ0, magZ1, magnet.sides)
+      : cylinder(0, 0, magnetR, -0.5, cfg.magnetH, magnet.sides));
   if (cfg.screws) {
     if (cfg.screwHeadD > cfg.screwHoleD)
-      add(cylinder(0, 0, cfg.screwHeadD/2 / Math.cos(Math.PI/14), -0.5, cfg.screwHeadDepth, 14));
-    add(cylinder(0, 0, cfg.screwHoleD/2 / Math.cos(Math.PI/12), -0.5, shankTop, 12));
+      add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
+    add(cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides));
   }
   return cut;
 }
@@ -873,15 +890,15 @@ function movePolys(polys, dx, dy) {
   }));
 }
 
-// counterbore: hole cylinder full height + wider recess from chosen face, each with its
-// flats on its size as fastenerCutter cuts them
+// counterbore: hole cylinder full height + wider recess from chosen face, each bore as
+// MOUNT_BORE shapes it
 function screwCutter(cx, cy, holeD, headD, z0, z1, headDepth, fromTop) {
-  let polys = cylinder(cx, cy, holeD/2 / Math.cos(Math.PI/12), z0 - 0.5, z1 + 0.5, 12);
+  const { head, hole } = MOUNT_BORE;
+  let polys = cylinder(cx, cy, hole.r(holeD), z0 - 0.5, z1 + 0.5, hole.sides);
   if (headD > holeD) {
-    const headR = headD/2 / Math.cos(Math.PI/14);
     const rec = fromTop
-      ? cylinder(cx, cy, headR, z1 - headDepth, z1 + 0.5, 14)
-      : cylinder(cx, cy, headR, z0 - 0.5, z0 + headDepth, 14);
+      ? cylinder(cx, cy, head.r(headD), z1 - headDepth, z1 + 0.5, head.sides)
+      : cylinder(cx, cy, head.r(headD), z0 - 0.5, z0 + headDepth, head.sides);
     polys = csgUnion(polys, rec);
   }
   return polys;
@@ -2490,13 +2507,10 @@ function mountLimits(cfg, layout) {
   const own = fit(cfg.magnetSide === 'top' ? top : under);
   const room = Math.min(own, magnetJoint);
   return {
-    // a magnet pocket's corners are 0.1 mm over the magnet's radius, or out to where its
-    // flats stand on that radius if that is further (fastenerCutter)
-    magnetD: r10(2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14))),
-    // a screw's bores have their flats on its size, so their corners stand 1/cos(π/n) of
-    // it out: the shank's 12 sides and the counterbore's 14 (fastenerCutter)
-    screwHoleD: r10(2 * Math.min(fit(top), below) * Math.cos(Math.PI / 12)),
-    screwHeadD: r10(2 * Math.min(fit(under), below) * Math.cos(Math.PI / 14)),
+    // every room above is to a bore's corners, which stand out past its size (MOUNT_BORE)
+    magnetD: r10(MOUNT_BORE.magnet.fits(room)),
+    screwHoleD: r10(MOUNT_BORE.hole.fits(Math.min(fit(top), below))),
+    screwHeadD: r10(MOUNT_BORE.head.fits(Math.min(fit(under), below))),
     // in the solid floor the pad grows to suit, so only a boss caps the depth
     depth: bosses ? r10(BOSS_H - MOUNT_SKIN) : Infinity,
     // which of the sizes the cut beside it stops, rather than the floor, cell or boss

From 5b0dda0498ace00084738d0625a1875064e8a23a Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 11:23:13 +0000
Subject: [PATCH 03/58] Explain why the no-room screw check moved to 34.5 mm,
 and tidy the settle note

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md                    | 22 +++++++++++-----------
 test/ui/plates-robustness.spec.js |  8 +++++---
 2 files changed, 16 insertions(+), 14 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index 13397bb..237570d 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -813,17 +813,17 @@ currently installed):
   a screw shank 22.2 mm across its corners at 56.5 mm, on main too). With pockets on the
   piece, every cell and margin is checked against the shells built beside it (`settle`),
   and the pockets of one or the other are cut again moved 1.7 microns, turned a 28th of a
-  turn, or both. The
-  cut kept is the one that shares the fewest edges with every shell beside it: keeping one
-  that touched fewer shells, as `settle` first did, left a cell built later sharing an edge
-  nothing cleared (10.1 to 11.1 mm magnets at 47.91 to 50.05 mm, clean on main). And once
-  the cells are built, if the shells `settle` cut again have more bad edges with those
-  beside them than they started with, or more open or turned over, they all go back to
-  their first cut. That check sees only those shells and their neighbours as the cells
-  left them: the dovetail and puzzle tabs are made after it, and the top-insert pass cuts
-  its housings out of shells after it, so neither is judged by it. Two cups put in
-  from above from each side of a piece one cell deep meet face to face at 14.44 mm (twice a
-  cup's reach), and there they are built as one solid with `csgUnion`.
+  turn, or both. The cut kept is the one that shares the fewest edges with every shell
+  beside it: keeping one that touched fewer shells, as `settle` first did, left a cell
+  built later sharing an edge nothing cleared (10.1 to 11.1 mm magnets at 47.91 to
+  50.05 mm, clean on main). And once the cells are built, if the shells `settle` cut
+  again have more bad edges with those beside them than they started with, or more open
+  or turned over, they all go back to their first cut. That check sees only those shells
+  and their neighbours as the cells left them: the dovetail and puzzle tabs are made
+  after it, and the top-insert pass cuts its housings out of shells after it, so neither
+  is judged by it. Two cups put in from above from each side of a piece one cell deep
+  meet face to face at 14.44 mm (twice a cup's reach), and there they are built as one
+  solid with `csgUnion`.
 - **A face that is nothing but a straight line has no middle.** A weld that closes a
   T-junction can leave three corners on one line. Fanned from its average, the spokes land
   a fraction of a micron from a corner and read, to `checkManifold`'s thousandths, as the
diff --git a/test/ui/plates-robustness.spec.js b/test/ui/plates-robustness.spec.js
index ef96ee4..177de84 100644
--- a/test/ui/plates-robustness.spec.js
+++ b/test/ui/plates-robustness.spec.js
@@ -386,9 +386,11 @@ test.describe('limits no tighter than the geometry', () => {
   });
 
   /* The 34.5 mm case takes no joint: the default dovetail's notches hold its 6 mm screw
-     head to 4.1 mm there, which is a field error of its own. Nor 34 mm, where the head's
-     flats on its size leave the cell room for 5.8. The puzzle tabs' are what leave a
-     magnet no room at 36 mm, where the cell alone would take 7.7. */
+     head to 4.1 mm there, which is a field error of its own. It was 34 mm until a head
+     was cut with its flats on its size; at 34 the cell now has room for a 5.8 mm head,
+     so the 6 mm one would be a field error too, and 34.5 still has no room for a shank.
+     The puzzle tabs' are what leave a magnet no room at 36 mm, where the cell alone
+     would take 7.7. */
   for (const [hash, id, errId, carried, msg] of [
     ['#cn=none&sc=1&pi=34.5', 'screwHoleD', 'errScrew', 3,
      /Screw hole Ø: there is no room for one at a 34\.5 mm pitch.*Use a larger pitch, or turn off screw holes\./],

From c72699e282c487cd97f783c3c976d7d5de91d45a Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 11:44:17 +0000
Subject: [PATCH 04/58] Let a bowtie in the floor take the full fit clearance
 on small pitches, and say what holds the other ceilings

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md                    | 16 +++++++
 src/core.js                       | 64 ++++++++++++++++++----------
 src/ui.js                         | 16 ++++---
 test/plate-audit.js               | 71 ++++++++++++++++---------------
 test/ui/plates-robustness.spec.js | 22 +++++-----
 5 files changed, 117 insertions(+), 72 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index 237570d..2e543cb 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -824,6 +824,22 @@ currently installed):
   is judged by it. Two cups put in from above from each side of a piece one cell deep
   meet face to face at 14.44 mm (twice a cup's reach), and there they are built as one
   solid with `csgUnion`.
+- **None of the fit clearance's ceilings that waited on a sweep can go up but the
+  bowtie's.** `connClrCeiling` caps the field for each joint, and five of its ceilings
+  were set by open edges one step past them that `cutAgain` closes. Swept again on 2 × 2
+  and 1-cell pieces, every 0.01 mm of pitch over each ceiling's band, every 0.05 of the
+  field past it and every 0.01 near a leak: the dovetail's step past its 0.3 is open
+  still at one pitch (0.35 at 42.35 mm), and the puzzle key in the floor's past its 0.8
+  leaks at another (0.85 at 29.74). The puzzle and the puzzle key under 20 mm leak within
+  two steps of their 0.3 (0.38 at 18.54 mm, 0.37 at 18.07). The puzzle key's and the
+  puzzle's are no longer holes: the joint's cut lands on the edge of the `BLOAT` band two
+  cells overlap in, along a line that climbs with the field, and the two shells share
+  that edge, as the dovetail's do from 0.39. A ceiling goes up a step only where the
+  field builds clean to the step after it, so all four stay. The bowtie in the floor
+  under 20 mm leaked nowhere up to 1.05, at every 0.01 mm from 13.5 to 20 and loose and
+  tight at every 0.1, and takes the plain 1 mm. `test/plate-audit.js` builds each leak,
+  which has to stay one and be refused, and the bowtie's step to spare, which has to
+  build closed.
 - **A face that is nothing but a straight line has no middle.** A weld that closes a
   T-junction can leave three corners on one line. Fanned from its average, the spokes land
   a fraction of a micron from a corner and read, to `checkManifold`'s thousandths, as the
diff --git a/src/core.js b/src/core.js
index 2bf36e8..3e9e3be 100644
--- a/src/core.js
+++ b/src/core.js
@@ -1021,13 +1021,23 @@ function fitClearances(field) {
  * for everything but the dovetail let a snap clip's housing into the next piece and let
  * small pitches leak.
  *
- * Measured on 2 × 2 and 1-cell pieces from 13.5 to 60 mm, every 0.5 mm of pitch — at
- * every 0.05 of clearance for the puzzle, the bowtie and the puzzle key, at six for the
- * rest — and at every 0.01 of clearance at 20, 25, 30, 35, 42 and 60:
+ * Measured first on 2 × 2 and 1-cell pieces from 13.5 to 60 mm, every 0.5 mm of pitch —
+ * at every 0.05 of clearance for the puzzle, the bowtie and the puzzle key, at six for
+ * the rest — and at every 0.01 of clearance at 20, 25, 30, 35, 42 and 60. What leaked
+ * there was the sliver class, and buildPiece now cuts a joint again when its cut comes
+ * out open (cutAgain), so each ceiling was swept again on both layouts: every 0.01 mm of
+ * pitch over the band it governs (13.5 to 60 mm for the dovetail), every 0.05 of the
+ * field past it, and every 0.01 near anything that leaked. A ceiling goes up a step only
+ * where the field builds clean to the step after that one, which is then its step to
+ * spare; anything that leaks within two steps of a ceiling earns it.
  *
- *   dovetail  0.3. Past it the pocket, cut 1.9 mm + this into the piece, breaks through
- *             the 2.15 mm socket wall and crosses the chamfer cone; it leaked from 0.34.
- *             The hint's own advice stops at 0.25.
+ *   dovetail  0.3, earned. The pocket, cut 1.9 mm + this into the piece, breaks through
+ *             the 2.15 mm socket wall from 0.25 and crosses the chamfer cone. It leaked
+ *             from 0.34, and cutAgain closes most of that, but one step past, 0.35 still
+ *             leaves edges open at 42.35 mm on both layouts. Past that two cells' shells
+ *             share an edge from 0.39, where the notch's wide end stands on the edge of
+ *             the band they share (22.64 mm, and 22.65 at 0.4), and more leak or fold at
+ *             0.55, 0.75 and 0.8. The hint's own advice stops at 0.25.
  *   snaptop   0.3, in either housing. The clip's slot puts its seam-side wall
  *             0.3 − (the key's clearance) from the seam, so past a field of 0.35 that
  *             wall stands in the next piece — by 0.65 mm at 1 — and two pieces that print
@@ -1038,15 +1048,23 @@ function fitClearances(field) {
  *             pair did the same for any field from 0.3 up. 0.3 holds the wall one BLOAT,
  *             0.05, inside the piece, the overlap the cell regions keep; the coupon's
  *             slackest pair is this ceiling cut the key's way, so it stops there too.
- *   pitch     0.3 below 20 mm, for the three housings the field cuts that leaked there:
- *             the puzzle, and the bowtie and puzzle key in the floor. Past 0.3 they left
- *             holes from 13.5 to 19 mm — a puzzle key at 14 from 0.4, a bowtie at 18 at
- *             1, a puzzle at 19 from 0.35 — and from the default 0.2 to 0.3 none did. The
- *             puzzle's lobe also needs room in its cell: it opens the plate once its
- *             clearance passes half the pitch less 6.475 mm, so it stops at half the pitch
- *             less 6.5 — 0.25 at 13.5, and 0.3 from 13.6.
- *   joint     0.8 for a puzzle key in the floor from 20 mm up: between 0.82 and 0.96 its
- *             recess leaked at every pitch measured, 20 to 60.
+ *   pitch     0.3 below 20 mm for the puzzle and a puzzle key in the floor, earned. Past
+ *             it they left holes from 13.5 to 19 mm — a puzzle key at 14 from 0.4, a
+ *             puzzle at 19 from 0.35 — which cutAgain closes, and 0.35 builds clean at
+ *             every pitch; but on 1-cell pieces a line across the pitch that climbs with
+ *             the field puts the cut on the edge of the band two cells share, and the
+ *             shells share it: a puzzle key from 0.37 (at 18.07 mm), a puzzle tab from
+ *             0.38 (at 18.54). The puzzle's lobe also needs room in its cell: it opens the
+ *             plate once its clearance passes half the pitch less 6.475 mm, so it stops at
+ *             half the pitch less 6.5 — 0.25 at 13.5, and 0.3 from 13.6. A bowtie in the
+ *             floor was held here too, for holes at 18 mm at 1. It builds clean at every
+ *             0.01 mm from 13.5 to 20 and every 0.05 up to 1.05, on both layouts, and
+ *             loose and tight at every 0.1 mm, so it takes the plain 1 mm.
+ *   joint     0.8 for a puzzle key in the floor from 20 mm up, earned. Its recess leaked
+ *             between 0.82 and 0.96 at every pitch measured, 20 to 60, until cutAgain;
+ *             at 0.85 it now stands on the edge of the band two cells share at 29.74 mm
+ *             on 1-cell pieces, and at 0.86 at 29.79, though nowhere else from 20 to
+ *             51.7 at 0.85 or 0.9.
  *   slip      1 for the rest. A key in the walls is cut to keySlim's own clearance, which
  *             the field does not move. The snap and the H-clip did not leak above 0.3 at
  *             any pitch measured but in one band — an H-clip dropped in from above leaks
@@ -1055,19 +1073,21 @@ function fitClearances(field) {
  *             0.39–0.4 at 21 and 32.5–35 mm and here and there from 0.52 to 0.87. That is
  *             the sliver class again, not a ceiling — no limit short of 0.38 misses them,
  *             and the same class turns up under the default too: a snap at 20 mm at 0.29,
- *             a bowtie at 17 mm at 0.15 and under.
+ *             a bowtie at 17 mm at 0.15 and under. One is not isolated: on 2 × 2 pieces
+ *             a puzzle at 0.35 exactly, and not 0.34 or 0.36, has two shells sharing an
+ *             edge at every pitch from 31.6 to 52.2 mm, where a corner of a notch's lobe,
+ *             centred on the line between two cells, stands on the edge of the band they
+ *             share. That wants mending in the cut; no ceiling misses a single value.
  *
- * The leaks that set the pitch and joint ceilings, and the dovetail's at 0.34, were that
- * class as well: buildPiece now cuts a joint again when its cut comes out open
- * (cutAgain), and the step past each that test/plate-audit.js builds is closed, as is the
- * H-clip from above at 0.74. The ceilings stay where they are until a sweep as fine as
- * the one that found the small-pitch leaks says how far each can go. */
+ * test/plate-audit.js builds the step that earns each ceiling, which has to leak or cross
+ * the seam and be refused, and the bowtie's step to spare, which has to build closed and
+ * be refused. */
 function connClrCeiling(cfg) {
   const R = PLATE_RANGES.connClr;
   const kind = jointKind(cfg.connector, cfg.keyMount, cfg.keyInsert);
   if (kind === 'dovetail') return { max: R.dovetail, by: 'dovetail' };
   if (kind === 'snaptop') return { max: R.snapTop, by: 'snaptop' };
-  const floorKey = ['bowtie', 'puzzlekey'].includes(cfg.connector) && cfg.keyMount !== 'wall';
+  const floorKey = cfg.connector === 'puzzlekey' && cfg.keyMount !== 'wall';
   if (cfg.connector !== 'puzzle' && !floorKey) return { max: R.max, by: 'slip' };
   if (cfg.pitch < R.smallPitch) {
     const room = cfg.connector === 'puzzle'
diff --git a/src/ui.js b/src/ui.js
index d35fe29..41c5793 100644
--- a/src/ui.js
+++ b/src/ui.js
@@ -140,15 +140,21 @@ const LIMITS = {
 /* What sets the clearance's ceiling, in words: core.js connClrCeiling decides it and says
    which reason applies. A ceiling that moves with the pitch names the pitch, as the mount
    sizes do, because that is the number to change; 'slip' is the plain 1 mm and keeps the
-   millimetres advice. */
-const CLR_JOINT = { puzzle: 'puzzle tab', bowtie: 'bowtie key', puzzlekey: 'puzzle key' };
+   millimetres advice. The puzzle and the puzzle key said they opened holes in the plate,
+   as they did until a joint's cut was taken again when it came out open (cutAgain in
+   core.js); past each ceiling now two cells' shells share an edge at some pitches, which
+   is not watertight either but is no hole. The dovetail said its pocket broke through
+   into the socket beside it, which it does from 0.25, under its ceiling. */
+const CLR_JOINT = { puzzle: 'puzzle tab', puzzlekey: 'puzzle key' };
 const clrWhy = (by) => ({
-  dovetail: '— any looser and a dovetail pocket breaks through into the socket beside it',
+  dovetail: '— any looser and a dovetail pocket leaves the plate not watertight at some ' +
+    'pitches',
   snaptop: '— any looser and the housing of a snap clip dropped in from above runs up to ' +
     'the seam and on into the next piece',
   pitch: `${atPitch()} — on cells under ${RANGES.connClr.smallPitch} mm a ` +
-    `looser ${CLR_JOINT[state.connector]} opens holes in the plate`,
-  joint: `— any looser and a ${CLR_JOINT[state.connector]}'s recess opens holes in the plate`,
+    `looser ${CLR_JOINT[state.connector]} leaves the plate not watertight`,
+  joint: `— any looser and a ${CLR_JOINT[state.connector]}'s recess leaves the plate not ` +
+    'watertight at some pitches',
 })[by] || '';
 /* id -> the message that goes under it. Rebuilt from scratch on every read, so a field
    that has come good stops complaining without anything having to remember it once did. */
diff --git a/test/plate-audit.js b/test/plate-audit.js
index c7fdcf5..b1d3e52 100644
--- a/test/plate-audit.js
+++ b/test/plate-audit.js
@@ -2061,17 +2061,16 @@ console.log('\nthe other limits, built at their ends:');
     if (r.bad) bad++;
   }
   /* The clearance one step past its end, which leaked, and that was why the end is where
-     it is. It no longer does: the joint's cut taken again when it comes out open
-     (cutAgain in core.js) closes it, as it closes the steps past the ceilings below. So it
-     has to stay closed, and the field has to go on refusing it: the cap stays where it is
-     until a sweep says how far it can go, the dovetail every 0.01 mm of pitch and every
-     0.05 of the field past 0.3, on both piece layouts, clean up to the new cap. */
-  const past = buildAll({ ...split, connector: 'dovetail', clr: 0.35 });
+     it is. The joint's cut taken again when it comes out open (cutAgain in core.js)
+     closed it at 42 mm, so it waited on a sweep; the sweep connClrCeiling describes found
+     0.35 open still at 42.35 mm, on two of the four pieces, so the cap is earned. It has
+     to leak still, or the cap can go up, and the field has to go on refusing it. */
+  const past = buildAll({ pitch: 42.35, ...PIECE_LAYOUTS['2x2 pieces'](42.35), connector: 'dovetail', clr: 0.35 });
   const capped = 0.35 > G.connClrCeiling({ ...G.DEFAULTS, connector: 'dovetail' }).max + 1e-9;
-  console.log(`  ${'dovetail at 0.35 clearance'.padEnd(28)} ${leakText(past)}` +
-              (!capped ? '   THE FIELD TAKES IT' : past.bad ? '   OPEN AGAIN — cutAgain no longer closes it'
-                : ' — closed, and the cap waits on a sweep'));
-  if (!capped || past.bad) bad++;
+  console.log(`  ${'dovetail, 0.35 at 42.35 mm'.padEnd(28)} ${leakText(past)}` +
+              (!capped ? '   THE FIELD TAKES IT' : !past.bad ? '   NOW CLEAN — the cap can go up'
+                : ' — the cap is earned'));
+  if (!capped || !past.bad) bad++;
 
   /* A corner boss is 2.6 mm tall and does not grow, so the pocket in it is capped — at
      what leaves a layer over it, which takes the spec's 6.5 × 2.4 magnet. Built at every
@@ -2115,12 +2114,12 @@ console.log('\nthe other limits, built at their ends:');
  * pitches between. Each has to come back closed and inside its own width: nothing past
  * its footprint but the tabs and lobes buildPiece declares.
  *
- * Then the step past each ceiling that set it, which has to be open or across the seam
- * still: if the engine closes one, this says that ceiling can go up (four are closed, and
- * wait on a sweep to say how far; see PAST below). It has to be past the
- * ceiling as well, refused by the field. A puzzle key in the floor loosened to 0.9 built
- * clean at 20, 30 and 42 and its step past, 0.82, leaked as before, so a ceiling moved
- * over the very number that earned it passed; now the field taking that number fails.
+ * Then the step that earns each ceiling, which has to be open, touching or across the
+ * seam still: if the engine closes one, this says that ceiling can go up (see PAST
+ * below). It has to be past the ceiling as well, refused by the field. A puzzle key in
+ * the floor loosened to 0.9 built clean at 20, 30 and 42 and its step past, 0.82, leaked
+ * as before, so a ceiling moved over the very number that earned it passed; now the
+ * field taking that number fails.
  * And the fit coupon at each ceiling, which is the same joint at four clearances up to
  * it — its pairs have to stay at or under the ceiling, and a housing must not reach into
  * the gap between a pair's two tiles, where it meets the other tile's.
@@ -2234,25 +2233,27 @@ console.log('\nthe fit clearance at its ceiling, every joint and pitch band:');
     ? `HELD TO IT: ${held.join(', ')}` : `every other joint but the snap from above, at its own ${C.snapTop}`));
   if (held.length) bad++;
 
-  /* The puzzle key in the floor's step is 0.82, the first clearance that leaked at every
-     pitch measured from 20 to 60; a ceiling at or over it lets the field take it.
-
-     The last four were earned by open edges alone, and the joint's cut taken again when
-     it comes out open (cutAgain in core.js) closes all four. Those ceilings stay where
-     they are until a sweep as fine as the one that found the small-pitch leaks says how
-     far each can go: the joint every 0.01 mm over its pitch band and every 0.05 of the
-     field past its ceiling, on both piece layouts, clean up to the new one. `waits` marks
-     such a step: it has to stay closed, or cutAgain has lost ground, and the field still
-     has to refuse it. */
+  /* The snap from above and the puzzle's lobe are earned by their geometry, above. The
+     rest were earned by open edges — a puzzle at 19 and a bowtie at 15 at 0.35, a puzzle
+     key at 14 at 0.4 and at 42 at 0.82, the dovetail from 0.34 — and the joint's cut taken
+     again when it comes out open (cutAgain in core.js) closes every one. So each was swept
+     as connClrCeiling says: every 0.01 mm of pitch over its band and every 0.05 of the
+     field past it, on both piece layouts, and every 0.01 near anything that leaked. The
+     dovetail's step is open still, and is built with the other ends, above. Three more
+     have a leak within two steps, two cells' shells sharing an edge in the band they
+     overlap in, and the first is their row: it has to leak still, or that ceiling can go
+     up. The bowtie in the floor below 20 mm leaked nowhere up to 1.05 and takes the plain
+     1 mm; `spare` marks its step to spare, which has to build closed, or cutAgain has lost
+     ground. Each has to be refused by the field. */
   const PAST = [
     ['snap from above, 0.35 at 42', { connector: 'snap', keyInsert: 'top', pitch: 42, clr: 0.35 }, '2x2 pieces'],
     ['puzzle, 0.3 at 13.5', { connector: 'puzzle', pitch: 13.5, clr: 0.3 }, '1-cell pieces'],
-    ['puzzle, 0.35 at 19', { connector: 'puzzle', pitch: 19, clr: 0.35 }, '2x2 pieces', 'waits'],
-    ['bowtie, 0.35 at 15', { connector: 'bowtie', pitch: 15, clr: 0.35 }, '2x2 pieces', 'waits'],
-    ['puzzle key, 0.4 at 14', { connector: 'puzzlekey', pitch: 14, clr: 0.4 }, '2x2 pieces', 'waits'],
-    ['puzzle key, 0.82 at 42', { connector: 'puzzlekey', pitch: 42, clr: 0.82 }, '2x2 pieces', 'waits'],
+    ['puzzle, 0.38 at 18.54', { connector: 'puzzle', pitch: 18.54, clr: 0.38 }, '1-cell pieces'],
+    ['puzzle key, 0.37 at 18.07', { connector: 'puzzlekey', pitch: 18.07, clr: 0.37 }, '1-cell pieces'],
+    ['puzzle key, 0.85 at 29.74', { connector: 'puzzlekey', pitch: 29.74, clr: 0.85 }, '1-cell pieces'],
+    ['bowtie, 1.05 at 18', { connector: 'bowtie', pitch: 18, clr: 1.05 }, '2x2 pieces', 'spare'],
   ];
-  for (const [what, o, ln, waits] of PAST) {
+  for (const [what, o, ln, spare] of PAST) {
     const r = buildAll({ ...PIECE_LAYOUTS[ln](o.pitch), ...o });
     /* A snap from above earns its ceiling in the seam face, before anything crosses the
        seam: one step past, its slot's wall is nearer the face than a BLOAT. */
@@ -2263,16 +2264,16 @@ console.log('\nthe fit clearance at its ceiling, every joint and pitch band:');
         r.L.pieces[i]).keyed.map((st) => ({ ...st, clr: r.cfg.key.clr })), H));
     }
     const inFace = face.sites > 0 && face.near < BLOAT - 1e-6;
-    const still = r.open > 0 || r.beyond > OVER || inFace;
+    const still = r.bad > 0 || r.beyond > OVER || inFace;
     const most = G.connClrCeiling(r.cfg).max, refused = o.clr > most + 1e-9;
     console.log(`  ${what.padEnd(28)} ${r.beyond > OVER ? `${r.beyond} mm into the next piece`
       : inFace ? `its slot ${(Math.round(face.near * 1e4) / 1e4 + 0).toFixed(3)} mm off the seam face`
       : leakText(r)}` +
                 (!refused ? `   THE FIELD TAKES IT: the ceiling went up to ${most}`
-                  : waits ? (still ? '   OPEN AGAIN — cutAgain no longer closes it'
-                                   : ' — closed, and the ceiling waits on a sweep')
+                  : spare ? (still ? '   OPEN AGAIN — cutAgain no longer closes it'
+                                   : ' — closed, a step to spare')
                   : still ? ' — the ceiling is earned' : '   NOW CLEAN — that ceiling can go up'));
-    if (!refused || (waits ? still : !still)) bad++;
+    if (!refused || (spare ? still : !still)) bad++;
   }
 
   /* activeJoint in src/ui.js, with the field at the ceiling — a fixture, as in the coupon
diff --git a/test/ui/plates-robustness.spec.js b/test/ui/plates-robustness.spec.js
index 177de84..7e5a26e 100644
--- a/test/ui/plates-robustness.spec.js
+++ b/test/ui/plates-robustness.spec.js
@@ -353,7 +353,7 @@ test.describe('limits no tighter than the geometry', () => {
                                           // whose slot stands a BLOAT off the seam face
                                           [`${SEAM}&cn=snap&km=wall&ki=top&cl=0.3`, 0.25, 0.25],
                                           [`${SEAM}&cn=puzzlekey&cl=0.8`, 0.75, 0.75],
-                                          [`${seamAt(18)}&cn=bowtie&cl=0.3`, 0.25, 0.25],
+                                          [`${seamAt(18)}&cn=puzzlekey&cl=0.3`, 0.25, 0.25],
                                           [`${seamAt(13.5)}&cn=puzzle&cl=0.25`, 0.25, 0.25]])
     test(`the fit sample stays inside the range: ${hash}`, async ({ page }) => {
       const errors = await openAt(page, hash);
@@ -424,24 +424,25 @@ test.describe('limits no tighter than the geometry', () => {
    clip dropped in from above is housed in a slot whose seam-side wall stands 0.3 mm less
    the clearance from the seam, so at 0.35 on the field the wall lies in the seam face and
    past it in the next piece — the field stops at 0.3, a BLOAT short of the face;
-   and under 20 mm the puzzle, the bowtie and the puzzle key leave holes in the plate at
+   and under 20 mm the puzzle and the puzzle key leave plates that are not watertight at
    clearances that build closed at 42. Each case is refused at the field, clamped to the
    ceiling in the state a link loads into, and says which joint and which pitch — the
    pitch is the number to change. A joint that builds closed at a small pitch is not held
-   to the others' reason. */
+   to the others' reason: the bowtie in the floor was, until a sweep built it closed from
+   13.5 to 20 mm at every clearance to 1. */
 test.describe('the clearance ceiling is the joint\'s and the pitch\'s', () => {
   const SEAM = '#w=168&d=84&sp=manual&rc=&cc=2';
   for (const [hash, ceiling, msg] of [
     [`${SEAM}&cn=snap&km=wall&ki=top&cl=0.35`, 0.3,
      /Fit clearance must be 0\.3 mm or less — any looser and the housing of a snap clip dropped in from above runs up to the seam and on into the next piece\./],
-    ['#pi=18&cn=bowtie&cl=1', 0.3,
-     /Fit clearance must be 0\.3 mm or less at an 18 mm pitch — on cells under 20 mm a looser bowtie key opens holes in the plate\./],
+    ['#pi=18&cn=puzzle&cl=1', 0.3,
+     /Fit clearance must be 0\.3 mm or less at an 18 mm pitch — on cells under 20 mm a looser puzzle tab leaves the plate not watertight\./],
     ['#pi=14&cn=puzzlekey&cl=0.5', 0.3,
-     /Fit clearance must be 0\.3 mm or less at a 14 mm pitch — on cells under 20 mm a looser puzzle key opens holes in the plate\./],
+     /Fit clearance must be 0\.3 mm or less at a 14 mm pitch — on cells under 20 mm a looser puzzle key leaves the plate not watertight\./],
     ['#pi=13.5&cn=puzzle&cl=0.3', 0.25,
-     /Fit clearance must be 0\.25 mm or less at a 13\.5 mm pitch — on cells under 20 mm a looser puzzle tab opens holes in the plate\./],
+     /Fit clearance must be 0\.25 mm or less at a 13\.5 mm pitch — on cells under 20 mm a looser puzzle tab leaves the plate not watertight\./],
     ['#cn=puzzlekey&cl=0.85', 0.8,
-     /Fit clearance must be 0\.8 mm or less — any looser and a puzzle key's recess opens holes in the plate\./],
+     /Fit clearance must be 0\.8 mm or less — any looser and a puzzle key's recess leaves the plate not watertight at some pitches\./],
   ])
     test(`${hash} is held to ${ceiling}, and says why`, async ({ page }) => {
       const errors = await openAt(page, hash);
@@ -457,9 +458,10 @@ test.describe('the clearance ceiling is the joint\'s and the pitch\'s', () => {
       expect(errors).toEqual([]);
     });
 
-  // the snap and the H-clip built closed at every clearance and pitch measured
+  // the snap, the H-clip and the bowtie built closed at every clearance and pitch measured
   for (const hash of ['#pi=16&w=64&d=32&sp=manual&rc=&cc=2&cn=hclip&cl=1',
-                      '#pi=16&w=64&d=32&sp=manual&rc=&cc=2&cn=snap&cl=1'])
+                      '#pi=16&w=64&d=32&sp=manual&rc=&cc=2&cn=snap&cl=1',
+                      '#pi=16&w=64&d=32&sp=manual&rc=&cc=2&cn=bowtie&cl=1'])
     test(`${hash} builds — the small-pitch hold is not every joint's`, async ({ page }) => {
       const errors = await openAt(page, hash);
       expect(await shown(page, 'errConnClr')).toBe(false);

From 43cee557ec714588483dcac55e9fe41202f70b29 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 11:44:29 +0000
Subject: [PATCH 05/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html | 139 ++++++++++++++++++++++++++++---------------
 index.html      | 155 ++++++++++++++++++++++++++++++++----------------
 sw.js           |   2 +-
 3 files changed, 196 insertions(+), 100 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index 7e64f5e..a85366c 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -2419,6 +2419,36 @@ <h2 id="drawersTitle">Your drawers</h2>
   return polys;
 }
 
+/* The polygon each mounting bore is cut as: how many sides, and how far out its corners
+ * stand for a size typed (`r`), and back the other way, the largest size whose corners
+ * stay inside a room (`fits`). fastenerCutter and screwCutter cut these and mountLimits
+ * holds the sizes to them, so a bore's shape is decided here and nowhere else. Each is
+ * cylinder's polygon about the site, a corner at every 2πk/sides from +x.
+ *
+ * Every bore stands its flats on the size asked, so its corners are 1/cos(π/sides) of the
+ * radius out and it is no narrower anywhere than the size typed.
+ *   - magnet: 14 sides, cut 0.1 mm over the magnet's radius at its corners: 0.2 over the
+ *     diameter, the press fit bins/bin.js keeps as well ("the plate's rule"). Its flats
+ *     are cos(π/14) of that, and past a 7.78 mm magnet they came inside the magnet
+ *     itself: 4.972 mm for a 10 mm one, a pocket narrower than what goes in it, where
+ *     bins/bin.js's 16 sides keep their flats outside every magnet its field takes. So
+ *     the corners go out as far as it takes for the flats to stand on the magnet's
+ *     radius. For a magnet up to 7.77 mm, the 6 mm default among them, nothing moves.
+ *   - head, the counterbore: 14 sides, and hole, the shank: 12. Both had their corners on
+ *     the size asked, so their flats came inside it at every size, 5.85 mm across for the
+ *     default 6 mm head and 2.90 for the 3 mm hole. Now their corners go out the same
+ *     way, and no further: the magnet's 0.1 is a press fit, and a screw head is not
+ *     pressed in. It drops into its counterbore, which the field already sizes with room
+ *     round it (6 mm for an M3's 5.5 mm head), and the shank is a clearance hole. */
+const MOUNT_BORE = {
+  magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
+            fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },
+  head: { sides: 14, r: (d) => d/2 / Math.cos(Math.PI/14),
+          fits: (room) => 2 * room * Math.cos(Math.PI / 14) },
+  hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
+          fits: (room) => 2 * room * Math.cos(Math.PI / 12) },
+};
+
 /* Everything removed at one mounting site, as ONE solid.
  *
  * Up to three cylinders share this axis: a magnet pocket, a screw shank, and the head's
@@ -2440,22 +2470,17 @@ <h2 id="drawersTitle">Your drawers</h2>
 function fastenerCutter(cfg, magZ0, magZ1, shankTop) {
   let cut = null;
   const add = (c) => { cut = cut ? csgUnion(cut, c) : c; };
-  /* A magnet's pocket is 14-sided, cut 0.1 mm over the magnet's radius at its corners:
-     0.2 over the diameter, the press fit bins/bin.js keeps as well ("the plate's rule").
-     Its flats are cos(π/14) of that, and past a 7.78 mm magnet they came inside the
-     magnet itself: 4.972 mm for a 10 mm one, a pocket narrower than what goes in it,
-     where bins/bin.js's 16 sides keep their flats outside every magnet its field takes.
-     So the corners go out as far as it takes for the flats to stand on the magnet's
-     radius. For a magnet up to 7.77 mm, the 6 mm default among them, nothing moves. */
-  const magnetR = Math.max(cfg.magnetD/2 + 0.1, cfg.magnetD/2 / Math.cos(Math.PI/14));
+  // each bore as MOUNT_BORE shapes it
+  const { magnet, head, hole } = MOUNT_BORE;
+  const magnetR = magnet.r(cfg.magnetD);
   if (cfg.magnets)
     add(cfg.magnetSide === 'top'
-      ? cylinder(0, 0, magnetR, magZ0, magZ1, 14)
-      : cylinder(0, 0, magnetR, -0.5, cfg.magnetH, 14));
+      ? cylinder(0, 0, magnetR, magZ0, magZ1, magnet.sides)
+      : cylinder(0, 0, magnetR, -0.5, cfg.magnetH, magnet.sides));
   if (cfg.screws) {
     if (cfg.screwHeadD > cfg.screwHoleD)
-      add(cylinder(0, 0, cfg.screwHeadD/2, -0.5, cfg.screwHeadDepth, 14));
-    add(cylinder(0, 0, cfg.screwHoleD/2, -0.5, shankTop, 12));
+      add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
+    add(cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides));
   }
   return cut;
 }
@@ -2471,13 +2496,15 @@ <h2 id="drawersTitle">Your drawers</h2>
   }));
 }
 
-// counterbore: hole cylinder full height + wider recess from chosen face
+// counterbore: hole cylinder full height + wider recess from chosen face, each bore as
+// MOUNT_BORE shapes it
 function screwCutter(cx, cy, holeD, headD, z0, z1, headDepth, fromTop) {
-  let polys = cylinder(cx, cy, holeD/2, z0 - 0.5, z1 + 0.5, 12);
+  const { head, hole } = MOUNT_BORE;
+  let polys = cylinder(cx, cy, hole.r(holeD), z0 - 0.5, z1 + 0.5, hole.sides);
   if (headD > holeD) {
     const rec = fromTop
-      ? cylinder(cx, cy, headD/2, z1 - headDepth, z1 + 0.5, 14)
-      : cylinder(cx, cy, headD/2, z0 - 0.5, z0 + headDepth, 14);
+      ? cylinder(cx, cy, head.r(headD), z1 - headDepth, z1 + 0.5, head.sides)
+      : cylinder(cx, cy, head.r(headD), z0 - 0.5, z0 + headDepth, head.sides);
     polys = csgUnion(polys, rec);
   }
   return polys;
@@ -2600,13 +2627,23 @@ <h2 id="drawersTitle">Your drawers</h2>
  * for everything but the dovetail let a snap clip's housing into the next piece and let
  * small pitches leak.
  *
- * Measured on 2 × 2 and 1-cell pieces from 13.5 to 60 mm, every 0.5 mm of pitch — at
- * every 0.05 of clearance for the puzzle, the bowtie and the puzzle key, at six for the
- * rest — and at every 0.01 of clearance at 20, 25, 30, 35, 42 and 60:
+ * Measured first on 2 × 2 and 1-cell pieces from 13.5 to 60 mm, every 0.5 mm of pitch —
+ * at every 0.05 of clearance for the puzzle, the bowtie and the puzzle key, at six for
+ * the rest — and at every 0.01 of clearance at 20, 25, 30, 35, 42 and 60. What leaked
+ * there was the sliver class, and buildPiece now cuts a joint again when its cut comes
+ * out open (cutAgain), so each ceiling was swept again on both layouts: every 0.01 mm of
+ * pitch over the band it governs (13.5 to 60 mm for the dovetail), every 0.05 of the
+ * field past it, and every 0.01 near anything that leaked. A ceiling goes up a step only
+ * where the field builds clean to the step after that one, which is then its step to
+ * spare; anything that leaks within two steps of a ceiling earns it.
  *
- *   dovetail  0.3. Past it the pocket, cut 1.9 mm + this into the piece, breaks through
- *             the 2.15 mm socket wall and crosses the chamfer cone; it leaked from 0.34.
- *             The hint's own advice stops at 0.25.
+ *   dovetail  0.3, earned. The pocket, cut 1.9 mm + this into the piece, breaks through
+ *             the 2.15 mm socket wall from 0.25 and crosses the chamfer cone. It leaked
+ *             from 0.34, and cutAgain closes most of that, but one step past, 0.35 still
+ *             leaves edges open at 42.35 mm on both layouts. Past that two cells' shells
+ *             share an edge from 0.39, where the notch's wide end stands on the edge of
+ *             the band they share (22.64 mm, and 22.65 at 0.4), and more leak or fold at
+ *             0.55, 0.75 and 0.8. The hint's own advice stops at 0.25.
  *   snaptop   0.3, in either housing. The clip's slot puts its seam-side wall
  *             0.3 − (the key's clearance) from the seam, so past a field of 0.35 that
  *             wall stands in the next piece — by 0.65 mm at 1 — and two pieces that print
@@ -2617,15 +2654,23 @@ <h2 id="drawersTitle">Your drawers</h2>
  *             pair did the same for any field from 0.3 up. 0.3 holds the wall one BLOAT,
  *             0.05, inside the piece, the overlap the cell regions keep; the coupon's
  *             slackest pair is this ceiling cut the key's way, so it stops there too.
- *   pitch     0.3 below 20 mm, for the three housings the field cuts that leaked there:
- *             the puzzle, and the bowtie and puzzle key in the floor. Past 0.3 they left
- *             holes from 13.5 to 19 mm — a puzzle key at 14 from 0.4, a bowtie at 18 at
- *             1, a puzzle at 19 from 0.35 — and from the default 0.2 to 0.3 none did. The
- *             puzzle's lobe also needs room in its cell: it opens the plate once its
- *             clearance passes half the pitch less 6.475 mm, so it stops at half the pitch
- *             less 6.5 — 0.25 at 13.5, and 0.3 from 13.6.
- *   joint     0.8 for a puzzle key in the floor from 20 mm up: between 0.82 and 0.96 its
- *             recess leaked at every pitch measured, 20 to 60.
+ *   pitch     0.3 below 20 mm for the puzzle and a puzzle key in the floor, earned. Past
+ *             it they left holes from 13.5 to 19 mm — a puzzle key at 14 from 0.4, a
+ *             puzzle at 19 from 0.35 — which cutAgain closes, and 0.35 builds clean at
+ *             every pitch; but on 1-cell pieces a line across the pitch that climbs with
+ *             the field puts the cut on the edge of the band two cells share, and the
+ *             shells share it: a puzzle key from 0.37 (at 18.07 mm), a puzzle tab from
+ *             0.38 (at 18.54). The puzzle's lobe also needs room in its cell: it opens the
+ *             plate once its clearance passes half the pitch less 6.475 mm, so it stops at
+ *             half the pitch less 6.5 — 0.25 at 13.5, and 0.3 from 13.6. A bowtie in the
+ *             floor was held here too, for holes at 18 mm at 1. It builds clean at every
+ *             0.01 mm from 13.5 to 20 and every 0.05 up to 1.05, on both layouts, and
+ *             loose and tight at every 0.1 mm, so it takes the plain 1 mm.
+ *   joint     0.8 for a puzzle key in the floor from 20 mm up, earned. Its recess leaked
+ *             between 0.82 and 0.96 at every pitch measured, 20 to 60, until cutAgain;
+ *             at 0.85 it now stands on the edge of the band two cells share at 29.74 mm
+ *             on 1-cell pieces, and at 0.86 at 29.79, though nowhere else from 20 to
+ *             51.7 at 0.85 or 0.9.
  *   slip      1 for the rest. A key in the walls is cut to keySlim's own clearance, which
  *             the field does not move. The snap and the H-clip did not leak above 0.3 at
  *             any pitch measured but in one band — an H-clip dropped in from above leaks
@@ -2634,19 +2679,21 @@ <h2 id="drawersTitle">Your drawers</h2>
  *             0.39–0.4 at 21 and 32.5–35 mm and here and there from 0.52 to 0.87. That is
  *             the sliver class again, not a ceiling — no limit short of 0.38 misses them,
  *             and the same class turns up under the default too: a snap at 20 mm at 0.29,
- *             a bowtie at 17 mm at 0.15 and under.
+ *             a bowtie at 17 mm at 0.15 and under. One is not isolated: on 2 × 2 pieces
+ *             a puzzle at 0.35 exactly, and not 0.34 or 0.36, has two shells sharing an
+ *             edge at every pitch from 31.6 to 52.2 mm, where a corner of a notch's lobe,
+ *             centred on the line between two cells, stands on the edge of the band they
+ *             share. That wants mending in the cut; no ceiling misses a single value.
  *
- * The leaks that set the pitch and joint ceilings, and the dovetail's at 0.34, were that
- * class as well: buildPiece now cuts a joint again when its cut comes out open
- * (cutAgain), and the step past each that test/plate-audit.js builds is closed, as is the
- * H-clip from above at 0.74. The ceilings stay where they are until a sweep as fine as
- * the one that found the small-pitch leaks says how far each can go. */
+ * test/plate-audit.js builds the step that earns each ceiling, which has to leak or cross
+ * the seam and be refused, and the bowtie's step to spare, which has to build closed and
+ * be refused. */
 function connClrCeiling(cfg) {
   const R = PLATE_RANGES.connClr;
   const kind = jointKind(cfg.connector, cfg.keyMount, cfg.keyInsert);
   if (kind === 'dovetail') return { max: R.dovetail, by: 'dovetail' };
   if (kind === 'snaptop') return { max: R.snapTop, by: 'snaptop' };
-  const floorKey = ['bowtie', 'puzzlekey'].includes(cfg.connector) && cfg.keyMount !== 'wall';
+  const floorKey = cfg.connector === 'puzzlekey' && cfg.keyMount !== 'wall';
   if (cfg.connector !== 'puzzle' && !floorKey) return { max: R.max, by: 'slip' };
   if (cfg.pitch < R.smallPitch) {
     const room = cfg.connector === 'puzzle'
@@ -4086,12 +4133,10 @@ <h2 id="drawersTitle">Your drawers</h2>
   const own = fit(cfg.magnetSide === 'top' ? top : under);
   const room = Math.min(own, magnetJoint);
   return {
-    // a magnet pocket's corners are 0.1 mm over the magnet's radius, or out to where its
-    // flats stand on that radius if that is further (fastenerCutter)
-    magnetD: r10(2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14))),
-    // a screw's bores have their corners on its size
-    screwHoleD: r10(2 * Math.min(fit(top), below)),
-    screwHeadD: r10(2 * Math.min(fit(under), below)),
+    // every room above is to a bore's corners, which stand out past its size (MOUNT_BORE)
+    magnetD: r10(MOUNT_BORE.magnet.fits(room)),
+    screwHoleD: r10(MOUNT_BORE.hole.fits(Math.min(fit(top), below))),
+    screwHeadD: r10(MOUNT_BORE.head.fits(Math.min(fit(under), below))),
     // in the solid floor the pad grows to suit, so only a boss caps the depth
     depth: bosses ? r10(BOSS_H - MOUNT_SKIN) : Infinity,
     // which of the sizes the cut beside it stops, rather than the floor, cell or boss
@@ -4717,9 +4762,9 @@ <h2 id="drawersTitle">Your drawers</h2>
    * A 21.7 mm magnet from beneath at a 55 mm pitch did it: a flat of the pocket in the
    * cell at the back left, on the magnet's radius, crosses that cell's front side 0.03
    * microns from the corner of the cell at the back right. A 22.2 mm screw shank at 56.5
-   * mm did it twice over, from the cell at the back right as well, on main too. Each shell
-   * is closed on its own, so the pockets' own retries never see it, and it comes and goes
-   * with the size and the pitch.
+   * mm (22.2 across its corners, as shanks were cut then) did it twice over, from the cell
+   * at the back right as well, on main too. Each shell is closed on its own, so the
+   * pockets' own retries never see it, and it comes and goes with the size and the pitch.
    *
    * So with mounting pockets on the piece, every shell the cells and margins make is
    * checked against those built before it beside it, as jointed cells are above. One that
diff --git a/index.html b/index.html
index 5a940b7..04ab7c0 100644
--- a/index.html
+++ b/index.html
@@ -2206,6 +2206,36 @@ <h2 id="drawersTitle">Your drawers</h2>
   return polys;
 }
 
+/* The polygon each mounting bore is cut as: how many sides, and how far out its corners
+ * stand for a size typed (`r`), and back the other way, the largest size whose corners
+ * stay inside a room (`fits`). fastenerCutter and screwCutter cut these and mountLimits
+ * holds the sizes to them, so a bore's shape is decided here and nowhere else. Each is
+ * cylinder's polygon about the site, a corner at every 2πk/sides from +x.
+ *
+ * Every bore stands its flats on the size asked, so its corners are 1/cos(π/sides) of the
+ * radius out and it is no narrower anywhere than the size typed.
+ *   - magnet: 14 sides, cut 0.1 mm over the magnet's radius at its corners: 0.2 over the
+ *     diameter, the press fit bins/bin.js keeps as well ("the plate's rule"). Its flats
+ *     are cos(π/14) of that, and past a 7.78 mm magnet they came inside the magnet
+ *     itself: 4.972 mm for a 10 mm one, a pocket narrower than what goes in it, where
+ *     bins/bin.js's 16 sides keep their flats outside every magnet its field takes. So
+ *     the corners go out as far as it takes for the flats to stand on the magnet's
+ *     radius. For a magnet up to 7.77 mm, the 6 mm default among them, nothing moves.
+ *   - head, the counterbore: 14 sides, and hole, the shank: 12. Both had their corners on
+ *     the size asked, so their flats came inside it at every size, 5.85 mm across for the
+ *     default 6 mm head and 2.90 for the 3 mm hole. Now their corners go out the same
+ *     way, and no further: the magnet's 0.1 is a press fit, and a screw head is not
+ *     pressed in. It drops into its counterbore, which the field already sizes with room
+ *     round it (6 mm for an M3's 5.5 mm head), and the shank is a clearance hole. */
+const MOUNT_BORE = {
+  magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
+            fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },
+  head: { sides: 14, r: (d) => d/2 / Math.cos(Math.PI/14),
+          fits: (room) => 2 * room * Math.cos(Math.PI / 14) },
+  hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
+          fits: (room) => 2 * room * Math.cos(Math.PI / 12) },
+};
+
 /* Everything removed at one mounting site, as ONE solid.
  *
  * Up to three cylinders share this axis: a magnet pocket, a screw shank, and the head's
@@ -2227,22 +2257,17 @@ <h2 id="drawersTitle">Your drawers</h2>
 function fastenerCutter(cfg, magZ0, magZ1, shankTop) {
   let cut = null;
   const add = (c) => { cut = cut ? csgUnion(cut, c) : c; };
-  /* A magnet's pocket is 14-sided, cut 0.1 mm over the magnet's radius at its corners:
-     0.2 over the diameter, the press fit bins/bin.js keeps as well ("the plate's rule").
-     Its flats are cos(π/14) of that, and past a 7.78 mm magnet they came inside the
-     magnet itself: 4.972 mm for a 10 mm one, a pocket narrower than what goes in it,
-     where bins/bin.js's 16 sides keep their flats outside every magnet its field takes.
-     So the corners go out as far as it takes for the flats to stand on the magnet's
-     radius. For a magnet up to 7.77 mm, the 6 mm default among them, nothing moves. */
-  const magnetR = Math.max(cfg.magnetD/2 + 0.1, cfg.magnetD/2 / Math.cos(Math.PI/14));
+  // each bore as MOUNT_BORE shapes it
+  const { magnet, head, hole } = MOUNT_BORE;
+  const magnetR = magnet.r(cfg.magnetD);
   if (cfg.magnets)
     add(cfg.magnetSide === 'top'
-      ? cylinder(0, 0, magnetR, magZ0, magZ1, 14)
-      : cylinder(0, 0, magnetR, -0.5, cfg.magnetH, 14));
+      ? cylinder(0, 0, magnetR, magZ0, magZ1, magnet.sides)
+      : cylinder(0, 0, magnetR, -0.5, cfg.magnetH, magnet.sides));
   if (cfg.screws) {
     if (cfg.screwHeadD > cfg.screwHoleD)
-      add(cylinder(0, 0, cfg.screwHeadD/2, -0.5, cfg.screwHeadDepth, 14));
-    add(cylinder(0, 0, cfg.screwHoleD/2, -0.5, shankTop, 12));
+      add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
+    add(cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides));
   }
   return cut;
 }
@@ -2258,13 +2283,15 @@ <h2 id="drawersTitle">Your drawers</h2>
   }));
 }
 
-// counterbore: hole cylinder full height + wider recess from chosen face
+// counterbore: hole cylinder full height + wider recess from chosen face, each bore as
+// MOUNT_BORE shapes it
 function screwCutter(cx, cy, holeD, headD, z0, z1, headDepth, fromTop) {
-  let polys = cylinder(cx, cy, holeD/2, z0 - 0.5, z1 + 0.5, 12);
+  const { head, hole } = MOUNT_BORE;
+  let polys = cylinder(cx, cy, hole.r(holeD), z0 - 0.5, z1 + 0.5, hole.sides);
   if (headD > holeD) {
     const rec = fromTop
-      ? cylinder(cx, cy, headD/2, z1 - headDepth, z1 + 0.5, 14)
-      : cylinder(cx, cy, headD/2, z0 - 0.5, z0 + headDepth, 14);
+      ? cylinder(cx, cy, head.r(headD), z1 - headDepth, z1 + 0.5, head.sides)
+      : cylinder(cx, cy, head.r(headD), z0 - 0.5, z0 + headDepth, head.sides);
     polys = csgUnion(polys, rec);
   }
   return polys;
@@ -2387,13 +2414,23 @@ <h2 id="drawersTitle">Your drawers</h2>
  * for everything but the dovetail let a snap clip's housing into the next piece and let
  * small pitches leak.
  *
- * Measured on 2 × 2 and 1-cell pieces from 13.5 to 60 mm, every 0.5 mm of pitch — at
- * every 0.05 of clearance for the puzzle, the bowtie and the puzzle key, at six for the
- * rest — and at every 0.01 of clearance at 20, 25, 30, 35, 42 and 60:
+ * Measured first on 2 × 2 and 1-cell pieces from 13.5 to 60 mm, every 0.5 mm of pitch —
+ * at every 0.05 of clearance for the puzzle, the bowtie and the puzzle key, at six for
+ * the rest — and at every 0.01 of clearance at 20, 25, 30, 35, 42 and 60. What leaked
+ * there was the sliver class, and buildPiece now cuts a joint again when its cut comes
+ * out open (cutAgain), so each ceiling was swept again on both layouts: every 0.01 mm of
+ * pitch over the band it governs (13.5 to 60 mm for the dovetail), every 0.05 of the
+ * field past it, and every 0.01 near anything that leaked. A ceiling goes up a step only
+ * where the field builds clean to the step after that one, which is then its step to
+ * spare; anything that leaks within two steps of a ceiling earns it.
  *
- *   dovetail  0.3. Past it the pocket, cut 1.9 mm + this into the piece, breaks through
- *             the 2.15 mm socket wall and crosses the chamfer cone; it leaked from 0.34.
- *             The hint's own advice stops at 0.25.
+ *   dovetail  0.3, earned. The pocket, cut 1.9 mm + this into the piece, breaks through
+ *             the 2.15 mm socket wall from 0.25 and crosses the chamfer cone. It leaked
+ *             from 0.34, and cutAgain closes most of that, but one step past, 0.35 still
+ *             leaves edges open at 42.35 mm on both layouts. Past that two cells' shells
+ *             share an edge from 0.39, where the notch's wide end stands on the edge of
+ *             the band they share (22.64 mm, and 22.65 at 0.4), and more leak or fold at
+ *             0.55, 0.75 and 0.8. The hint's own advice stops at 0.25.
  *   snaptop   0.3, in either housing. The clip's slot puts its seam-side wall
  *             0.3 − (the key's clearance) from the seam, so past a field of 0.35 that
  *             wall stands in the next piece — by 0.65 mm at 1 — and two pieces that print
@@ -2404,15 +2441,23 @@ <h2 id="drawersTitle">Your drawers</h2>
  *             pair did the same for any field from 0.3 up. 0.3 holds the wall one BLOAT,
  *             0.05, inside the piece, the overlap the cell regions keep; the coupon's
  *             slackest pair is this ceiling cut the key's way, so it stops there too.
- *   pitch     0.3 below 20 mm, for the three housings the field cuts that leaked there:
- *             the puzzle, and the bowtie and puzzle key in the floor. Past 0.3 they left
- *             holes from 13.5 to 19 mm — a puzzle key at 14 from 0.4, a bowtie at 18 at
- *             1, a puzzle at 19 from 0.35 — and from the default 0.2 to 0.3 none did. The
- *             puzzle's lobe also needs room in its cell: it opens the plate once its
- *             clearance passes half the pitch less 6.475 mm, so it stops at half the pitch
- *             less 6.5 — 0.25 at 13.5, and 0.3 from 13.6.
- *   joint     0.8 for a puzzle key in the floor from 20 mm up: between 0.82 and 0.96 its
- *             recess leaked at every pitch measured, 20 to 60.
+ *   pitch     0.3 below 20 mm for the puzzle and a puzzle key in the floor, earned. Past
+ *             it they left holes from 13.5 to 19 mm — a puzzle key at 14 from 0.4, a
+ *             puzzle at 19 from 0.35 — which cutAgain closes, and 0.35 builds clean at
+ *             every pitch; but on 1-cell pieces a line across the pitch that climbs with
+ *             the field puts the cut on the edge of the band two cells share, and the
+ *             shells share it: a puzzle key from 0.37 (at 18.07 mm), a puzzle tab from
+ *             0.38 (at 18.54). The puzzle's lobe also needs room in its cell: it opens the
+ *             plate once its clearance passes half the pitch less 6.475 mm, so it stops at
+ *             half the pitch less 6.5 — 0.25 at 13.5, and 0.3 from 13.6. A bowtie in the
+ *             floor was held here too, for holes at 18 mm at 1. It builds clean at every
+ *             0.01 mm from 13.5 to 20 and every 0.05 up to 1.05, on both layouts, and
+ *             loose and tight at every 0.1 mm, so it takes the plain 1 mm.
+ *   joint     0.8 for a puzzle key in the floor from 20 mm up, earned. Its recess leaked
+ *             between 0.82 and 0.96 at every pitch measured, 20 to 60, until cutAgain;
+ *             at 0.85 it now stands on the edge of the band two cells share at 29.74 mm
+ *             on 1-cell pieces, and at 0.86 at 29.79, though nowhere else from 20 to
+ *             51.7 at 0.85 or 0.9.
  *   slip      1 for the rest. A key in the walls is cut to keySlim's own clearance, which
  *             the field does not move. The snap and the H-clip did not leak above 0.3 at
  *             any pitch measured but in one band — an H-clip dropped in from above leaks
@@ -2421,19 +2466,21 @@ <h2 id="drawersTitle">Your drawers</h2>
  *             0.39–0.4 at 21 and 32.5–35 mm and here and there from 0.52 to 0.87. That is
  *             the sliver class again, not a ceiling — no limit short of 0.38 misses them,
  *             and the same class turns up under the default too: a snap at 20 mm at 0.29,
- *             a bowtie at 17 mm at 0.15 and under.
+ *             a bowtie at 17 mm at 0.15 and under. One is not isolated: on 2 × 2 pieces
+ *             a puzzle at 0.35 exactly, and not 0.34 or 0.36, has two shells sharing an
+ *             edge at every pitch from 31.6 to 52.2 mm, where a corner of a notch's lobe,
+ *             centred on the line between two cells, stands on the edge of the band they
+ *             share. That wants mending in the cut; no ceiling misses a single value.
  *
- * The leaks that set the pitch and joint ceilings, and the dovetail's at 0.34, were that
- * class as well: buildPiece now cuts a joint again when its cut comes out open
- * (cutAgain), and the step past each that test/plate-audit.js builds is closed, as is the
- * H-clip from above at 0.74. The ceilings stay where they are until a sweep as fine as
- * the one that found the small-pitch leaks says how far each can go. */
+ * test/plate-audit.js builds the step that earns each ceiling, which has to leak or cross
+ * the seam and be refused, and the bowtie's step to spare, which has to build closed and
+ * be refused. */
 function connClrCeiling(cfg) {
   const R = PLATE_RANGES.connClr;
   const kind = jointKind(cfg.connector, cfg.keyMount, cfg.keyInsert);
   if (kind === 'dovetail') return { max: R.dovetail, by: 'dovetail' };
   if (kind === 'snaptop') return { max: R.snapTop, by: 'snaptop' };
-  const floorKey = ['bowtie', 'puzzlekey'].includes(cfg.connector) && cfg.keyMount !== 'wall';
+  const floorKey = cfg.connector === 'puzzlekey' && cfg.keyMount !== 'wall';
   if (cfg.connector !== 'puzzle' && !floorKey) return { max: R.max, by: 'slip' };
   if (cfg.pitch < R.smallPitch) {
     const room = cfg.connector === 'puzzle'
@@ -3873,12 +3920,10 @@ <h2 id="drawersTitle">Your drawers</h2>
   const own = fit(cfg.magnetSide === 'top' ? top : under);
   const room = Math.min(own, magnetJoint);
   return {
-    // a magnet pocket's corners are 0.1 mm over the magnet's radius, or out to where its
-    // flats stand on that radius if that is further (fastenerCutter)
-    magnetD: r10(2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14))),
-    // a screw's bores have their corners on its size
-    screwHoleD: r10(2 * Math.min(fit(top), below)),
-    screwHeadD: r10(2 * Math.min(fit(under), below)),
+    // every room above is to a bore's corners, which stand out past its size (MOUNT_BORE)
+    magnetD: r10(MOUNT_BORE.magnet.fits(room)),
+    screwHoleD: r10(MOUNT_BORE.hole.fits(Math.min(fit(top), below))),
+    screwHeadD: r10(MOUNT_BORE.head.fits(Math.min(fit(under), below))),
     // in the solid floor the pad grows to suit, so only a boss caps the depth
     depth: bosses ? r10(BOSS_H - MOUNT_SKIN) : Infinity,
     // which of the sizes the cut beside it stops, rather than the floor, cell or boss
@@ -4504,9 +4549,9 @@ <h2 id="drawersTitle">Your drawers</h2>
    * A 21.7 mm magnet from beneath at a 55 mm pitch did it: a flat of the pocket in the
    * cell at the back left, on the magnet's radius, crosses that cell's front side 0.03
    * microns from the corner of the cell at the back right. A 22.2 mm screw shank at 56.5
-   * mm did it twice over, from the cell at the back right as well, on main too. Each shell
-   * is closed on its own, so the pockets' own retries never see it, and it comes and goes
-   * with the size and the pitch.
+   * mm (22.2 across its corners, as shanks were cut then) did it twice over, from the cell
+   * at the back right as well, on main too. Each shell is closed on its own, so the
+   * pockets' own retries never see it, and it comes and goes with the size and the pitch.
    *
    * So with mounting pockets on the piece, every shell the cells and margins make is
    * checked against those built before it beside it, as jointed cells are above. One that
@@ -7464,15 +7509,21 @@ <h2 id="drawersTitle">Your drawers</h2>
 /* What sets the clearance's ceiling, in words: core.js connClrCeiling decides it and says
    which reason applies. A ceiling that moves with the pitch names the pitch, as the mount
    sizes do, because that is the number to change; 'slip' is the plain 1 mm and keeps the
-   millimetres advice. */
-const CLR_JOINT = { puzzle: 'puzzle tab', bowtie: 'bowtie key', puzzlekey: 'puzzle key' };
+   millimetres advice. The puzzle and the puzzle key said they opened holes in the plate,
+   as they did until a joint's cut was taken again when it came out open (cutAgain in
+   core.js); past each ceiling now two cells' shells share an edge at some pitches, which
+   is not watertight either but is no hole. The dovetail said its pocket broke through
+   into the socket beside it, which it does from 0.25, under its ceiling. */
+const CLR_JOINT = { puzzle: 'puzzle tab', puzzlekey: 'puzzle key' };
 const clrWhy = (by) => ({
-  dovetail: '— any looser and a dovetail pocket breaks through into the socket beside it',
+  dovetail: '— any looser and a dovetail pocket leaves the plate not watertight at some ' +
+    'pitches',
   snaptop: '— any looser and the housing of a snap clip dropped in from above runs up to ' +
     'the seam and on into the next piece',
   pitch: `${atPitch()} — on cells under ${RANGES.connClr.smallPitch} mm a ` +
-    `looser ${CLR_JOINT[state.connector]} opens holes in the plate`,
-  joint: `— any looser and a ${CLR_JOINT[state.connector]}'s recess opens holes in the plate`,
+    `looser ${CLR_JOINT[state.connector]} leaves the plate not watertight`,
+  joint: `— any looser and a ${CLR_JOINT[state.connector]}'s recess leaves the plate not ` +
+    'watertight at some pitches',
 })[by] || '';
 /* id -> the message that goes under it. Rebuilt from scratch on every read, so a field
    that has come good stops complaining without anything having to remember it once did. */
diff --git a/sw.js b/sw.js
index 827cb0e..c43f938 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "508e30fe00d3";
+const VERSION = "9ddeb0107071";
 const FILES = [
   "./",
   "bins/",

From 69e610d8eaaf3b1b083df17d9b35399ea2552e7d Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 12:19:23 +0000
Subject: [PATCH 06/58] Keep puzzle plates watertight on pitches just past 20
 mm by holding the fit clearance at 0.3 up to 20.7 mm

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md                    | 33 ++++++++--------
 src/core.js                       | 63 +++++++++++++++++--------------
 src/ui.js                         | 19 +++++-----
 test/plate-audit.js               | 23 +++++++----
 test/ui/plates-robustness.spec.js | 18 +++++----
 5 files changed, 88 insertions(+), 68 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index 2e543cb..a0c478a 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -825,21 +825,24 @@ currently installed):
   meet face to face at 14.44 mm (twice a cup's reach), and there they are built as one
   solid with `csgUnion`.
 - **None of the fit clearance's ceilings that waited on a sweep can go up but the
-  bowtie's.** `connClrCeiling` caps the field for each joint, and five of its ceilings
-  were set by open edges one step past them that `cutAgain` closes. Swept again on 2 × 2
-  and 1-cell pieces, every 0.01 mm of pitch over each ceiling's band, every 0.05 of the
-  field past it and every 0.01 near a leak: the dovetail's step past its 0.3 is open
-  still at one pitch (0.35 at 42.35 mm), and the puzzle key in the floor's past its 0.8
-  leaks at another (0.85 at 29.74). The puzzle and the puzzle key under 20 mm leak within
-  two steps of their 0.3 (0.38 at 18.54 mm, 0.37 at 18.07). The puzzle key's and the
-  puzzle's are no longer holes: the joint's cut lands on the edge of the `BLOAT` band two
-  cells overlap in, along a line that climbs with the field, and the two shells share
-  that edge, as the dovetail's do from 0.39. A ceiling goes up a step only where the
-  field builds clean to the step after it, so all four stay. The bowtie in the floor
-  under 20 mm leaked nowhere up to 1.05, at every 0.01 mm from 13.5 to 20 and loose and
-  tight at every 0.1, and takes the plain 1 mm. `test/plate-audit.js` builds each leak,
-  which has to stay one and be refused, and the bowtie's step to spare, which has to
-  build closed.
+  bowtie's, and the puzzle's runs on to 20.7 mm.** `connClrCeiling` caps the field for
+  each joint, and five of its ceilings were set by open edges one step past them that
+  `cutAgain` closes. Swept again on 2 × 2 and 1-cell pieces, every 0.01 mm of pitch over
+  each ceiling's band, every 0.05 of the field past it and every 0.01 near a leak: the
+  dovetail's step past its 0.3 is open still at one pitch (0.35 at 42.35 mm), and the
+  puzzle key in the floor's past its 0.8 leaks at another (0.85 at 29.74). The puzzle and
+  the puzzle key under 20 mm leak within two steps of their 0.3 (0.38 at 18.54 mm, 0.37 at
+  18.07). The puzzle key's and the puzzle's are no longer holes: the joint's cut lands on
+  the edge of the `BLOAT` band two cells overlap in, along a line that climbs with the
+  field, and the two shells share that edge, as the dovetail's do from 0.39. The puzzle's
+  line runs on past 20 mm, 0.05 higher every 0.16 mm (0.85 at 20.05, 0.9 at 20.21, 1 at
+  20.53, 1.05 at 20.69), so its 0.3 holds on to 20.7, where the plain 1 mm has its step to
+  spare. A ceiling goes up a step only where the field builds clean to the step after it,
+  so all four stay. The bowtie in the floor under 20 mm leaked nowhere up to 1.05, at
+  every 0.01 mm from 13.5 to 20 and loose and tight at every 0.1, and takes the plain
+  1 mm. `test/plate-audit.js` builds each leak, which has to stay one and be refused, and
+  the bowtie's step to spare and the step under the puzzle's line at 20.05 mm, which have
+  to build closed.
 - **A face that is nothing but a straight line has no middle.** A weld that closes a
   T-junction can leave three corners on one line. Fanned from its average, the spokes land
   a fraction of a micron from a corner and read, to `checkManifold`'s thousandths, as the
diff --git a/src/core.js b/src/core.js
index 3e9e3be..2602c9f 100644
--- a/src/core.js
+++ b/src/core.js
@@ -999,7 +999,7 @@ const PLATE_RANGES = {
   pitch: { min: 13.5, max: 200 },
   topCutoff: { min: 0.1, max: 1 },
   connClr: { min: 0, max: 1, dovetail: 0.3, snapTop: 0.3, puzzleKey: 0.8,
-             smallPitch: 20, small: 0.3, puzzleRoom: 6.5 },
+             smallPitch: 20, puzzlePitch: 20.7, small: 0.3, puzzleRoom: 6.5 },
   bottomPad: { min: 0, max: 20 },
   magnetD: { min: 1 }, magnetH: { min: 0.5, max: 10 },
   screwHoleD: { min: 1 }, screwHeadD: { min: 1 }, screwHeadDepth: { min: 0.5, max: 10 },
@@ -1014,12 +1014,12 @@ function fitClearances(field) {
 }
 /* The fit clearance's ceiling for one design, as { max, by }; `by` says what sets it, for
  * the page to put in words: 'dovetail', 'snaptop', 'pitch', 'joint', or 'slip' for the
- * plain 1 mm. One function, because four things have to agree on it — the field's range,
- * the clamp on a number a link brings in, the message saying why, and the fit coupon's
- * slackest pair — and it takes the whole design because the answer depends on the joint,
- * which way its key goes in and the pitch. It took a connector name, and a 1 mm ceiling
- * for everything but the dovetail let a snap clip's housing into the next piece and let
- * small pitches leak.
+ * plain 1 mm, and with 'pitch', `below` is the pitch its band runs up to. One function,
+ * because four things have to agree on it — the field's range, the clamp on a number a
+ * link brings in, the message saying why, and the fit coupon's slackest pair — and it
+ * takes the whole design because the answer depends on the joint, which way its key goes
+ * in and the pitch. It took a connector name, and a 1 mm ceiling for everything but the
+ * dovetail let a snap clip's housing into the next piece and let small pitches leak.
  *
  * Measured first on 2 × 2 and 1-cell pieces from 13.5 to 60 mm, every 0.5 mm of pitch —
  * at every 0.05 of clearance for the puzzle, the bowtie and the puzzle key, at six for
@@ -1048,13 +1048,18 @@ function fitClearances(field) {
  *             pair did the same for any field from 0.3 up. 0.3 holds the wall one BLOAT,
  *             0.05, inside the piece, the overlap the cell regions keep; the coupon's
  *             slackest pair is this ceiling cut the key's way, so it stops there too.
- *   pitch     0.3 below 20 mm for the puzzle and a puzzle key in the floor, earned. Past
- *             it they left holes from 13.5 to 19 mm — a puzzle key at 14 from 0.4, a
- *             puzzle at 19 from 0.35 — which cutAgain closes, and 0.35 builds clean at
- *             every pitch; but on 1-cell pieces a line across the pitch that climbs with
- *             the field puts the cut on the edge of the band two cells share, and the
- *             shells share it: a puzzle key from 0.37 (at 18.07 mm), a puzzle tab from
- *             0.38 (at 18.54). The puzzle's lobe also needs room in its cell: it opens the
+ *   pitch     0.3 for a puzzle below 20.7 mm and a puzzle key in the floor below 20,
+ *             earned. Past it they left holes from 13.5 to 19 mm — a puzzle key at 14
+ *             from 0.4, a puzzle at 19 from 0.35 — which cutAgain closes, and 0.35 builds
+ *             clean at every pitch; but on 1-cell pieces a line across the pitch that
+ *             climbs with the field puts the cut on the edge of the band two cells share,
+ *             and the shells share it: a puzzle key from 0.37 (at 18.07 mm), a puzzle tab
+ *             from 0.38 (at 18.54). The puzzle's line climbs 0.05 every 0.16 mm and runs
+ *             on past 20 — 0.8 at 19.89, 0.85 at 20.05, 0.9 at 20.21 — out of the field,
+ *             1 at 20.53 and 1.05 at 20.69, so its band runs to 20.7, where the plain
+ *             1 mm has its step to spare. Off the line the field builds clean from 20 to
+ *             20.7, and a ceiling that followed the line would gain only there; one band
+ *             is simpler. The puzzle's lobe also needs room in its cell: it opens the
  *             plate once its clearance passes half the pitch less 6.475 mm, so it stops at
  *             half the pitch less 6.5 — 0.25 at 13.5, and 0.3 from 13.6. A bowtie in the
  *             floor was held here too, for holes at 18 mm at 1. It builds clean at every
@@ -1068,20 +1073,21 @@ function fitClearances(field) {
  *   slip      1 for the rest. A key in the walls is cut to keySlim's own clearance, which
  *             the field does not move. The snap and the H-clip did not leak above 0.3 at
  *             any pitch measured but in one band — an H-clip dropped in from above leaks
- *             at 0.74 to 0.745 and nowhere else. From 20 mm up the bowtie and the puzzle
- *             leak only at isolated values: the bowtie at 25 mm at 0.64, the puzzle at
- *             0.39–0.4 at 21 and 32.5–35 mm and here and there from 0.52 to 0.87. That is
- *             the sliver class again, not a ceiling — no limit short of 0.38 misses them,
- *             and the same class turns up under the default too: a snap at 20 mm at 0.29,
- *             a bowtie at 17 mm at 0.15 and under. One is not isolated: on 2 × 2 pieces
- *             a puzzle at 0.35 exactly, and not 0.34 or 0.36, has two shells sharing an
- *             edge at every pitch from 31.6 to 52.2 mm, where a corner of a notch's lobe,
- *             centred on the line between two cells, stands on the edge of the band they
- *             share. That wants mending in the cut; no ceiling misses a single value.
+ *             at 0.74 to 0.745 and nowhere else. From 20 mm up (20.7 for the puzzle) the
+ *             bowtie and the puzzle leak only at isolated values: the bowtie at 25 mm at
+ *             0.64, the puzzle at 0.39–0.4 at 21 and 32.5–35 mm and here and there from
+ *             0.52 to 0.87. That is the sliver class again, not a ceiling — no limit
+ *             short of 0.38 misses them, and the same class turns up under the default
+ *             too: a snap at 20 mm at 0.29, a bowtie at 17 mm at 0.15 and under. One is
+ *             not isolated: on 2 × 2 pieces a puzzle at 0.35 exactly, and not 0.34 or
+ *             0.36, has two shells sharing an edge at every pitch from 31.6 to 52.2 mm,
+ *             where a corner of a notch's lobe, centred on the line between two cells,
+ *             stands on the edge of the band they share. That wants mending in the cut
+ *             (issue #72); no ceiling misses a single value.
  *
  * test/plate-audit.js builds the step that earns each ceiling, which has to leak or cross
- * the seam and be refused, and the bowtie's step to spare, which has to build closed and
- * be refused. */
+ * the seam and be refused, and the bowtie's step to spare and the step under the puzzle's
+ * line past 20 mm, which have to build closed and be refused. */
 function connClrCeiling(cfg) {
   const R = PLATE_RANGES.connClr;
   const kind = jointKind(cfg.connector, cfg.keyMount, cfg.keyInsert);
@@ -1089,10 +1095,11 @@ function connClrCeiling(cfg) {
   if (kind === 'snaptop') return { max: R.snapTop, by: 'snaptop' };
   const floorKey = cfg.connector === 'puzzlekey' && cfg.keyMount !== 'wall';
   if (cfg.connector !== 'puzzle' && !floorKey) return { max: R.max, by: 'slip' };
-  if (cfg.pitch < R.smallPitch) {
+  const below = cfg.connector === 'puzzle' ? R.puzzlePitch : R.smallPitch;
+  if (cfg.pitch < below) {
     const room = cfg.connector === 'puzzle'
       ? Math.floor((cfg.pitch / 2 - R.puzzleRoom) * 100 + 1e-9) / 100 : Infinity;
-    return { max: Math.min(R.small, room), by: 'pitch' };
+    return { max: Math.min(R.small, room), by: 'pitch', below };
   }
   if (cfg.connector === 'puzzlekey') return { max: R.puzzleKey, by: 'joint' };
   return { max: R.max, by: 'slip' };
diff --git a/src/ui.js b/src/ui.js
index 41c5793..b951c94 100644
--- a/src/ui.js
+++ b/src/ui.js
@@ -135,23 +135,24 @@ const LIMITS = {
     label: 'Screw head depth', when: () => state.screws, why: bossDepth },
   // each joint's ceiling is its own, so none is held to another's reason; see clrWhy
   connClr: { min: RANGES.connClr.min, max: () => connClrCeiling(state).max, label: 'Fit clearance',
-    when: () => state.connector !== 'none', why: () => clrWhy(connClrCeiling(state).by) },
+    when: () => state.connector !== 'none', why: () => clrWhy(connClrCeiling(state)) },
 };
 /* What sets the clearance's ceiling, in words: core.js connClrCeiling decides it and says
    which reason applies. A ceiling that moves with the pitch names the pitch, as the mount
-   sizes do, because that is the number to change; 'slip' is the plain 1 mm and keeps the
-   millimetres advice. The puzzle and the puzzle key said they opened holes in the plate,
-   as they did until a joint's cut was taken again when it came out open (cutAgain in
-   core.js); past each ceiling now two cells' shells share an edge at some pitches, which
-   is not watertight either but is no hole. The dovetail said its pocket broke through
-   into the socket beside it, which it does from 0.25, under its ceiling. */
+   sizes do, because that is the number to change, and the pitch its band runs up to,
+   which for the puzzle is its own; 'slip' is the plain 1 mm and keeps the millimetres
+   advice. The puzzle and the puzzle key said they opened holes in the plate, as they did
+   until a joint's cut was taken again when it came out open (cutAgain in core.js); past
+   each ceiling now two cells' shells share an edge at some pitches, which is not
+   watertight either but is no hole. The dovetail said its pocket broke through into the
+   socket beside it, which it does from 0.25, under its ceiling. */
 const CLR_JOINT = { puzzle: 'puzzle tab', puzzlekey: 'puzzle key' };
-const clrWhy = (by) => ({
+const clrWhy = ({ by, below }) => ({
   dovetail: '— any looser and a dovetail pocket leaves the plate not watertight at some ' +
     'pitches',
   snaptop: '— any looser and the housing of a snap clip dropped in from above runs up to ' +
     'the seam and on into the next piece',
-  pitch: `${atPitch()} — on cells under ${RANGES.connClr.smallPitch} mm a ` +
+  pitch: `${atPitch()} — on cells under ${below} mm a ` +
     `looser ${CLR_JOINT[state.connector]} leaves the plate not watertight`,
   joint: `— any looser and a ${CLR_JOINT[state.connector]}'s recess leaves the plate not ` +
     'watertight at some pitches',
diff --git a/test/plate-audit.js b/test/plate-audit.js
index b1d3e52..78d9fb8 100644
--- a/test/plate-audit.js
+++ b/test/plate-audit.js
@@ -2242,18 +2242,26 @@ console.log('\nthe fit clearance at its ceiling, every joint and pitch band:');
      dovetail's step is open still, and is built with the other ends, above. Three more
      have a leak within two steps, two cells' shells sharing an edge in the band they
      overlap in, and the first is their row: it has to leak still, or that ceiling can go
-     up. The bowtie in the floor below 20 mm leaked nowhere up to 1.05 and takes the plain
-     1 mm; `spare` marks its step to spare, which has to build closed, or cutAgain has lost
-     ground. Each has to be refused by the field. */
+     up. The puzzle's leak runs on past 20 mm as a line, and its band with it to 20.7.
+     The line's first leak past 20 is a row, with the step under it, which has to build
+     closed so the row stays on the line; so is the field's own 1 mm on the line, which
+     the band has to reach past. The bowtie in the floor below 20 mm leaked nowhere up to
+     1.05 and takes the plain 1 mm; its step to spare has to build closed, or cutAgain
+     has lost ground. A row that has to build closed says why. Each has to be refused by
+     the field. */
   const PAST = [
     ['snap from above, 0.35 at 42', { connector: 'snap', keyInsert: 'top', pitch: 42, clr: 0.35 }, '2x2 pieces'],
     ['puzzle, 0.3 at 13.5', { connector: 'puzzle', pitch: 13.5, clr: 0.3 }, '1-cell pieces'],
     ['puzzle, 0.38 at 18.54', { connector: 'puzzle', pitch: 18.54, clr: 0.38 }, '1-cell pieces'],
+    ['puzzle, 0.85 at 20.05', { connector: 'puzzle', pitch: 20.05, clr: 0.85 }, '1-cell pieces'],
+    ['puzzle, 0.8 at 20.05', { connector: 'puzzle', pitch: 20.05, clr: 0.8 }, '1-cell pieces',
+      'the step under the line'],
+    ['puzzle, 1 at 20.53', { connector: 'puzzle', pitch: 20.53, clr: 1 }, '1-cell pieces'],
     ['puzzle key, 0.37 at 18.07', { connector: 'puzzlekey', pitch: 18.07, clr: 0.37 }, '1-cell pieces'],
     ['puzzle key, 0.85 at 29.74', { connector: 'puzzlekey', pitch: 29.74, clr: 0.85 }, '1-cell pieces'],
-    ['bowtie, 1.05 at 18', { connector: 'bowtie', pitch: 18, clr: 1.05 }, '2x2 pieces', 'spare'],
+    ['bowtie, 1.05 at 18', { connector: 'bowtie', pitch: 18, clr: 1.05 }, '2x2 pieces', 'a step to spare'],
   ];
-  for (const [what, o, ln, spare] of PAST) {
+  for (const [what, o, ln, closed] of PAST) {
     const r = buildAll({ ...PIECE_LAYOUTS[ln](o.pitch), ...o });
     /* A snap from above earns its ceiling in the seam face, before anything crosses the
        seam: one step past, its slot's wall is nearer the face than a BLOAT. */
@@ -2270,10 +2278,9 @@ console.log('\nthe fit clearance at its ceiling, every joint and pitch band:');
       : inFace ? `its slot ${(Math.round(face.near * 1e4) / 1e4 + 0).toFixed(3)} mm off the seam face`
       : leakText(r)}` +
                 (!refused ? `   THE FIELD TAKES IT: the ceiling went up to ${most}`
-                  : spare ? (still ? '   OPEN AGAIN — cutAgain no longer closes it'
-                                   : ' — closed, a step to spare')
+                  : closed ? (still ? `   OPEN — no longer ${closed}` : ` — closed, ${closed}`)
                   : still ? ' — the ceiling is earned' : '   NOW CLEAN — that ceiling can go up'));
-    if (!refused || (spare ? still : !still)) bad++;
+    if (!refused || (closed ? still : !still)) bad++;
   }
 
   /* activeJoint in src/ui.js, with the field at the ceiling — a fixture, as in the coupon
diff --git a/test/ui/plates-robustness.spec.js b/test/ui/plates-robustness.spec.js
index 7e5a26e..e86b832 100644
--- a/test/ui/plates-robustness.spec.js
+++ b/test/ui/plates-robustness.spec.js
@@ -424,23 +424,25 @@ test.describe('limits no tighter than the geometry', () => {
    clip dropped in from above is housed in a slot whose seam-side wall stands 0.3 mm less
    the clearance from the seam, so at 0.35 on the field the wall lies in the seam face and
    past it in the next piece — the field stops at 0.3, a BLOAT short of the face;
-   and under 20 mm the puzzle and the puzzle key leave plates that are not watertight at
-   clearances that build closed at 42. Each case is refused at the field, clamped to the
-   ceiling in the state a link loads into, and says which joint and which pitch — the
-   pitch is the number to change. A joint that builds closed at a small pitch is not held
-   to the others' reason: the bowtie in the floor was, until a sweep built it closed from
-   13.5 to 20 mm at every clearance to 1. */
+   and under 20 mm (20.7 for the puzzle) the puzzle and the puzzle key leave plates that
+   are not watertight at clearances that build closed at 42. Each case is refused at the
+   field, clamped to the ceiling in the state a link loads into, and says which joint and
+   which pitch — the pitch is the number to change. A joint that builds closed at a small
+   pitch is not held to the others' reason: the bowtie in the floor was, until a sweep
+   built it closed from 13.5 to 20 mm at every clearance to 1. */
 test.describe('the clearance ceiling is the joint\'s and the pitch\'s', () => {
   const SEAM = '#w=168&d=84&sp=manual&rc=&cc=2';
   for (const [hash, ceiling, msg] of [
     [`${SEAM}&cn=snap&km=wall&ki=top&cl=0.35`, 0.3,
      /Fit clearance must be 0\.3 mm or less — any looser and the housing of a snap clip dropped in from above runs up to the seam and on into the next piece\./],
     ['#pi=18&cn=puzzle&cl=1', 0.3,
-     /Fit clearance must be 0\.3 mm or less at an 18 mm pitch — on cells under 20 mm a looser puzzle tab leaves the plate not watertight\./],
+     /Fit clearance must be 0\.3 mm or less at an 18 mm pitch — on cells under 20\.7 mm a looser puzzle tab leaves the plate not watertight\./],
     ['#pi=14&cn=puzzlekey&cl=0.5', 0.3,
      /Fit clearance must be 0\.3 mm or less at a 14 mm pitch — on cells under 20 mm a looser puzzle key leaves the plate not watertight\./],
     ['#pi=13.5&cn=puzzle&cl=0.3', 0.25,
-     /Fit clearance must be 0\.25 mm or less at a 13\.5 mm pitch — on cells under 20 mm a looser puzzle tab leaves the plate not watertight\./],
+     /Fit clearance must be 0\.25 mm or less at a 13\.5 mm pitch — on cells under 20\.7 mm a looser puzzle tab leaves the plate not watertight\./],
+    ['#pi=20.3&cn=puzzle&cl=0.9', 0.3,
+     /Fit clearance must be 0\.3 mm or less at a 20\.3 mm pitch — on cells under 20\.7 mm a looser puzzle tab leaves the plate not watertight\./],
     ['#cn=puzzlekey&cl=0.85', 0.8,
      /Fit clearance must be 0\.8 mm or less — any looser and a puzzle key's recess leaves the plate not watertight at some pitches\./],
   ])

From 07fe871469f3caffd6a630b1a4aab948877ede62 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 12:19:31 +0000
Subject: [PATCH 07/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html | 63 ++++++++++++++++++++-----------------
 index.html      | 82 +++++++++++++++++++++++++++----------------------
 sw.js           |  2 +-
 3 files changed, 81 insertions(+), 66 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index a85366c..6119e71 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -2605,7 +2605,7 @@ <h2 id="drawersTitle">Your drawers</h2>
   pitch: { min: 13.5, max: 200 },
   topCutoff: { min: 0.1, max: 1 },
   connClr: { min: 0, max: 1, dovetail: 0.3, snapTop: 0.3, puzzleKey: 0.8,
-             smallPitch: 20, small: 0.3, puzzleRoom: 6.5 },
+             smallPitch: 20, puzzlePitch: 20.7, small: 0.3, puzzleRoom: 6.5 },
   bottomPad: { min: 0, max: 20 },
   magnetD: { min: 1 }, magnetH: { min: 0.5, max: 10 },
   screwHoleD: { min: 1 }, screwHeadD: { min: 1 }, screwHeadDepth: { min: 0.5, max: 10 },
@@ -2620,12 +2620,12 @@ <h2 id="drawersTitle">Your drawers</h2>
 }
 /* The fit clearance's ceiling for one design, as { max, by }; `by` says what sets it, for
  * the page to put in words: 'dovetail', 'snaptop', 'pitch', 'joint', or 'slip' for the
- * plain 1 mm. One function, because four things have to agree on it — the field's range,
- * the clamp on a number a link brings in, the message saying why, and the fit coupon's
- * slackest pair — and it takes the whole design because the answer depends on the joint,
- * which way its key goes in and the pitch. It took a connector name, and a 1 mm ceiling
- * for everything but the dovetail let a snap clip's housing into the next piece and let
- * small pitches leak.
+ * plain 1 mm, and with 'pitch', `below` is the pitch its band runs up to. One function,
+ * because four things have to agree on it — the field's range, the clamp on a number a
+ * link brings in, the message saying why, and the fit coupon's slackest pair — and it
+ * takes the whole design because the answer depends on the joint, which way its key goes
+ * in and the pitch. It took a connector name, and a 1 mm ceiling for everything but the
+ * dovetail let a snap clip's housing into the next piece and let small pitches leak.
  *
  * Measured first on 2 × 2 and 1-cell pieces from 13.5 to 60 mm, every 0.5 mm of pitch —
  * at every 0.05 of clearance for the puzzle, the bowtie and the puzzle key, at six for
@@ -2654,13 +2654,18 @@ <h2 id="drawersTitle">Your drawers</h2>
  *             pair did the same for any field from 0.3 up. 0.3 holds the wall one BLOAT,
  *             0.05, inside the piece, the overlap the cell regions keep; the coupon's
  *             slackest pair is this ceiling cut the key's way, so it stops there too.
- *   pitch     0.3 below 20 mm for the puzzle and a puzzle key in the floor, earned. Past
- *             it they left holes from 13.5 to 19 mm — a puzzle key at 14 from 0.4, a
- *             puzzle at 19 from 0.35 — which cutAgain closes, and 0.35 builds clean at
- *             every pitch; but on 1-cell pieces a line across the pitch that climbs with
- *             the field puts the cut on the edge of the band two cells share, and the
- *             shells share it: a puzzle key from 0.37 (at 18.07 mm), a puzzle tab from
- *             0.38 (at 18.54). The puzzle's lobe also needs room in its cell: it opens the
+ *   pitch     0.3 for a puzzle below 20.7 mm and a puzzle key in the floor below 20,
+ *             earned. Past it they left holes from 13.5 to 19 mm — a puzzle key at 14
+ *             from 0.4, a puzzle at 19 from 0.35 — which cutAgain closes, and 0.35 builds
+ *             clean at every pitch; but on 1-cell pieces a line across the pitch that
+ *             climbs with the field puts the cut on the edge of the band two cells share,
+ *             and the shells share it: a puzzle key from 0.37 (at 18.07 mm), a puzzle tab
+ *             from 0.38 (at 18.54). The puzzle's line climbs 0.05 every 0.16 mm and runs
+ *             on past 20 — 0.8 at 19.89, 0.85 at 20.05, 0.9 at 20.21 — out of the field,
+ *             1 at 20.53 and 1.05 at 20.69, so its band runs to 20.7, where the plain
+ *             1 mm has its step to spare. Off the line the field builds clean from 20 to
+ *             20.7, and a ceiling that followed the line would gain only there; one band
+ *             is simpler. The puzzle's lobe also needs room in its cell: it opens the
  *             plate once its clearance passes half the pitch less 6.475 mm, so it stops at
  *             half the pitch less 6.5 — 0.25 at 13.5, and 0.3 from 13.6. A bowtie in the
  *             floor was held here too, for holes at 18 mm at 1. It builds clean at every
@@ -2674,20 +2679,21 @@ <h2 id="drawersTitle">Your drawers</h2>
  *   slip      1 for the rest. A key in the walls is cut to keySlim's own clearance, which
  *             the field does not move. The snap and the H-clip did not leak above 0.3 at
  *             any pitch measured but in one band — an H-clip dropped in from above leaks
- *             at 0.74 to 0.745 and nowhere else. From 20 mm up the bowtie and the puzzle
- *             leak only at isolated values: the bowtie at 25 mm at 0.64, the puzzle at
- *             0.39–0.4 at 21 and 32.5–35 mm and here and there from 0.52 to 0.87. That is
- *             the sliver class again, not a ceiling — no limit short of 0.38 misses them,
- *             and the same class turns up under the default too: a snap at 20 mm at 0.29,
- *             a bowtie at 17 mm at 0.15 and under. One is not isolated: on 2 × 2 pieces
- *             a puzzle at 0.35 exactly, and not 0.34 or 0.36, has two shells sharing an
- *             edge at every pitch from 31.6 to 52.2 mm, where a corner of a notch's lobe,
- *             centred on the line between two cells, stands on the edge of the band they
- *             share. That wants mending in the cut; no ceiling misses a single value.
+ *             at 0.74 to 0.745 and nowhere else. From 20 mm up (20.7 for the puzzle) the
+ *             bowtie and the puzzle leak only at isolated values: the bowtie at 25 mm at
+ *             0.64, the puzzle at 0.39–0.4 at 21 and 32.5–35 mm and here and there from
+ *             0.52 to 0.87. That is the sliver class again, not a ceiling — no limit
+ *             short of 0.38 misses them, and the same class turns up under the default
+ *             too: a snap at 20 mm at 0.29, a bowtie at 17 mm at 0.15 and under. One is
+ *             not isolated: on 2 × 2 pieces a puzzle at 0.35 exactly, and not 0.34 or
+ *             0.36, has two shells sharing an edge at every pitch from 31.6 to 52.2 mm,
+ *             where a corner of a notch's lobe, centred on the line between two cells,
+ *             stands on the edge of the band they share. That wants mending in the cut
+ *             (issue #72); no ceiling misses a single value.
  *
  * test/plate-audit.js builds the step that earns each ceiling, which has to leak or cross
- * the seam and be refused, and the bowtie's step to spare, which has to build closed and
- * be refused. */
+ * the seam and be refused, and the bowtie's step to spare and the step under the puzzle's
+ * line past 20 mm, which have to build closed and be refused. */
 function connClrCeiling(cfg) {
   const R = PLATE_RANGES.connClr;
   const kind = jointKind(cfg.connector, cfg.keyMount, cfg.keyInsert);
@@ -2695,10 +2701,11 @@ <h2 id="drawersTitle">Your drawers</h2>
   if (kind === 'snaptop') return { max: R.snapTop, by: 'snaptop' };
   const floorKey = cfg.connector === 'puzzlekey' && cfg.keyMount !== 'wall';
   if (cfg.connector !== 'puzzle' && !floorKey) return { max: R.max, by: 'slip' };
-  if (cfg.pitch < R.smallPitch) {
+  const below = cfg.connector === 'puzzle' ? R.puzzlePitch : R.smallPitch;
+  if (cfg.pitch < below) {
     const room = cfg.connector === 'puzzle'
       ? Math.floor((cfg.pitch / 2 - R.puzzleRoom) * 100 + 1e-9) / 100 : Infinity;
-    return { max: Math.min(R.small, room), by: 'pitch' };
+    return { max: Math.min(R.small, room), by: 'pitch', below };
   }
   if (cfg.connector === 'puzzlekey') return { max: R.puzzleKey, by: 'joint' };
   return { max: R.max, by: 'slip' };
diff --git a/index.html b/index.html
index 04ab7c0..04d20a0 100644
--- a/index.html
+++ b/index.html
@@ -2392,7 +2392,7 @@ <h2 id="drawersTitle">Your drawers</h2>
   pitch: { min: 13.5, max: 200 },
   topCutoff: { min: 0.1, max: 1 },
   connClr: { min: 0, max: 1, dovetail: 0.3, snapTop: 0.3, puzzleKey: 0.8,
-             smallPitch: 20, small: 0.3, puzzleRoom: 6.5 },
+             smallPitch: 20, puzzlePitch: 20.7, small: 0.3, puzzleRoom: 6.5 },
   bottomPad: { min: 0, max: 20 },
   magnetD: { min: 1 }, magnetH: { min: 0.5, max: 10 },
   screwHoleD: { min: 1 }, screwHeadD: { min: 1 }, screwHeadDepth: { min: 0.5, max: 10 },
@@ -2407,12 +2407,12 @@ <h2 id="drawersTitle">Your drawers</h2>
 }
 /* The fit clearance's ceiling for one design, as { max, by }; `by` says what sets it, for
  * the page to put in words: 'dovetail', 'snaptop', 'pitch', 'joint', or 'slip' for the
- * plain 1 mm. One function, because four things have to agree on it — the field's range,
- * the clamp on a number a link brings in, the message saying why, and the fit coupon's
- * slackest pair — and it takes the whole design because the answer depends on the joint,
- * which way its key goes in and the pitch. It took a connector name, and a 1 mm ceiling
- * for everything but the dovetail let a snap clip's housing into the next piece and let
- * small pitches leak.
+ * plain 1 mm, and with 'pitch', `below` is the pitch its band runs up to. One function,
+ * because four things have to agree on it — the field's range, the clamp on a number a
+ * link brings in, the message saying why, and the fit coupon's slackest pair — and it
+ * takes the whole design because the answer depends on the joint, which way its key goes
+ * in and the pitch. It took a connector name, and a 1 mm ceiling for everything but the
+ * dovetail let a snap clip's housing into the next piece and let small pitches leak.
  *
  * Measured first on 2 × 2 and 1-cell pieces from 13.5 to 60 mm, every 0.5 mm of pitch —
  * at every 0.05 of clearance for the puzzle, the bowtie and the puzzle key, at six for
@@ -2441,13 +2441,18 @@ <h2 id="drawersTitle">Your drawers</h2>
  *             pair did the same for any field from 0.3 up. 0.3 holds the wall one BLOAT,
  *             0.05, inside the piece, the overlap the cell regions keep; the coupon's
  *             slackest pair is this ceiling cut the key's way, so it stops there too.
- *   pitch     0.3 below 20 mm for the puzzle and a puzzle key in the floor, earned. Past
- *             it they left holes from 13.5 to 19 mm — a puzzle key at 14 from 0.4, a
- *             puzzle at 19 from 0.35 — which cutAgain closes, and 0.35 builds clean at
- *             every pitch; but on 1-cell pieces a line across the pitch that climbs with
- *             the field puts the cut on the edge of the band two cells share, and the
- *             shells share it: a puzzle key from 0.37 (at 18.07 mm), a puzzle tab from
- *             0.38 (at 18.54). The puzzle's lobe also needs room in its cell: it opens the
+ *   pitch     0.3 for a puzzle below 20.7 mm and a puzzle key in the floor below 20,
+ *             earned. Past it they left holes from 13.5 to 19 mm — a puzzle key at 14
+ *             from 0.4, a puzzle at 19 from 0.35 — which cutAgain closes, and 0.35 builds
+ *             clean at every pitch; but on 1-cell pieces a line across the pitch that
+ *             climbs with the field puts the cut on the edge of the band two cells share,
+ *             and the shells share it: a puzzle key from 0.37 (at 18.07 mm), a puzzle tab
+ *             from 0.38 (at 18.54). The puzzle's line climbs 0.05 every 0.16 mm and runs
+ *             on past 20 — 0.8 at 19.89, 0.85 at 20.05, 0.9 at 20.21 — out of the field,
+ *             1 at 20.53 and 1.05 at 20.69, so its band runs to 20.7, where the plain
+ *             1 mm has its step to spare. Off the line the field builds clean from 20 to
+ *             20.7, and a ceiling that followed the line would gain only there; one band
+ *             is simpler. The puzzle's lobe also needs room in its cell: it opens the
  *             plate once its clearance passes half the pitch less 6.475 mm, so it stops at
  *             half the pitch less 6.5 — 0.25 at 13.5, and 0.3 from 13.6. A bowtie in the
  *             floor was held here too, for holes at 18 mm at 1. It builds clean at every
@@ -2461,20 +2466,21 @@ <h2 id="drawersTitle">Your drawers</h2>
  *   slip      1 for the rest. A key in the walls is cut to keySlim's own clearance, which
  *             the field does not move. The snap and the H-clip did not leak above 0.3 at
  *             any pitch measured but in one band — an H-clip dropped in from above leaks
- *             at 0.74 to 0.745 and nowhere else. From 20 mm up the bowtie and the puzzle
- *             leak only at isolated values: the bowtie at 25 mm at 0.64, the puzzle at
- *             0.39–0.4 at 21 and 32.5–35 mm and here and there from 0.52 to 0.87. That is
- *             the sliver class again, not a ceiling — no limit short of 0.38 misses them,
- *             and the same class turns up under the default too: a snap at 20 mm at 0.29,
- *             a bowtie at 17 mm at 0.15 and under. One is not isolated: on 2 × 2 pieces
- *             a puzzle at 0.35 exactly, and not 0.34 or 0.36, has two shells sharing an
- *             edge at every pitch from 31.6 to 52.2 mm, where a corner of a notch's lobe,
- *             centred on the line between two cells, stands on the edge of the band they
- *             share. That wants mending in the cut; no ceiling misses a single value.
+ *             at 0.74 to 0.745 and nowhere else. From 20 mm up (20.7 for the puzzle) the
+ *             bowtie and the puzzle leak only at isolated values: the bowtie at 25 mm at
+ *             0.64, the puzzle at 0.39–0.4 at 21 and 32.5–35 mm and here and there from
+ *             0.52 to 0.87. That is the sliver class again, not a ceiling — no limit
+ *             short of 0.38 misses them, and the same class turns up under the default
+ *             too: a snap at 20 mm at 0.29, a bowtie at 17 mm at 0.15 and under. One is
+ *             not isolated: on 2 × 2 pieces a puzzle at 0.35 exactly, and not 0.34 or
+ *             0.36, has two shells sharing an edge at every pitch from 31.6 to 52.2 mm,
+ *             where a corner of a notch's lobe, centred on the line between two cells,
+ *             stands on the edge of the band they share. That wants mending in the cut
+ *             (issue #72); no ceiling misses a single value.
  *
  * test/plate-audit.js builds the step that earns each ceiling, which has to leak or cross
- * the seam and be refused, and the bowtie's step to spare, which has to build closed and
- * be refused. */
+ * the seam and be refused, and the bowtie's step to spare and the step under the puzzle's
+ * line past 20 mm, which have to build closed and be refused. */
 function connClrCeiling(cfg) {
   const R = PLATE_RANGES.connClr;
   const kind = jointKind(cfg.connector, cfg.keyMount, cfg.keyInsert);
@@ -2482,10 +2488,11 @@ <h2 id="drawersTitle">Your drawers</h2>
   if (kind === 'snaptop') return { max: R.snapTop, by: 'snaptop' };
   const floorKey = cfg.connector === 'puzzlekey' && cfg.keyMount !== 'wall';
   if (cfg.connector !== 'puzzle' && !floorKey) return { max: R.max, by: 'slip' };
-  if (cfg.pitch < R.smallPitch) {
+  const below = cfg.connector === 'puzzle' ? R.puzzlePitch : R.smallPitch;
+  if (cfg.pitch < below) {
     const room = cfg.connector === 'puzzle'
       ? Math.floor((cfg.pitch / 2 - R.puzzleRoom) * 100 + 1e-9) / 100 : Infinity;
-    return { max: Math.min(R.small, room), by: 'pitch' };
+    return { max: Math.min(R.small, room), by: 'pitch', below };
   }
   if (cfg.connector === 'puzzlekey') return { max: R.puzzleKey, by: 'joint' };
   return { max: R.max, by: 'slip' };
@@ -7504,23 +7511,24 @@ <h2 id="drawersTitle">Your drawers</h2>
     label: 'Screw head depth', when: () => state.screws, why: bossDepth },
   // each joint's ceiling is its own, so none is held to another's reason; see clrWhy
   connClr: { min: RANGES.connClr.min, max: () => connClrCeiling(state).max, label: 'Fit clearance',
-    when: () => state.connector !== 'none', why: () => clrWhy(connClrCeiling(state).by) },
+    when: () => state.connector !== 'none', why: () => clrWhy(connClrCeiling(state)) },
 };
 /* What sets the clearance's ceiling, in words: core.js connClrCeiling decides it and says
    which reason applies. A ceiling that moves with the pitch names the pitch, as the mount
-   sizes do, because that is the number to change; 'slip' is the plain 1 mm and keeps the
-   millimetres advice. The puzzle and the puzzle key said they opened holes in the plate,
-   as they did until a joint's cut was taken again when it came out open (cutAgain in
-   core.js); past each ceiling now two cells' shells share an edge at some pitches, which
-   is not watertight either but is no hole. The dovetail said its pocket broke through
-   into the socket beside it, which it does from 0.25, under its ceiling. */
+   sizes do, because that is the number to change, and the pitch its band runs up to,
+   which for the puzzle is its own; 'slip' is the plain 1 mm and keeps the millimetres
+   advice. The puzzle and the puzzle key said they opened holes in the plate, as they did
+   until a joint's cut was taken again when it came out open (cutAgain in core.js); past
+   each ceiling now two cells' shells share an edge at some pitches, which is not
+   watertight either but is no hole. The dovetail said its pocket broke through into the
+   socket beside it, which it does from 0.25, under its ceiling. */
 const CLR_JOINT = { puzzle: 'puzzle tab', puzzlekey: 'puzzle key' };
-const clrWhy = (by) => ({
+const clrWhy = ({ by, below }) => ({
   dovetail: '— any looser and a dovetail pocket leaves the plate not watertight at some ' +
     'pitches',
   snaptop: '— any looser and the housing of a snap clip dropped in from above runs up to ' +
     'the seam and on into the next piece',
-  pitch: `${atPitch()} — on cells under ${RANGES.connClr.smallPitch} mm a ` +
+  pitch: `${atPitch()} — on cells under ${below} mm a ` +
     `looser ${CLR_JOINT[state.connector]} leaves the plate not watertight`,
   joint: `— any looser and a ${CLR_JOINT[state.connector]}'s recess leaves the plate not ` +
     'watertight at some pitches',
diff --git a/sw.js b/sw.js
index c43f938..eb73b81 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "9ddeb0107071";
+const VERSION = "4f0cfa58126c";
 const FILES = [
   "./",
   "bins/",

From 5f0bd5fdfe31d934606cc2d9b0f157ac060644c7 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 13:31:32 +0000
Subject: [PATCH 08/58] Cut no counterbore under a screw head too narrow to
 clear its shank's corners, so the plate stays watertight

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md                    |  7 +++++-
 src/core.js                       | 26 +++++++++++++++++-----
 src/ui.js                         | 10 ++++++++-
 test/plate-audit.js               | 36 +++++++++++++++++++++++++++++++
 test/ui/plates-robustness.spec.js | 27 +++++++++++++++++++++++
 5 files changed, 99 insertions(+), 7 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index a0c478a..fb546d5 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -702,7 +702,12 @@ currently installed):
   which the field already sizes with room round it. `MOUNT_BORE` says each bore's sides
   and corner radius, and the largest size whose corners fit a room; `fastenerCutter` cuts
   what it says, and `mountLimits`, which measures every room to the corners, reads its
-  sizes back from it, so the shape is decided in one place.
+  sizes back from it, so the shape is decided in one place. A counterbore is cut only over
+  a shank it clears, its flats outside the shank's corners: the hole over cos(π/12), and
+  0.01 mm more. Narrower, the 14 flats cross the 12 corners and the two cuts' walls weave
+  round the hole, and here and there a cell leaked by the hundred (#73: 2.03 mm over 2
+  with the corners on the sizes, 2.046 over 2 and 1.034 over 1 with the flats). Such a
+  head is cut as none, as one no wider than the hole always was.
 - **The socket's corner clearance is not uniform.** Known, documented, deliberately not
   fixed — see [socket-clearance.md](socket-clearance.md).
 - **The plate's outer corner radius has a ceiling, and it is the socket's.** Both the
diff --git a/src/core.js b/src/core.js
index 2602c9f..cb7506a 100644
--- a/src/core.js
+++ b/src/core.js
@@ -833,12 +833,28 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  *     default 6 mm head and 2.90 for the 3 mm hole. Now their corners go out the same
  *     way, and no further: the magnet's 0.1 is a press fit, and a screw head is not
  *     pressed in. It drops into its counterbore, which the field already sizes with room
- *     round it (6 mm for an M3's 5.5 mm head), and the shank is a clearance hole. */
+ *     round it (6 mm for an M3's 5.5 mm head), and the shank is a clearance hole.
+ *
+ * A counterbore is cut only over a shank it clears (head.cuts): its flats stand outside
+ * the shank's corners, the head the hole over cos(π/12), and 0.01 mm more (head.over).
+ * Narrower, the 14 flats cross the 12 corners, the two cuts' walls weave round the hole
+ * instead of one standing inside the other, and here and there a cell leaks by the
+ * hundred: 1.034 mm over 1, 2.063 over 2 (#73, where with the corners on the sizes it was
+ * 2.03 over 2). Measured on one-cell plates at eight pitches from 34.76 to 60 mm, shanks
+ * from 1 to 20 mm, every 0.001 mm from a hundredth under the corner circle to two past
+ * it and every 0.01 from the shank up to a tenth past: the last to leak by the circle
+ * was 0.003 mm past it (20.709 over 20), and from 0.004 nothing did but one head at one
+ * pitch, 3.59 over 3.4 at 60, open in the underside, the sliver class that comes and
+ * goes with a size. A head under the line is cut as none, as one no wider than the hole
+ * always was: within 3.5% of the hole it is no seat for a screw head, and all it would
+ * add is slivers between the shank's corners. */
 const MOUNT_BORE = {
   magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
             fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },
   head: { sides: 14, r: (d) => d/2 / Math.cos(Math.PI/14),
-          fits: (room) => 2 * room * Math.cos(Math.PI / 14) },
+          fits: (room) => 2 * room * Math.cos(Math.PI / 14),
+          over: (hole) => 2 * MOUNT_BORE.hole.r(hole) + 0.01,
+          cuts: (d, hole) => d >= MOUNT_BORE.head.over(hole) },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12) },
 };
@@ -872,7 +888,7 @@ function fastenerCutter(cfg, magZ0, magZ1, shankTop) {
       ? cylinder(0, 0, magnetR, magZ0, magZ1, magnet.sides)
       : cylinder(0, 0, magnetR, -0.5, cfg.magnetH, magnet.sides));
   if (cfg.screws) {
-    if (cfg.screwHeadD > cfg.screwHoleD)
+    if (head.cuts(cfg.screwHeadD, cfg.screwHoleD))
       add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
     add(cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides));
   }
@@ -895,7 +911,7 @@ function movePolys(polys, dx, dy) {
 function screwCutter(cx, cy, holeD, headD, z0, z1, headDepth, fromTop) {
   const { head, hole } = MOUNT_BORE;
   let polys = cylinder(cx, cy, hole.r(holeD), z0 - 0.5, z1 + 0.5, hole.sides);
-  if (headD > holeD) {
+  if (head.cuts(headD, holeD)) {
     const rec = fromTop
       ? cylinder(cx, cy, head.r(headD), z1 - headDepth, z1 + 0.5, head.sides)
       : cylinder(cx, cy, head.r(headD), z0 - 0.5, z0 + headDepth, head.sides);
@@ -2361,7 +2377,7 @@ function platePad(cfg) {
   if ((cfg.magnets || cfg.screws) && cfg.baseMode !== 'bosses') {
     pad = Math.max(pad, cfg.magnetBase || 2.8);
     if (cfg.magnets) pad = Math.max(pad, under(cfg.magnetH));
-    if (cfg.screws && cfg.screwHeadD > cfg.screwHoleD)
+    if (cfg.screws && MOUNT_BORE.head.cuts(cfg.screwHeadD, cfg.screwHoleD))
       pad = Math.max(pad, under(cfg.screwHeadDepth));
   }
   const keyedConn = ['bowtie', 'snap', 'puzzlekey'].includes(cfg.connector);
diff --git a/src/ui.js b/src/ui.js
index b951c94..71582f8 100644
--- a/src/ui.js
+++ b/src/ui.js
@@ -1764,7 +1764,15 @@ function readmeText() {
   lines.push(`Split: ${splitName()} | Pieces: ${layout.pieces.length} in ${plural(rows, 'row band')}`);
   lines.push(`Connectors: ${state.connector}` + (state.connector === 'dovetail' ? ` (clearance ${state.tab.clr} mm/side)` : ''));
   if (state.magnets) lines.push(`Magnets: ${state.magnetD} x ${state.magnetH} mm, from ${state.magnetSide}`);
-  if (state.screws) lines.push(`Screws: ${state.screwHoleD} mm holes, ${state.screwHeadD} mm counterbore`);
+  /* A head that does not clear the hole's corners is cut as none (MOUNT_BORE in core.js),
+     and one no wider than the hole always was; the README says so, and for a head that
+     was meant as a counterbore, the size that would be one. */
+  const { head } = MOUNT_BORE;
+  if (state.screws) lines.push(`Screws: ${state.screwHoleD} mm holes, ` +
+    (head.cuts(state.screwHeadD, state.screwHoleD) ? `${state.screwHeadD} mm counterbore`
+      : 'no counterbore' + (state.screwHeadD <= state.screwHoleD ? ''
+        : ` (a head clears a ${state.screwHoleD} mm hole from ` +
+          `${Math.ceil(head.over(state.screwHoleD) * 100 - 1e-9) / 100} mm)`)));
   /* The figure the dialog quotes, said the way it says it, with the price it was worked
      out at: the README is read away from the page. The ZIP is only made once every piece
      exists, so there is always a total to give. */
diff --git a/test/plate-audit.js b/test/plate-audit.js
index 78d9fb8..7e7fc07 100644
--- a/test/plate-audit.js
+++ b/test/plate-audit.js
@@ -2003,6 +2003,42 @@ console.log('\nthe other limits, built at their ends:');
     console.log(`  ${nm.padEnd(28)} ${leakText(r)}`);
     if (r.bad) bad++;
   }
+  /* A screw head only a hair wider than its shank (#73). The counterbore's 14 flats
+     crossed the shank's 12 corners, and here and there a cell leaked by the hundred: on
+     main, 2.03 mm over 2 left 196 edges a piece at 37.67 mm; with the flats on the sizes,
+     2.046 over 2 left 310 on these four cells and 1.034 over 1 at 42 mm 828. A head is cut
+     as a counterbore only once its flats clear the shank's corners, the hole over
+     cos(π/12) and 0.01 mm more (MOUNT_BORE in core.js), worked out here rather than read
+     from it. Under that it is cut as none: the plate has to be the very one a head no
+     wider than the hole builds, to the byte, a thousandth under the line too. The
+     narrowest head cut, a thousandth past it, has to build watertight and not be that
+     plate. */
+  {
+    const crypto = require('crypto');
+    const digest = (r) => {
+      const h = crypto.createHash('sha256');
+      for (const polys of r.pieces) h.update(Buffer.from(G.stlBinary(polys, 'p')));
+      return h.digest('hex');
+    };
+    const line = (d) => d / Math.cos(Math.PI / 12) + 0.01;
+    const none = new Map();
+    for (const [nm, p, d, h, cut] of [
+      ['2.03 mm head over 2, 37.67', 37.67, 2, 2.03, false],
+      ['2.046 mm head over 2, 37.67', 37.67, 2, 2.046, false],
+      ['1.034 mm head over 1, 42', 42, 1, 1.034, false],
+      ['just under the line, over 2', 37.67, 2, Math.floor(line(2) * 1000) / 1000, false],
+      ['narrowest head over 2', 37.67, 2, Math.ceil(line(2) * 1000) / 1000, true],
+    ]) {
+      const at = { pitch: p, drawerW: 2 * p, drawerD: 2 * p, connector: 'none', screws: true, screwHoleD: d };
+      if (!none.has(`${p} ${d}`)) none.set(`${p} ${d}`, digest(buildAll({ ...at, screwHeadD: d })));
+      const r = buildAll({ ...at, screwHeadD: h });
+      const same = digest(r) === none.get(`${p} ${d}`);
+      console.log(`  ${nm.padEnd(28)} ${h} mm: ${leakText(r)}, ` + (same
+        ? (cut ? 'NO COUNTERBORE CUT' : 'cut as no counterbore')
+        : (cut ? 'a counterbore' : 'A COUNTERBORE CUT')));
+      if (r.bad || same === cut) bad++;
+    }
+  }
   /* A pocket against a joint's cut in the floor (#64). A bowtie housed in the floor at
      42 mm, with magnets from beneath, built 12 bad edges at 7.9 mm and 19 at 10 with
      Download on: the pocket reached the key's recess, and with both ceilings 2 mm up the
diff --git a/test/ui/plates-robustness.spec.js b/test/ui/plates-robustness.spec.js
index e86b832..e32d6b5 100644
--- a/test/ui/plates-robustness.spec.js
+++ b/test/ui/plates-robustness.spec.js
@@ -473,6 +473,33 @@ test.describe('the clearance ceiling is the joint\'s and the pitch\'s', () => {
     });
 });
 
+/* ---- #73: a screw head only a hair wider than its shank ---------------------------- */
+/* Its counterbore's 14 flats crossed the shank's 12 corners, and the plate leaked by the
+   hundred with nothing said and Download on: on main, a 2.03 mm head over a 2 mm shank
+   left 196 edges in each of two pieces at 37.67 mm. A head that does not clear the shank's
+   corners is cut as none now, as one no wider than the hole always was (MOUNT_BORE in
+   core.js): within 3.5% of the hole it is no seat for a screw head. So the link builds
+   with Download on and nothing in Checks, and the README says there is no counterbore
+   and from what size there would be one. 2.1 mm clears a 2 mm hole and is cut. */
+test.describe('a screw head that does not clear its shank is cut as none', () => {
+  const AT = '#pi=37.67&w=150.68&d=75.34&mm=custom&ml=0&mr=0&mf=0&mb=0&bw=91.34&bd=400' +
+    '&sc=1&sh=2&cn=none';
+  for (const [sd, says] of [
+    ['2.03', 'Screws: 2 mm holes, no counterbore (a head clears a 2 mm hole from 2.09 mm)'],
+    ['2.1', 'Screws: 2 mm holes, 2.1 mm counterbore'],
+  ])
+    test(`a ${sd} mm head over a 2 mm shank builds, and the README says what was cut`,
+      async ({ page }) => {
+        const errors = await openAt(page, `${AT}&sd=${sd}`);
+        expect(await text(page, 'pieceTail')).toMatch(/ready/);
+        expect(await shown(page, 'errScrew')).toBe(false);
+        expect(await exportOff(page)).toBe(false);
+        const readme = (await page.evaluate(() => readmeText())).split('\n');
+        expect(readme).toContain(says);
+        expect(errors).toEqual([]);
+      });
+});
+
 test('a failed build says so in the table and the dialog, and Download goes off',
   async ({ page }) => {
     const pageErrors = [];

From b3787f6fe225b191db6b443191eae2f4f2e9f95a Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 13:36:52 +0000
Subject: [PATCH 09/58] Keep the test tile watertight with magnets and screws
 at their usual sizes

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 src/core.js         |  9 ++++++++-
 test/plate-audit.js | 14 ++++++++++++--
 2 files changed, 20 insertions(+), 3 deletions(-)

diff --git a/src/core.js b/src/core.js
index cb7506a..dcc4e8d 100644
--- a/src/core.js
+++ b/src/core.js
@@ -888,7 +888,14 @@ function fastenerCutter(cfg, magZ0, magZ1, shankTop) {
       ? cylinder(0, 0, magnetR, magZ0, magZ1, magnet.sides)
       : cylinder(0, 0, magnetR, -0.5, cfg.magnetH, magnet.sides));
   if (cfg.screws) {
-    if (head.cuts(cfg.screwHeadD, cfg.screwHoleD))
+    /* A counterbore the magnet pocket from beneath holds whole is that pocket already: both
+       14 sides, corners on the same rays, no deeper. Since the bores stand their flats on
+       the sizes, the default 6 mm head's walls stand 0.022 mm inside the 6 mm magnet's,
+       and unioned, the test tile at 42 mm with magnets and screws left 6 edges open in
+       its underside. Left out, the pocket is the same solid, and closed. */
+    const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
+      head.r(cfg.screwHeadD) <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
+    if (head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet)
       add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
     add(cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides));
   }
diff --git a/test/plate-audit.js b/test/plate-audit.js
index 7e7fc07..310e411 100644
--- a/test/plate-audit.js
+++ b/test/plate-audit.js
@@ -1037,6 +1037,14 @@ console.log('\nloose parts and samples, watertight and oriented:');
     drawerW: G.DEFAULTS.pitch, drawerD: G.DEFAULTS.pitch,
     marginMode: 'custom', mLeft: 0, mRight: 0, mFront: 0, mBack: 0 });
   report('test tile', G.buildTestTile(tileCfg).polys);
+  /* The tile with magnets and screws, the page's own sizes. Once a screw's bores stood
+     their flats on the sizes, the 6 mm counterbore's walls stood 0.022 mm inside the 6 mm
+     magnet pocket's from beneath, and the tile left 6 edges open in its underside; a
+     counterbore the magnet pocket holds whole is not cut now (fastenerCutter). A magnet
+     from above is cut from the other face, and that tile is built too. */
+  for (const side of ['bottom', 'top'])
+    report(`tile, magnets ${side === 'top' ? 'above' : 'below'}, screws`,
+      G.buildTestTile({ ...tileCfg, magnets: true, magnetSide: side, screws: true }).polys);
 
   for (const conn of CONNECTORS)
     for (const keyInsert of ['bottom', 'top']) {
@@ -2518,9 +2526,11 @@ console.log('\nplates without half cells build the same bytes:');
     // fanCentre moved four of its nine cells' bottom caps off a spoke a few thousandths from
     // a cutter's corner: the same bottom face fanned from another point, its area and the
     // volume unchanged. Then the screw's bores went out until their flats stood on the
-    // sizes asked, the counterbore and the shank wider by design
+    // sizes asked, the counterbore and the shank wider by design; then the counterbore the
+    // magnet pocket from beneath holds whole was left out of the cut, the same pocket with
+    // its faces no longer split by the head's walls (54138.661 mm³ to 54138.679)
     ['126 x 126, magnets and screws', { drawerW: 126, drawerD: 126, marginMode: 'custom',
-      mLeft: 0, mRight: 0, mFront: 0, mBack: 0, magnets: true, screws: true }, '7eaec017027d5a46'],
+      mLeft: 0, mRight: 0, mFront: 0, mBack: 0, magnets: true, screws: true }, 'e964beefa8b378bf'],
     ['140 x 140, corner pockets', { drawerW: 140, drawerD: 140, marginMode: 'auto',
       magnets: true, baseMode: 'bosses' }, '7088f24def428095'],
     ['168 x 180, skeleton', { drawerW: 168, drawerD: 180, marginMode: 'auto',

From 3a54fd5e366d989e543e0ed10472e7c060b9e1af Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 13:36:53 +0000
Subject: [PATCH 10/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html | 33 ++++++++++++++++++++++++++++-----
 index.html      | 43 +++++++++++++++++++++++++++++++++++++------
 sw.js           |  2 +-
 3 files changed, 66 insertions(+), 12 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index 6119e71..331f553 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -2439,12 +2439,28 @@ <h2 id="drawersTitle">Your drawers</h2>
  *     default 6 mm head and 2.90 for the 3 mm hole. Now their corners go out the same
  *     way, and no further: the magnet's 0.1 is a press fit, and a screw head is not
  *     pressed in. It drops into its counterbore, which the field already sizes with room
- *     round it (6 mm for an M3's 5.5 mm head), and the shank is a clearance hole. */
+ *     round it (6 mm for an M3's 5.5 mm head), and the shank is a clearance hole.
+ *
+ * A counterbore is cut only over a shank it clears (head.cuts): its flats stand outside
+ * the shank's corners, the head the hole over cos(π/12), and 0.01 mm more (head.over).
+ * Narrower, the 14 flats cross the 12 corners, the two cuts' walls weave round the hole
+ * instead of one standing inside the other, and here and there a cell leaks by the
+ * hundred: 1.034 mm over 1, 2.063 over 2 (#73, where with the corners on the sizes it was
+ * 2.03 over 2). Measured on one-cell plates at eight pitches from 34.76 to 60 mm, shanks
+ * from 1 to 20 mm, every 0.001 mm from a hundredth under the corner circle to two past
+ * it and every 0.01 from the shank up to a tenth past: the last to leak by the circle
+ * was 0.003 mm past it (20.709 over 20), and from 0.004 nothing did but one head at one
+ * pitch, 3.59 over 3.4 at 60, open in the underside, the sliver class that comes and
+ * goes with a size. A head under the line is cut as none, as one no wider than the hole
+ * always was: within 3.5% of the hole it is no seat for a screw head, and all it would
+ * add is slivers between the shank's corners. */
 const MOUNT_BORE = {
   magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
             fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },
   head: { sides: 14, r: (d) => d/2 / Math.cos(Math.PI/14),
-          fits: (room) => 2 * room * Math.cos(Math.PI / 14) },
+          fits: (room) => 2 * room * Math.cos(Math.PI / 14),
+          over: (hole) => 2 * MOUNT_BORE.hole.r(hole) + 0.01,
+          cuts: (d, hole) => d >= MOUNT_BORE.head.over(hole) },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12) },
 };
@@ -2478,7 +2494,14 @@ <h2 id="drawersTitle">Your drawers</h2>
       ? cylinder(0, 0, magnetR, magZ0, magZ1, magnet.sides)
       : cylinder(0, 0, magnetR, -0.5, cfg.magnetH, magnet.sides));
   if (cfg.screws) {
-    if (cfg.screwHeadD > cfg.screwHoleD)
+    /* A counterbore the magnet pocket from beneath holds whole is that pocket already: both
+       14 sides, corners on the same rays, no deeper. Since the bores stand their flats on
+       the sizes, the default 6 mm head's walls stand 0.022 mm inside the 6 mm magnet's,
+       and unioned, the test tile at 42 mm with magnets and screws left 6 edges open in
+       its underside. Left out, the pocket is the same solid, and closed. */
+    const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
+      head.r(cfg.screwHeadD) <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
+    if (head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet)
       add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
     add(cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides));
   }
@@ -2501,7 +2524,7 @@ <h2 id="drawersTitle">Your drawers</h2>
 function screwCutter(cx, cy, holeD, headD, z0, z1, headDepth, fromTop) {
   const { head, hole } = MOUNT_BORE;
   let polys = cylinder(cx, cy, hole.r(holeD), z0 - 0.5, z1 + 0.5, hole.sides);
-  if (headD > holeD) {
+  if (head.cuts(headD, holeD)) {
     const rec = fromTop
       ? cylinder(cx, cy, head.r(headD), z1 - headDepth, z1 + 0.5, head.sides)
       : cylinder(cx, cy, head.r(headD), z0 - 0.5, z0 + headDepth, head.sides);
@@ -3967,7 +3990,7 @@ <h2 id="drawersTitle">Your drawers</h2>
   if ((cfg.magnets || cfg.screws) && cfg.baseMode !== 'bosses') {
     pad = Math.max(pad, cfg.magnetBase || 2.8);
     if (cfg.magnets) pad = Math.max(pad, under(cfg.magnetH));
-    if (cfg.screws && cfg.screwHeadD > cfg.screwHoleD)
+    if (cfg.screws && MOUNT_BORE.head.cuts(cfg.screwHeadD, cfg.screwHoleD))
       pad = Math.max(pad, under(cfg.screwHeadDepth));
   }
   const keyedConn = ['bowtie', 'snap', 'puzzlekey'].includes(cfg.connector);
diff --git a/index.html b/index.html
index 04d20a0..0b3126d 100644
--- a/index.html
+++ b/index.html
@@ -2226,12 +2226,28 @@ <h2 id="drawersTitle">Your drawers</h2>
  *     default 6 mm head and 2.90 for the 3 mm hole. Now their corners go out the same
  *     way, and no further: the magnet's 0.1 is a press fit, and a screw head is not
  *     pressed in. It drops into its counterbore, which the field already sizes with room
- *     round it (6 mm for an M3's 5.5 mm head), and the shank is a clearance hole. */
+ *     round it (6 mm for an M3's 5.5 mm head), and the shank is a clearance hole.
+ *
+ * A counterbore is cut only over a shank it clears (head.cuts): its flats stand outside
+ * the shank's corners, the head the hole over cos(π/12), and 0.01 mm more (head.over).
+ * Narrower, the 14 flats cross the 12 corners, the two cuts' walls weave round the hole
+ * instead of one standing inside the other, and here and there a cell leaks by the
+ * hundred: 1.034 mm over 1, 2.063 over 2 (#73, where with the corners on the sizes it was
+ * 2.03 over 2). Measured on one-cell plates at eight pitches from 34.76 to 60 mm, shanks
+ * from 1 to 20 mm, every 0.001 mm from a hundredth under the corner circle to two past
+ * it and every 0.01 from the shank up to a tenth past: the last to leak by the circle
+ * was 0.003 mm past it (20.709 over 20), and from 0.004 nothing did but one head at one
+ * pitch, 3.59 over 3.4 at 60, open in the underside, the sliver class that comes and
+ * goes with a size. A head under the line is cut as none, as one no wider than the hole
+ * always was: within 3.5% of the hole it is no seat for a screw head, and all it would
+ * add is slivers between the shank's corners. */
 const MOUNT_BORE = {
   magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
             fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },
   head: { sides: 14, r: (d) => d/2 / Math.cos(Math.PI/14),
-          fits: (room) => 2 * room * Math.cos(Math.PI / 14) },
+          fits: (room) => 2 * room * Math.cos(Math.PI / 14),
+          over: (hole) => 2 * MOUNT_BORE.hole.r(hole) + 0.01,
+          cuts: (d, hole) => d >= MOUNT_BORE.head.over(hole) },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12) },
 };
@@ -2265,7 +2281,14 @@ <h2 id="drawersTitle">Your drawers</h2>
       ? cylinder(0, 0, magnetR, magZ0, magZ1, magnet.sides)
       : cylinder(0, 0, magnetR, -0.5, cfg.magnetH, magnet.sides));
   if (cfg.screws) {
-    if (cfg.screwHeadD > cfg.screwHoleD)
+    /* A counterbore the magnet pocket from beneath holds whole is that pocket already: both
+       14 sides, corners on the same rays, no deeper. Since the bores stand their flats on
+       the sizes, the default 6 mm head's walls stand 0.022 mm inside the 6 mm magnet's,
+       and unioned, the test tile at 42 mm with magnets and screws left 6 edges open in
+       its underside. Left out, the pocket is the same solid, and closed. */
+    const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
+      head.r(cfg.screwHeadD) <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
+    if (head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet)
       add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
     add(cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides));
   }
@@ -2288,7 +2311,7 @@ <h2 id="drawersTitle">Your drawers</h2>
 function screwCutter(cx, cy, holeD, headD, z0, z1, headDepth, fromTop) {
   const { head, hole } = MOUNT_BORE;
   let polys = cylinder(cx, cy, hole.r(holeD), z0 - 0.5, z1 + 0.5, hole.sides);
-  if (headD > holeD) {
+  if (head.cuts(headD, holeD)) {
     const rec = fromTop
       ? cylinder(cx, cy, head.r(headD), z1 - headDepth, z1 + 0.5, head.sides)
       : cylinder(cx, cy, head.r(headD), z0 - 0.5, z0 + headDepth, head.sides);
@@ -3754,7 +3777,7 @@ <h2 id="drawersTitle">Your drawers</h2>
   if ((cfg.magnets || cfg.screws) && cfg.baseMode !== 'bosses') {
     pad = Math.max(pad, cfg.magnetBase || 2.8);
     if (cfg.magnets) pad = Math.max(pad, under(cfg.magnetH));
-    if (cfg.screws && cfg.screwHeadD > cfg.screwHoleD)
+    if (cfg.screws && MOUNT_BORE.head.cuts(cfg.screwHeadD, cfg.screwHoleD))
       pad = Math.max(pad, under(cfg.screwHeadDepth));
   }
   const keyedConn = ['bowtie', 'snap', 'puzzlekey'].includes(cfg.connector);
@@ -9140,7 +9163,15 @@ <h2 id="drawersTitle">Your drawers</h2>
   lines.push(`Split: ${splitName()} | Pieces: ${layout.pieces.length} in ${plural(rows, 'row band')}`);
   lines.push(`Connectors: ${state.connector}` + (state.connector === 'dovetail' ? ` (clearance ${state.tab.clr} mm/side)` : ''));
   if (state.magnets) lines.push(`Magnets: ${state.magnetD} x ${state.magnetH} mm, from ${state.magnetSide}`);
-  if (state.screws) lines.push(`Screws: ${state.screwHoleD} mm holes, ${state.screwHeadD} mm counterbore`);
+  /* A head that does not clear the hole's corners is cut as none (MOUNT_BORE in core.js),
+     and one no wider than the hole always was; the README says so, and for a head that
+     was meant as a counterbore, the size that would be one. */
+  const { head } = MOUNT_BORE;
+  if (state.screws) lines.push(`Screws: ${state.screwHoleD} mm holes, ` +
+    (head.cuts(state.screwHeadD, state.screwHoleD) ? `${state.screwHeadD} mm counterbore`
+      : 'no counterbore' + (state.screwHeadD <= state.screwHoleD ? ''
+        : ` (a head clears a ${state.screwHoleD} mm hole from ` +
+          `${Math.ceil(head.over(state.screwHoleD) * 100 - 1e-9) / 100} mm)`)));
   /* The figure the dialog quotes, said the way it says it, with the price it was worked
      out at: the README is read away from the page. The ZIP is only made once every piece
      exists, so there is always a total to give. */
diff --git a/sw.js b/sw.js
index eb73b81..33a028c 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "4f0cfa58126c";
+const VERSION = "2d0ca3035d3c";
 const FILES = [
   "./",
   "bins/",

From 6bc8d5b36c44455fd3e53dc760067c719e4ef549 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 15:01:22 +0000
Subject: [PATCH 11/58] Keep plates watertight when a counterbore's corner
 lines up with a flat of its screw's shank

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md      |  9 +++++++-
 src/core.js         | 53 ++++++++++++++++++++++++++++++++++++++++-----
 test/plate-audit.js | 25 +++++++++++++++++++++
 3 files changed, 81 insertions(+), 6 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index fb546d5..d19aa88 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -707,7 +707,14 @@ currently installed):
   0.01 mm more. Narrower, the 14 flats cross the 12 corners and the two cuts' walls weave
   round the hole, and here and there a cell leaked by the hundred (#73: 2.03 mm over 2
   with the corners on the sizes, 2.046 over 2 and 1.034 over 1 with the flats). Such a
-  head is cut as none, as one no wider than the hole always was.
+  head is cut as none, as one no wider than the hole always was. And the shank is turned
+  π/84 about its axis where one of the counterbore's corners would otherwise stand within
+  0.005 mm of a flat's plane carried on past the shank (`MOUNT_BORE.hole.turn`): the BSP
+  splits a magnet pocket's floor or roof along that whole plane, the weld pulled the
+  corner onto the split, and the plate came out open by the dozen round every site (#74:
+  136 edges a piece for 1.0353 mm under 1.0873 with a magnet from above at 42 mm, on
+  main). Turned, no corner comes within 0.0039 mm of a flat at any size, and a shank no
+  corner came near is cut as before.
 - **The socket's corner clearance is not uniform.** Known, documented, deliberately not
   fixed — see [socket-clearance.md](socket-clearance.md).
 - **The plate's outer corner radius has a ceiling, and it is the socket's.** Both the
diff --git a/src/core.js b/src/core.js
index dcc4e8d..081c91c 100644
--- a/src/core.js
+++ b/src/core.js
@@ -817,7 +817,8 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * stand for a size typed (`r`), and back the other way, the largest size whose corners
  * stay inside a room (`fits`). fastenerCutter and screwCutter cut these and mountLimits
  * holds the sizes to them, so a bore's shape is decided here and nowhere else. Each is
- * cylinder's polygon about the site, a corner at every 2πk/sides from +x.
+ * cylinder's polygon about the site, a corner at every 2πk/sides from +x, but for a shank
+ * that `turn` moves (below).
  *
  * Every bore stands its flats on the size asked, so its corners are 1/cos(π/sides) of the
  * radius out and it is no narrower anywhere than the size typed.
@@ -847,7 +848,31 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * pitch, 3.59 over 3.4 at 60, open in the underside, the sliver class that comes and
  * goes with a size. A head under the line is cut as none, as one no wider than the hole
  * always was: within 3.5% of the hole it is no seat for a screw head, and all it would
- * add is slivers between the shank's corners. */
+ * add is slivers between the shank's corners.
+ *
+ * Under a counterbore the shank is turned a little about its axis (`turn`, #74) where one
+ * of the counterbore's corners would stand on one of its flats carried on past the shank.
+ * The BSP splits what it meets along a flat's whole plane, not just the flat: the floor
+ * of a magnet pocket from above, which is a ring round the counterbore, or the roof of one
+ * from beneath round a counterbore deeper than it. A split a micron or two from the
+ * corner was welded onto it (healCsgSeams), which bent the counterbore's wall off its
+ * plane, and the plate came out open by the dozen round every site: 136 edges a piece at
+ * 42 mm for main's 1.0353 mm shank under a 1.0873 head with a 6 x 2 magnet from above, 36
+ * a cell for 1.06 over 1 here, 62 for 3.305 over 3, 55 for 5.4959 over 3 under an 8 x 3
+ * magnet. Such sizes come every few hundredths at any ratio of head to shank. A corner
+ * meets a flat's plane at an odd multiple of 15/7° off the flat's normal; turned π/84,
+ * 15/7°, it meets them at the even ones, so a size that put a corner on a flat puts it
+ * midway between two. The turn is taken where a corner comes nearer than 0.005 mm
+ * unturned and the turn leaves it further off, so no corner comes within 0.0039 mm of a
+ * flat at any size, and a shank no corner came near is cut as it was. Half a facet, π/12,
+ * clears the corners as well, but it squares two flats to the cell's edges, and at
+ * 37.67 mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell
+ * plates with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15
+ * times them, every 0.001 mm round these sizes: 546 open before, 4 now. On 1,800 random
+ * designs the turn moves, every kind of mount: 90 open before, 26 now. It closed 83 and
+ * opened 19, 14 of them at 42 mm with a magnet from beneath under a deeper counterbore,
+ * where one size in nine leaks unturned too, by the same slivers at the magnet pocket's
+ * corners in the underside. */
 const MOUNT_BORE = {
   magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
             fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },
@@ -856,7 +881,19 @@ const MOUNT_BORE = {
           over: (hole) => 2 * MOUNT_BORE.hole.r(hole) + 0.01,
           cuts: (d, hole) => d >= MOUNT_BORE.head.over(hole) },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
-          fits: (room) => 2 * room * Math.cos(Math.PI / 12) },
+          fits: (room) => 2 * room * Math.cos(Math.PI / 12),
+          // how far to turn the shank under a counterbore headD across (see above)
+          turn: (d, headD) => {
+            const { head, hole } = MOUNT_BORE, R = head.r(headD);
+            const clear = (t) => {   // the nearest a corner of the counterbore comes to a flat's plane
+              let g = Infinity;
+              for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
+                g = Math.min(g, Math.abs(R * Math.cos(2*Math.PI*k/head.sides - (2*m + 1)*Math.PI/hole.sides - t) - d/2));
+              return g;
+            };
+            const now = clear(0);
+            return now < 0.005 && clear(Math.PI / 84) > now ? Math.PI / 84 : 0;
+          } },
 };
 
 /* Everything removed at one mounting site, as ONE solid.
@@ -895,9 +932,15 @@ function fastenerCutter(cfg, magZ0, magZ1, shankTop) {
        its underside. Left out, the pocket is the same solid, and closed. */
     const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
       head.r(cfg.screwHeadD) <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
-    if (head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet)
+    const counterbore = head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet;
+    if (counterbore)
       add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
-    add(cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides));
+    // the shank, turned off the counterbore's corners where one would stand on a flat (#74)
+    const shank = cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides);
+    const t = counterbore ? hole.turn(cfg.screwHoleD, cfg.screwHeadD) : 0;
+    const c = Math.cos(t), s = Math.sin(t), turn = (v) => [v[0]*c - v[1]*s, v[0]*s + v[1]*c, v[2]];
+    add(t ? shank.map((p) => ({ verts: p.verts.map(turn), plane: { n: turn(p.plane.n), w: p.plane.w } }))
+          : shank);
   }
   return cut;
 }
diff --git a/test/plate-audit.js b/test/plate-audit.js
index 310e411..bec4933 100644
--- a/test/plate-audit.js
+++ b/test/plate-audit.js
@@ -2047,6 +2047,31 @@ console.log('\nthe other limits, built at their ends:');
       if (r.bad || same === cut) bad++;
     }
   }
+  /* A counterbore with a corner on one of its shank's flats, carried on past the shank
+     (#74). The BSP split the magnet pocket's floor along that flat's plane a micron or
+     two from the corner, the weld moved the corner onto the split, and its wall left its
+     plane: main's 1.0353 mm shank under a 1.0873 head, with a 6 x 2 magnet from above,
+     left 136 edges in each of two pieces at 42 mm, and the same bores here, with their
+     flats on the sizes, are a 1 mm shank under 1.06 (36 a cell). 4.25 over 4 left 26 and
+     3.305 over 3 62; 5.4959 over 3 under an 8 x 3 magnet, a head nearly twice the shank,
+     55; and from beneath, the magnet's roof round a counterbore deeper than it, 1.06 over
+     1 left 12. The shank is turned off the corners now (MOUNT_BORE.hole.turn). Each has
+     to build closed, with no folds. */
+  for (const [nm, o] of [
+    ['main\'s 1.0353 under 1.0873, 42', { pitch: 42, drawerW: 168, drawerD: 84, bedW: 100, bedD: 400,
+      screwHoleD: 1.0353 * Math.cos(Math.PI / 12), screwHeadD: 1.0873 * Math.cos(Math.PI / 14) }],
+    ['1.06 mm head over 1, 42', { screwHoleD: 1, screwHeadD: 1.06 }],
+    ['4.25 mm head over 4, 42', { screwHoleD: 4, screwHeadD: 4.25 }],
+    ['3.305 mm head over 3, 42', { screwHoleD: 3, screwHeadD: 3.305 }],
+    ['5.4959 over 3, 8 x 3 magnet', { screwHoleD: 3, screwHeadD: 5.4959, magnetD: 8, magnetH: 3 }],
+    ['1.06 over 1, from beneath', { screwHoleD: 1, screwHeadD: 1.06, magnetSide: 'bottom', screwHeadDepth: 3 }],
+  ]) {
+    const r = buildAll({ pitch: 42, drawerW: 42, drawerD: 42, connector: 'none', magnets: true,
+                         magnetSide: 'top', screws: true, ...o });
+    const folds = r.pieces.reduce((s, pp) => s + checkOrientation(pp).folds, 0);
+    console.log(`  ${nm.padEnd(30)} ${leakText(r)}${folds ? `, ${folds} FOLDS` : ''}`);
+    if (r.bad || folds) bad++;
+  }
   /* A pocket against a joint's cut in the floor (#64). A bowtie housed in the floor at
      42 mm, with magnets from beneath, built 12 bad edges at 7.9 mm and 19 at 10 with
      Download on: the pocket reached the key's recess, and with both ceilings 2 mm up the

From b9508b9b6a0ad28fc0a405cfb4a287f25d89945d Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 15:01:30 +0000
Subject: [PATCH 12/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html | 53 ++++++++++++++++++++++++++++++++++++++++++++-----
 index.html      | 53 ++++++++++++++++++++++++++++++++++++++++++++-----
 sw.js           |  2 +-
 3 files changed, 97 insertions(+), 11 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index 331f553..b3453ee 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -2423,7 +2423,8 @@ <h2 id="drawersTitle">Your drawers</h2>
  * stand for a size typed (`r`), and back the other way, the largest size whose corners
  * stay inside a room (`fits`). fastenerCutter and screwCutter cut these and mountLimits
  * holds the sizes to them, so a bore's shape is decided here and nowhere else. Each is
- * cylinder's polygon about the site, a corner at every 2πk/sides from +x.
+ * cylinder's polygon about the site, a corner at every 2πk/sides from +x, but for a shank
+ * that `turn` moves (below).
  *
  * Every bore stands its flats on the size asked, so its corners are 1/cos(π/sides) of the
  * radius out and it is no narrower anywhere than the size typed.
@@ -2453,7 +2454,31 @@ <h2 id="drawersTitle">Your drawers</h2>
  * pitch, 3.59 over 3.4 at 60, open in the underside, the sliver class that comes and
  * goes with a size. A head under the line is cut as none, as one no wider than the hole
  * always was: within 3.5% of the hole it is no seat for a screw head, and all it would
- * add is slivers between the shank's corners. */
+ * add is slivers between the shank's corners.
+ *
+ * Under a counterbore the shank is turned a little about its axis (`turn`, #74) where one
+ * of the counterbore's corners would stand on one of its flats carried on past the shank.
+ * The BSP splits what it meets along a flat's whole plane, not just the flat: the floor
+ * of a magnet pocket from above, which is a ring round the counterbore, or the roof of one
+ * from beneath round a counterbore deeper than it. A split a micron or two from the
+ * corner was welded onto it (healCsgSeams), which bent the counterbore's wall off its
+ * plane, and the plate came out open by the dozen round every site: 136 edges a piece at
+ * 42 mm for main's 1.0353 mm shank under a 1.0873 head with a 6 x 2 magnet from above, 36
+ * a cell for 1.06 over 1 here, 62 for 3.305 over 3, 55 for 5.4959 over 3 under an 8 x 3
+ * magnet. Such sizes come every few hundredths at any ratio of head to shank. A corner
+ * meets a flat's plane at an odd multiple of 15/7° off the flat's normal; turned π/84,
+ * 15/7°, it meets them at the even ones, so a size that put a corner on a flat puts it
+ * midway between two. The turn is taken where a corner comes nearer than 0.005 mm
+ * unturned and the turn leaves it further off, so no corner comes within 0.0039 mm of a
+ * flat at any size, and a shank no corner came near is cut as it was. Half a facet, π/12,
+ * clears the corners as well, but it squares two flats to the cell's edges, and at
+ * 37.67 mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell
+ * plates with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15
+ * times them, every 0.001 mm round these sizes: 546 open before, 4 now. On 1,800 random
+ * designs the turn moves, every kind of mount: 90 open before, 26 now. It closed 83 and
+ * opened 19, 14 of them at 42 mm with a magnet from beneath under a deeper counterbore,
+ * where one size in nine leaks unturned too, by the same slivers at the magnet pocket's
+ * corners in the underside. */
 const MOUNT_BORE = {
   magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
             fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },
@@ -2462,7 +2487,19 @@ <h2 id="drawersTitle">Your drawers</h2>
           over: (hole) => 2 * MOUNT_BORE.hole.r(hole) + 0.01,
           cuts: (d, hole) => d >= MOUNT_BORE.head.over(hole) },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
-          fits: (room) => 2 * room * Math.cos(Math.PI / 12) },
+          fits: (room) => 2 * room * Math.cos(Math.PI / 12),
+          // how far to turn the shank under a counterbore headD across (see above)
+          turn: (d, headD) => {
+            const { head, hole } = MOUNT_BORE, R = head.r(headD);
+            const clear = (t) => {   // the nearest a corner of the counterbore comes to a flat's plane
+              let g = Infinity;
+              for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
+                g = Math.min(g, Math.abs(R * Math.cos(2*Math.PI*k/head.sides - (2*m + 1)*Math.PI/hole.sides - t) - d/2));
+              return g;
+            };
+            const now = clear(0);
+            return now < 0.005 && clear(Math.PI / 84) > now ? Math.PI / 84 : 0;
+          } },
 };
 
 /* Everything removed at one mounting site, as ONE solid.
@@ -2501,9 +2538,15 @@ <h2 id="drawersTitle">Your drawers</h2>
        its underside. Left out, the pocket is the same solid, and closed. */
     const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
       head.r(cfg.screwHeadD) <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
-    if (head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet)
+    const counterbore = head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet;
+    if (counterbore)
       add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
-    add(cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides));
+    // the shank, turned off the counterbore's corners where one would stand on a flat (#74)
+    const shank = cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides);
+    const t = counterbore ? hole.turn(cfg.screwHoleD, cfg.screwHeadD) : 0;
+    const c = Math.cos(t), s = Math.sin(t), turn = (v) => [v[0]*c - v[1]*s, v[0]*s + v[1]*c, v[2]];
+    add(t ? shank.map((p) => ({ verts: p.verts.map(turn), plane: { n: turn(p.plane.n), w: p.plane.w } }))
+          : shank);
   }
   return cut;
 }
diff --git a/index.html b/index.html
index 0b3126d..9e5e0e5 100644
--- a/index.html
+++ b/index.html
@@ -2210,7 +2210,8 @@ <h2 id="drawersTitle">Your drawers</h2>
  * stand for a size typed (`r`), and back the other way, the largest size whose corners
  * stay inside a room (`fits`). fastenerCutter and screwCutter cut these and mountLimits
  * holds the sizes to them, so a bore's shape is decided here and nowhere else. Each is
- * cylinder's polygon about the site, a corner at every 2πk/sides from +x.
+ * cylinder's polygon about the site, a corner at every 2πk/sides from +x, but for a shank
+ * that `turn` moves (below).
  *
  * Every bore stands its flats on the size asked, so its corners are 1/cos(π/sides) of the
  * radius out and it is no narrower anywhere than the size typed.
@@ -2240,7 +2241,31 @@ <h2 id="drawersTitle">Your drawers</h2>
  * pitch, 3.59 over 3.4 at 60, open in the underside, the sliver class that comes and
  * goes with a size. A head under the line is cut as none, as one no wider than the hole
  * always was: within 3.5% of the hole it is no seat for a screw head, and all it would
- * add is slivers between the shank's corners. */
+ * add is slivers between the shank's corners.
+ *
+ * Under a counterbore the shank is turned a little about its axis (`turn`, #74) where one
+ * of the counterbore's corners would stand on one of its flats carried on past the shank.
+ * The BSP splits what it meets along a flat's whole plane, not just the flat: the floor
+ * of a magnet pocket from above, which is a ring round the counterbore, or the roof of one
+ * from beneath round a counterbore deeper than it. A split a micron or two from the
+ * corner was welded onto it (healCsgSeams), which bent the counterbore's wall off its
+ * plane, and the plate came out open by the dozen round every site: 136 edges a piece at
+ * 42 mm for main's 1.0353 mm shank under a 1.0873 head with a 6 x 2 magnet from above, 36
+ * a cell for 1.06 over 1 here, 62 for 3.305 over 3, 55 for 5.4959 over 3 under an 8 x 3
+ * magnet. Such sizes come every few hundredths at any ratio of head to shank. A corner
+ * meets a flat's plane at an odd multiple of 15/7° off the flat's normal; turned π/84,
+ * 15/7°, it meets them at the even ones, so a size that put a corner on a flat puts it
+ * midway between two. The turn is taken where a corner comes nearer than 0.005 mm
+ * unturned and the turn leaves it further off, so no corner comes within 0.0039 mm of a
+ * flat at any size, and a shank no corner came near is cut as it was. Half a facet, π/12,
+ * clears the corners as well, but it squares two flats to the cell's edges, and at
+ * 37.67 mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell
+ * plates with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15
+ * times them, every 0.001 mm round these sizes: 546 open before, 4 now. On 1,800 random
+ * designs the turn moves, every kind of mount: 90 open before, 26 now. It closed 83 and
+ * opened 19, 14 of them at 42 mm with a magnet from beneath under a deeper counterbore,
+ * where one size in nine leaks unturned too, by the same slivers at the magnet pocket's
+ * corners in the underside. */
 const MOUNT_BORE = {
   magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
             fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },
@@ -2249,7 +2274,19 @@ <h2 id="drawersTitle">Your drawers</h2>
           over: (hole) => 2 * MOUNT_BORE.hole.r(hole) + 0.01,
           cuts: (d, hole) => d >= MOUNT_BORE.head.over(hole) },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
-          fits: (room) => 2 * room * Math.cos(Math.PI / 12) },
+          fits: (room) => 2 * room * Math.cos(Math.PI / 12),
+          // how far to turn the shank under a counterbore headD across (see above)
+          turn: (d, headD) => {
+            const { head, hole } = MOUNT_BORE, R = head.r(headD);
+            const clear = (t) => {   // the nearest a corner of the counterbore comes to a flat's plane
+              let g = Infinity;
+              for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
+                g = Math.min(g, Math.abs(R * Math.cos(2*Math.PI*k/head.sides - (2*m + 1)*Math.PI/hole.sides - t) - d/2));
+              return g;
+            };
+            const now = clear(0);
+            return now < 0.005 && clear(Math.PI / 84) > now ? Math.PI / 84 : 0;
+          } },
 };
 
 /* Everything removed at one mounting site, as ONE solid.
@@ -2288,9 +2325,15 @@ <h2 id="drawersTitle">Your drawers</h2>
        its underside. Left out, the pocket is the same solid, and closed. */
     const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
       head.r(cfg.screwHeadD) <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
-    if (head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet)
+    const counterbore = head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet;
+    if (counterbore)
       add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
-    add(cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides));
+    // the shank, turned off the counterbore's corners where one would stand on a flat (#74)
+    const shank = cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides);
+    const t = counterbore ? hole.turn(cfg.screwHoleD, cfg.screwHeadD) : 0;
+    const c = Math.cos(t), s = Math.sin(t), turn = (v) => [v[0]*c - v[1]*s, v[0]*s + v[1]*c, v[2]];
+    add(t ? shank.map((p) => ({ verts: p.verts.map(turn), plane: { n: turn(p.plane.n), w: p.plane.w } }))
+          : shank);
   }
   return cut;
 }
diff --git a/sw.js b/sw.js
index 33a028c..a182340 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "2d0ca3035d3c";
+const VERSION = "c6f9b690c5d9";
 const FILES = [
   "./",
   "bins/",

From ef97415a36943fdf0427173eac6c1930e7200fd5 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 15:51:49 +0000
Subject: [PATCH 13/58] Keep plates watertight where turning the shank would
 line a magnet pocket's corner up with one of its flats

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md      |  7 ++++--
 src/core.js         | 52 +++++++++++++++++++++++++++++----------------
 test/plate-audit.js |  8 +++++--
 3 files changed, 45 insertions(+), 22 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index d19aa88..8100f4a 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -713,8 +713,11 @@ currently installed):
   splits a magnet pocket's floor or roof along that whole plane, the weld pulled the
   corner onto the split, and the plate came out open by the dozen round every site (#74:
   136 edges a piece for 1.0353 mm under 1.0873 with a magnet from above at 42 mm, on
-  main). Turned, no corner comes within 0.0039 mm of a flat at any size, and a shank no
-  corner came near is cut as before.
+  main). The magnet pocket's corners stand on the same rays, so where π/84 would bring one
+  of those within 0.005 mm of a flat instead, the shank takes the step of the 24 across
+  those 30/7° that keeps both furthest off. Turned, no corner of either comes within
+  0.0039 mm of a flat, and a shank no corner of the counterbore's came near is cut as
+  before.
 - **The socket's corner clearance is not uniform.** Known, documented, deliberately not
   fixed — see [socket-clearance.md](socket-clearance.md).
 - **The plate's outer corner radius has a ceiling, and it is the socket's.** Both the
diff --git a/src/core.js b/src/core.js
index 081c91c..2cc20ea 100644
--- a/src/core.js
+++ b/src/core.js
@@ -863,16 +863,25 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * meets a flat's plane at an odd multiple of 15/7° off the flat's normal; turned π/84,
  * 15/7°, it meets them at the even ones, so a size that put a corner on a flat puts it
  * midway between two. The turn is taken where a corner comes nearer than 0.005 mm
- * unturned and the turn leaves it further off, so no corner comes within 0.0039 mm of a
- * flat at any size, and a shank no corner came near is cut as it was. Half a facet, π/12,
- * clears the corners as well, but it squares two flats to the cell's edges, and at
- * 37.67 mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell
- * plates with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15
- * times them, every 0.001 mm round these sizes: 546 open before, 4 now. On 1,800 random
- * designs the turn moves, every kind of mount: 90 open before, 26 now. It closed 83 and
- * opened 19, 14 of them at 42 mm with a magnet from beneath under a deeper counterbore,
- * where one size in nine leaks unturned too, by the same slivers at the magnet pocket's
- * corners in the underside. */
+ * unturned and the turn leaves it further off, and a shank no corner came near is cut as
+ * it was. A magnet pocket's corners stand on the same rays as the counterbore's, and π/84
+ * could bring one of those onto a flat instead: 4.85 mm under 7.246 with a 6 mm magnet
+ * from above left 35 edges in the socket floor at 49.02 mm, and 5.773 under 12.053 25 at
+ * 55 mm, where the flats unturned miss them by 0.07 and 0.04 (unturned shanks meet them at
+ * other sizes: 4.9911 under 7.246 leaves 44 at 49.02 mm, with no turn). So where π/84
+ * leaves a corner of either nearer than 0.005 mm, the turn is the one of 24 steps across
+ * those 30/7° that keeps them furthest off. Wherever the counterbore's corners call for a
+ * turn, no corner of either then comes within 0.0039 mm of a flat (6 and 8 mm magnets,
+ * heads up to 2.2 times the shank). Half a facet, π/12, clears the corners as well, but
+ * it squares two flats to the cell's edges, and at 37.67 mm those folded the socket floor
+ * beside the pocket. Measured on 3,846 one-cell plates with a magnet from above, 37.67 to
+ * 55 mm, shanks 1 to 5 mm and heads up to 1.15 times them, every 0.001 mm round these
+ * sizes: 546 open before, and 1 now, a size the turn leaves alone; none came out worse.
+ * On 1,800 random designs the turn moves, every kind of mount: 90 open before, 24 now. It
+ * closed 83 and opened 17: 14 at 42 mm with a magnet from beneath under a deeper
+ * counterbore, where one size in nine leaks unturned too, by the same slivers at the
+ * magnet pocket's corners in the underside, and 3 in corner bosses, each at that one size
+ * alone. */
 const MOUNT_BORE = {
   magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
             fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },
@@ -882,17 +891,24 @@ const MOUNT_BORE = {
           cuts: (d, hole) => d >= MOUNT_BORE.head.over(hole) },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12),
-          // how far to turn the shank under a counterbore headD across (see above)
-          turn: (d, headD) => {
-            const { head, hole } = MOUNT_BORE, R = head.r(headD);
-            const clear = (t) => {   // the nearest a corner of the counterbore comes to a flat's plane
+          // how far to turn the shank under a counterbore headD across, in a magnet pocket
+          // magnetR out at its corners or none (see above)
+          turn: (d, headD, magnetR) => {
+            const { head, hole } = MOUNT_BORE, rs = [head.r(headD)];
+            const clear = (t) => {   // the nearest a corner comes to one of the flats' planes
               let g = Infinity;
-              for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
+              for (const R of rs) for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
                 g = Math.min(g, Math.abs(R * Math.cos(2*Math.PI*k/head.sides - (2*m + 1)*Math.PI/hole.sides - t) - d/2));
               return g;
             };
-            const now = clear(0);
-            return now < 0.005 && clear(Math.PI / 84) > now ? Math.PI / 84 : 0;
+            if (clear(0) >= 0.005) return 0;
+            if (magnetR) rs.push(magnetR);   // the magnet pocket's corners stand on the same rays
+            let best = Math.PI / 84, most = clear(best);
+            if (most < 0.005) for (let j = 1; j < 24; j++) {
+              const t = (Math.PI / 42) * j / 24, g = clear(t);
+              if (g > most + 1e-9) { most = g; best = t; }
+            }
+            return most > clear(0) ? best : 0;
           } },
 };
 
@@ -937,7 +953,7 @@ function fastenerCutter(cfg, magZ0, magZ1, shankTop) {
       add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
     // the shank, turned off the counterbore's corners where one would stand on a flat (#74)
     const shank = cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides);
-    const t = counterbore ? hole.turn(cfg.screwHoleD, cfg.screwHeadD) : 0;
+    const t = counterbore ? hole.turn(cfg.screwHoleD, cfg.screwHeadD, cfg.magnets ? magnetR : 0) : 0;
     const c = Math.cos(t), s = Math.sin(t), turn = (v) => [v[0]*c - v[1]*s, v[0]*s + v[1]*c, v[2]];
     add(t ? shank.map((p) => ({ verts: p.verts.map(turn), plane: { n: turn(p.plane.n), w: p.plane.w } }))
           : shank);
diff --git a/test/plate-audit.js b/test/plate-audit.js
index bec4933..b2a972f 100644
--- a/test/plate-audit.js
+++ b/test/plate-audit.js
@@ -2055,8 +2055,10 @@ console.log('\nthe other limits, built at their ends:');
      flats on the sizes, are a 1 mm shank under 1.06 (36 a cell). 4.25 over 4 left 26 and
      3.305 over 3 62; 5.4959 over 3 under an 8 x 3 magnet, a head nearly twice the shank,
      55; and from beneath, the magnet's roof round a counterbore deeper than it, 1.06 over
-     1 left 12. The shank is turned off the corners now (MOUNT_BORE.hole.turn). Each has
-     to build closed, with no folds. */
+     1 left 12. The shank is turned off the corners now (MOUNT_BORE.hole.turn). The last
+     two are where π/84 alone put a corner of the magnet pocket's on a flat instead (35 and
+     25 edges in the socket floor), so the turn keeps those clear too. Each has to build
+     closed, with no folds. */
   for (const [nm, o] of [
     ['main\'s 1.0353 under 1.0873, 42', { pitch: 42, drawerW: 168, drawerD: 84, bedW: 100, bedD: 400,
       screwHoleD: 1.0353 * Math.cos(Math.PI / 12), screwHeadD: 1.0873 * Math.cos(Math.PI / 14) }],
@@ -2065,6 +2067,8 @@ console.log('\nthe other limits, built at their ends:');
     ['3.305 mm head over 3, 42', { screwHoleD: 3, screwHeadD: 3.305 }],
     ['5.4959 over 3, 8 x 3 magnet', { screwHoleD: 3, screwHeadD: 5.4959, magnetD: 8, magnetH: 3 }],
     ['1.06 over 1, from beneath', { screwHoleD: 1, screwHeadD: 1.06, magnetSide: 'bottom', screwHeadDepth: 3 }],
+    ['4.85 under 7.246, 49.02', { pitch: 49.02, drawerW: 49.02, drawerD: 49.02, screwHoleD: 4.85, screwHeadD: 7.246 }],
+    ['5.773 under 12.053, 55', { pitch: 55, drawerW: 55, drawerD: 55, screwHoleD: 5.773, screwHeadD: 12.053 }],
   ]) {
     const r = buildAll({ pitch: 42, drawerW: 42, drawerD: 42, connector: 'none', magnets: true,
                          magnetSide: 'top', screws: true, ...o });

From 705b8fb8d4000463a482ff34e94ae1c79b2a3644 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 15:51:50 +0000
Subject: [PATCH 14/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html | 52 ++++++++++++++++++++++++++++++++-----------------
 index.html      | 52 ++++++++++++++++++++++++++++++++-----------------
 sw.js           |  2 +-
 3 files changed, 69 insertions(+), 37 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index b3453ee..ceee5ad 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -2469,16 +2469,25 @@ <h2 id="drawersTitle">Your drawers</h2>
  * meets a flat's plane at an odd multiple of 15/7° off the flat's normal; turned π/84,
  * 15/7°, it meets them at the even ones, so a size that put a corner on a flat puts it
  * midway between two. The turn is taken where a corner comes nearer than 0.005 mm
- * unturned and the turn leaves it further off, so no corner comes within 0.0039 mm of a
- * flat at any size, and a shank no corner came near is cut as it was. Half a facet, π/12,
- * clears the corners as well, but it squares two flats to the cell's edges, and at
- * 37.67 mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell
- * plates with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15
- * times them, every 0.001 mm round these sizes: 546 open before, 4 now. On 1,800 random
- * designs the turn moves, every kind of mount: 90 open before, 26 now. It closed 83 and
- * opened 19, 14 of them at 42 mm with a magnet from beneath under a deeper counterbore,
- * where one size in nine leaks unturned too, by the same slivers at the magnet pocket's
- * corners in the underside. */
+ * unturned and the turn leaves it further off, and a shank no corner came near is cut as
+ * it was. A magnet pocket's corners stand on the same rays as the counterbore's, and π/84
+ * could bring one of those onto a flat instead: 4.85 mm under 7.246 with a 6 mm magnet
+ * from above left 35 edges in the socket floor at 49.02 mm, and 5.773 under 12.053 25 at
+ * 55 mm, where the flats unturned miss them by 0.07 and 0.04 (unturned shanks meet them at
+ * other sizes: 4.9911 under 7.246 leaves 44 at 49.02 mm, with no turn). So where π/84
+ * leaves a corner of either nearer than 0.005 mm, the turn is the one of 24 steps across
+ * those 30/7° that keeps them furthest off. Wherever the counterbore's corners call for a
+ * turn, no corner of either then comes within 0.0039 mm of a flat (6 and 8 mm magnets,
+ * heads up to 2.2 times the shank). Half a facet, π/12, clears the corners as well, but
+ * it squares two flats to the cell's edges, and at 37.67 mm those folded the socket floor
+ * beside the pocket. Measured on 3,846 one-cell plates with a magnet from above, 37.67 to
+ * 55 mm, shanks 1 to 5 mm and heads up to 1.15 times them, every 0.001 mm round these
+ * sizes: 546 open before, and 1 now, a size the turn leaves alone; none came out worse.
+ * On 1,800 random designs the turn moves, every kind of mount: 90 open before, 24 now. It
+ * closed 83 and opened 17: 14 at 42 mm with a magnet from beneath under a deeper
+ * counterbore, where one size in nine leaks unturned too, by the same slivers at the
+ * magnet pocket's corners in the underside, and 3 in corner bosses, each at that one size
+ * alone. */
 const MOUNT_BORE = {
   magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
             fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },
@@ -2488,17 +2497,24 @@ <h2 id="drawersTitle">Your drawers</h2>
           cuts: (d, hole) => d >= MOUNT_BORE.head.over(hole) },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12),
-          // how far to turn the shank under a counterbore headD across (see above)
-          turn: (d, headD) => {
-            const { head, hole } = MOUNT_BORE, R = head.r(headD);
-            const clear = (t) => {   // the nearest a corner of the counterbore comes to a flat's plane
+          // how far to turn the shank under a counterbore headD across, in a magnet pocket
+          // magnetR out at its corners or none (see above)
+          turn: (d, headD, magnetR) => {
+            const { head, hole } = MOUNT_BORE, rs = [head.r(headD)];
+            const clear = (t) => {   // the nearest a corner comes to one of the flats' planes
               let g = Infinity;
-              for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
+              for (const R of rs) for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
                 g = Math.min(g, Math.abs(R * Math.cos(2*Math.PI*k/head.sides - (2*m + 1)*Math.PI/hole.sides - t) - d/2));
               return g;
             };
-            const now = clear(0);
-            return now < 0.005 && clear(Math.PI / 84) > now ? Math.PI / 84 : 0;
+            if (clear(0) >= 0.005) return 0;
+            if (magnetR) rs.push(magnetR);   // the magnet pocket's corners stand on the same rays
+            let best = Math.PI / 84, most = clear(best);
+            if (most < 0.005) for (let j = 1; j < 24; j++) {
+              const t = (Math.PI / 42) * j / 24, g = clear(t);
+              if (g > most + 1e-9) { most = g; best = t; }
+            }
+            return most > clear(0) ? best : 0;
           } },
 };
 
@@ -2543,7 +2559,7 @@ <h2 id="drawersTitle">Your drawers</h2>
       add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
     // the shank, turned off the counterbore's corners where one would stand on a flat (#74)
     const shank = cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides);
-    const t = counterbore ? hole.turn(cfg.screwHoleD, cfg.screwHeadD) : 0;
+    const t = counterbore ? hole.turn(cfg.screwHoleD, cfg.screwHeadD, cfg.magnets ? magnetR : 0) : 0;
     const c = Math.cos(t), s = Math.sin(t), turn = (v) => [v[0]*c - v[1]*s, v[0]*s + v[1]*c, v[2]];
     add(t ? shank.map((p) => ({ verts: p.verts.map(turn), plane: { n: turn(p.plane.n), w: p.plane.w } }))
           : shank);
diff --git a/index.html b/index.html
index 9e5e0e5..d1040bd 100644
--- a/index.html
+++ b/index.html
@@ -2256,16 +2256,25 @@ <h2 id="drawersTitle">Your drawers</h2>
  * meets a flat's plane at an odd multiple of 15/7° off the flat's normal; turned π/84,
  * 15/7°, it meets them at the even ones, so a size that put a corner on a flat puts it
  * midway between two. The turn is taken where a corner comes nearer than 0.005 mm
- * unturned and the turn leaves it further off, so no corner comes within 0.0039 mm of a
- * flat at any size, and a shank no corner came near is cut as it was. Half a facet, π/12,
- * clears the corners as well, but it squares two flats to the cell's edges, and at
- * 37.67 mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell
- * plates with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15
- * times them, every 0.001 mm round these sizes: 546 open before, 4 now. On 1,800 random
- * designs the turn moves, every kind of mount: 90 open before, 26 now. It closed 83 and
- * opened 19, 14 of them at 42 mm with a magnet from beneath under a deeper counterbore,
- * where one size in nine leaks unturned too, by the same slivers at the magnet pocket's
- * corners in the underside. */
+ * unturned and the turn leaves it further off, and a shank no corner came near is cut as
+ * it was. A magnet pocket's corners stand on the same rays as the counterbore's, and π/84
+ * could bring one of those onto a flat instead: 4.85 mm under 7.246 with a 6 mm magnet
+ * from above left 35 edges in the socket floor at 49.02 mm, and 5.773 under 12.053 25 at
+ * 55 mm, where the flats unturned miss them by 0.07 and 0.04 (unturned shanks meet them at
+ * other sizes: 4.9911 under 7.246 leaves 44 at 49.02 mm, with no turn). So where π/84
+ * leaves a corner of either nearer than 0.005 mm, the turn is the one of 24 steps across
+ * those 30/7° that keeps them furthest off. Wherever the counterbore's corners call for a
+ * turn, no corner of either then comes within 0.0039 mm of a flat (6 and 8 mm magnets,
+ * heads up to 2.2 times the shank). Half a facet, π/12, clears the corners as well, but
+ * it squares two flats to the cell's edges, and at 37.67 mm those folded the socket floor
+ * beside the pocket. Measured on 3,846 one-cell plates with a magnet from above, 37.67 to
+ * 55 mm, shanks 1 to 5 mm and heads up to 1.15 times them, every 0.001 mm round these
+ * sizes: 546 open before, and 1 now, a size the turn leaves alone; none came out worse.
+ * On 1,800 random designs the turn moves, every kind of mount: 90 open before, 24 now. It
+ * closed 83 and opened 17: 14 at 42 mm with a magnet from beneath under a deeper
+ * counterbore, where one size in nine leaks unturned too, by the same slivers at the
+ * magnet pocket's corners in the underside, and 3 in corner bosses, each at that one size
+ * alone. */
 const MOUNT_BORE = {
   magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
             fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },
@@ -2275,17 +2284,24 @@ <h2 id="drawersTitle">Your drawers</h2>
           cuts: (d, hole) => d >= MOUNT_BORE.head.over(hole) },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12),
-          // how far to turn the shank under a counterbore headD across (see above)
-          turn: (d, headD) => {
-            const { head, hole } = MOUNT_BORE, R = head.r(headD);
-            const clear = (t) => {   // the nearest a corner of the counterbore comes to a flat's plane
+          // how far to turn the shank under a counterbore headD across, in a magnet pocket
+          // magnetR out at its corners or none (see above)
+          turn: (d, headD, magnetR) => {
+            const { head, hole } = MOUNT_BORE, rs = [head.r(headD)];
+            const clear = (t) => {   // the nearest a corner comes to one of the flats' planes
               let g = Infinity;
-              for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
+              for (const R of rs) for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
                 g = Math.min(g, Math.abs(R * Math.cos(2*Math.PI*k/head.sides - (2*m + 1)*Math.PI/hole.sides - t) - d/2));
               return g;
             };
-            const now = clear(0);
-            return now < 0.005 && clear(Math.PI / 84) > now ? Math.PI / 84 : 0;
+            if (clear(0) >= 0.005) return 0;
+            if (magnetR) rs.push(magnetR);   // the magnet pocket's corners stand on the same rays
+            let best = Math.PI / 84, most = clear(best);
+            if (most < 0.005) for (let j = 1; j < 24; j++) {
+              const t = (Math.PI / 42) * j / 24, g = clear(t);
+              if (g > most + 1e-9) { most = g; best = t; }
+            }
+            return most > clear(0) ? best : 0;
           } },
 };
 
@@ -2330,7 +2346,7 @@ <h2 id="drawersTitle">Your drawers</h2>
       add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
     // the shank, turned off the counterbore's corners where one would stand on a flat (#74)
     const shank = cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides);
-    const t = counterbore ? hole.turn(cfg.screwHoleD, cfg.screwHeadD) : 0;
+    const t = counterbore ? hole.turn(cfg.screwHoleD, cfg.screwHeadD, cfg.magnets ? magnetR : 0) : 0;
     const c = Math.cos(t), s = Math.sin(t), turn = (v) => [v[0]*c - v[1]*s, v[0]*s + v[1]*c, v[2]];
     add(t ? shank.map((p) => ({ verts: p.verts.map(turn), plane: { n: turn(p.plane.n), w: p.plane.w } }))
           : shank);
diff --git a/sw.js b/sw.js
index a182340..8984595 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "c6f9b690c5d9";
+const VERSION = "4c17bd60043c";
 const FILES = [
   "./",
   "bins/",

From a9a445c1dde5d958300c4cbc89cfbff7ebb019af Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 16:31:29 +0000
Subject: [PATCH 15/58] Measure a screw's shank turned, as it is cut, where a
 joint's cut beside it sets its size

Where a counterbore's corner would stand on a flat of its shank, fastenerCutter turns
the shank a little (#74), and a turned shank reaches a joint's cut a little sooner or
later than one that is not. MOUNT_BORE.screw now says, for the cutter and for
mountLimits alike, whether the counterbore is cut and how far the shank is turned, and
mountLimits measures that shank turned (boreReach takes the turn). On 400 random
designs with a turned shank its limit moved by a tenth in 2; no design whose head and
magnet the limits also take changed.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md |  4 ++-
 src/core.js    | 67 +++++++++++++++++++++++++++++++-------------------
 2 files changed, 45 insertions(+), 26 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index 67ad889..8da14c6 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -717,7 +717,9 @@ currently installed):
   rays, so where π/84 would bring one of those within 0.005 mm of a flat instead, the
   shank takes the step of the 24 across those 30/7° that keeps both furthest off. Turned,
   no corner of either comes within 0.0039 mm of a flat, and a shank no corner of the
-  counterbore's came near is cut as before.
+  counterbore's came near is cut as before. `MOUNT_BORE.screw` says whether a design's
+  counterbore is cut and how far its shank is turned, for the cutter and for
+  `mountLimits`, which measures that shank turned.
 - **The socket's corner clearance is not uniform.** Known, documented, deliberately not
   fixed — see [socket-clearance.md](socket-clearance.md).
 - **The plate's outer corner radius has a ceiling, and it is the socket's.** Both the
diff --git a/src/core.js b/src/core.js
index adc2903..6d45497 100644
--- a/src/core.js
+++ b/src/core.js
@@ -910,6 +910,22 @@ const MOUNT_BORE = {
             }
             return most > clear(0) ? best : 0;
           } },
+  /* What fastenerCutter cuts for a design's screw, as { counterbore, turn }: whether the
+     counterbore is cut, and how far the shank is turned under it. Here so that mountLimits
+     measures the same shank the cutter cuts.
+     A counterbore the magnet pocket from beneath holds whole is that pocket already: both
+     14 sides, corners on the same rays, no deeper. Since the bores stand their flats on
+     the sizes, the default 6 mm head's walls stand 0.022 mm inside the 6 mm magnet's,
+     and unioned, the test tile at 42 mm with magnets and screws left 6 edges open in
+     its underside. Left out, the pocket is the same solid, and closed. */
+  screw: (cfg) => {
+    const { magnet, head, hole } = MOUNT_BORE, magnetR = magnet.r(cfg.magnetD);
+    const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
+      head.r(cfg.screwHeadD) <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
+    const counterbore = head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet;
+    return { counterbore,
+             turn: counterbore ? hole.turn(cfg.screwHoleD, cfg.screwHeadD, cfg.magnets ? magnetR : 0) : 0 };
+  },
 };
 
 /* Everything removed at one mounting site, as ONE solid.
@@ -941,19 +957,12 @@ function fastenerCutter(cfg, magZ0, magZ1, shankTop) {
       ? cylinder(0, 0, magnetR, magZ0, magZ1, magnet.sides)
       : cylinder(0, 0, magnetR, -0.5, cfg.magnetH, magnet.sides));
   if (cfg.screws) {
-    /* A counterbore the magnet pocket from beneath holds whole is that pocket already: both
-       14 sides, corners on the same rays, no deeper. Since the bores stand their flats on
-       the sizes, the default 6 mm head's walls stand 0.022 mm inside the 6 mm magnet's,
-       and unioned, the test tile at 42 mm with magnets and screws left 6 edges open in
-       its underside. Left out, the pocket is the same solid, and closed. */
-    const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
-      head.r(cfg.screwHeadD) <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
-    const counterbore = head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet;
+    // the counterbore, unless the magnet pocket from beneath is that already (MOUNT_BORE.screw)
+    const { counterbore, turn: t } = MOUNT_BORE.screw(cfg);
     if (counterbore)
       add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
     // the shank, turned off the counterbore's corners where one would stand on a flat (#74)
     const shank = cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides);
-    const t = counterbore ? hole.turn(cfg.screwHoleD, cfg.screwHeadD, cfg.magnets ? magnetR : 0) : 0;
     const c = Math.cos(t), s = Math.sin(t), turn = (v) => [v[0]*c - v[1]*s, v[0]*s + v[1]*c, v[2]];
     add(t ? shank.map((p) => ({ verts: p.verts.map(turn), plane: { n: turn(p.plane.n), w: p.plane.w } }))
           : shank);
@@ -2464,16 +2473,17 @@ const MOUNT_WALL = 1.0;
 const MOUNT_LEVEL = 0.05, MOUNT_SEAM = 0.01;
 /* How far a mounting bore about (x, y) can grow before it meets any of `segs`, as the
    radius of the circle through its corners: the polygon cylinder() cuts, `sides` flats
-   with a corner at every 2πk/sides from +x. A point is in that polygon when it stands no
-   further out along any flat's normal than R cos(π/sides), so along one segment the
-   least R that takes a point of it in is at an end, or where the segment crosses the
-   line out through a corner, on which a point's R is its distance. */
-function boreReach(sides, segs, x, y) {
+   with a corner at every 2πk/sides from +x, or that turned `turn` about its axis, as
+   fastenerCutter turns a shank (MOUNT_BORE.screw). A point is in that polygon when it
+   stands no further out along any flat's normal than R cos(π/sides), so along one
+   segment the least R that takes a point of it in is at an end, or where the segment
+   crosses the line out through a corner, on which a point's R is its distance. */
+function boreReach(sides, segs, x, y, turn = 0) {
   const step = 2 * Math.PI / sides, h = Math.cos(step / 2);
   const cx = [], cy = [], nx = [], ny = [];
   for (let k = 0; k < sides; k++) {
-    cx.push(Math.cos(k * step)); cy.push(Math.sin(k * step));
-    nx.push(Math.cos((k + 0.5) * step)); ny.push(Math.sin((k + 0.5) * step));
+    cx.push(Math.cos(k * step + turn)); cy.push(Math.sin(k * step + turn));
+    nx.push(Math.cos((k + 0.5) * step + turn)); ny.push(Math.sin((k + 0.5) * step + turn));
   }
   const at = (dx, dy) => {
     let m = -Infinity;
@@ -2609,10 +2619,11 @@ function mountLimits(cfg, layout, known) {
      magnet from beneath with a bowtie at 42 mm, which has 0.84 mm to spare and always
      built clean. */
   const pad = platePad(cfg), again = !!known && known.pad === pad;
-  /* Each cut as { top, sites }: its ceiling, and each site in reach of it as how far a
-     bore's corner circle (`room`) and the bores themselves (`bore`, by their sides) can
-     grow before they meet the cut, and a magnet or screw (`body`) before it meets the
-     part in it. */
+  /* Each cut as { top, segs, sites }: its ceiling, its footprint, and each site in reach
+     of it as how far a bore's corner circle (`room`) and the bores themselves (`bore`, by
+     their sides) can grow before they meet the cut, and a magnet or screw (`body`) before
+     it meets the part in it. Where the site stands from the cut's own origin (`x`, `y`)
+     is kept for a shank turned under its counterbore, measured for the sizes asked. */
   const jointCuts = again ? known.list : [];
   /* Room past the most the cell or the floor leaves cannot stop a size, so nothing
      further off than that is measured, and nothing at all where neither leaves any. A
@@ -2689,17 +2700,20 @@ function mountLimits(cfg, layout, known) {
             const room = from(segs, x, y);
             if (room >= reach) continue;
             const bore = (n) => room > 0 ? boreReach(n, segs, x, y) : room;
-            sites.push({ room, body: from(part, x, y), bore: { 12: bore(12), 14: bore(14) } });
+            sites.push({ x, y, room, body: from(part, x, y), bore: { 12: bore(12), 14: bore(14) } });
           }
-        if (sites.length) jointCuts.push({ top: ceiling, sites });
+        if (sites.length) jointCuts.push({ top: ceiling, segs, sites });
       }
     }
   }
   /* The bores as fastenerCutter cuts them (MOUNT_BORE): how many sides, and the largest
      size whose corners stay inside a radius. Each stands its flats on its size, so its
      corners stand out past it, and a magnet's 0.1 mm over its radius where that is
-     further. */
+     further. The shank is turned where the cutter turns it, and measured so: its turn
+     goes by the sizes asked, the head's and the magnet's as well as its own, so it is
+     the shank of this design that is measured. */
   const BORE = { magnetD: MOUNT_BORE.magnet, screwHeadD: MOUNT_BORE.head, screwHoleD: MOUNT_BORE.hole };
+  const shankTurn = cfg.screws ? MOUNT_BORE.screw(cfg).turn : 0;
   // the room the cell, the floor or a boss leaves, and the hole beside
   const own = { magnetD: fit(cfg.magnetSide === 'top' ? top : under), screwHoleD: fit(top), screwHeadD: fit(under) };
   // a dovetail's notch takes a pocket from beneath that breaks into it; every other cut does not
@@ -2713,6 +2727,9 @@ function mountLimits(cfg, layout, known) {
      into, but not stop just short of. */
   const jointFor = (f) => {
     const { sides, fits } = BORE[f];
+    // the room a bore has, measured again for a shank turned under its counterbore
+    const turn = f === 'screwHoleD' ? shankTurn : 0;
+    const reach = (c, s) => !turn ? s.bore[sides] : s.room > 0 ? boreReach(sides, c.segs, s.x, s.y, turn) : s.room;
     const above = f === 'magnetD' && cfg.magnetSide === 'top';
     // how high a pocket from beneath goes; a shank goes through
     const ceiling = f === 'magnetD' ? cfg.magnetH : f === 'screwHeadD' ? cfg.screwHeadDepth : Infinity;
@@ -2728,10 +2745,10 @@ function mountLimits(cfg, layout, known) {
       const level = Math.round(Math.abs(ceiling - c.top) * 1e6) / 1e6 < MOUNT_LEVEL;
       const stop = above ? 'floor' : !notch ? 'cut' : level ? 'level' : 'part';
       for (const s of c.sites) {
-        const short = fits(s.bore[sides] - MOUNT_SEAM);
+        const bore = reach(c, s), short = fits(bore - MOUNT_SEAM);
         const size = stop === 'part' ? 2 * s.body : short;
         if (size < cap) { cap = size; why = stop; }
-        if (stop === 'part') near.push([short, fits(s.bore[sides])]);
+        if (stop === 'part') near.push([short, fits(bore)]);
       }
     }
     return { cap, why, near };

From 0e12f68cf08e3db6cfd68ba3e35f22e5433dd3a5 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 16:31:29 +0000
Subject: [PATCH 16/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html | 67 +++++++++++++++++++++++++++++++------------------
 index.html      | 67 +++++++++++++++++++++++++++++++------------------
 sw.js           |  2 +-
 3 files changed, 85 insertions(+), 51 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index 418f362..e2f5e6b 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -2516,6 +2516,22 @@ <h2 id="drawersTitle">Your drawers</h2>
             }
             return most > clear(0) ? best : 0;
           } },
+  /* What fastenerCutter cuts for a design's screw, as { counterbore, turn }: whether the
+     counterbore is cut, and how far the shank is turned under it. Here so that mountLimits
+     measures the same shank the cutter cuts.
+     A counterbore the magnet pocket from beneath holds whole is that pocket already: both
+     14 sides, corners on the same rays, no deeper. Since the bores stand their flats on
+     the sizes, the default 6 mm head's walls stand 0.022 mm inside the 6 mm magnet's,
+     and unioned, the test tile at 42 mm with magnets and screws left 6 edges open in
+     its underside. Left out, the pocket is the same solid, and closed. */
+  screw: (cfg) => {
+    const { magnet, head, hole } = MOUNT_BORE, magnetR = magnet.r(cfg.magnetD);
+    const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
+      head.r(cfg.screwHeadD) <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
+    const counterbore = head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet;
+    return { counterbore,
+             turn: counterbore ? hole.turn(cfg.screwHoleD, cfg.screwHeadD, cfg.magnets ? magnetR : 0) : 0 };
+  },
 };
 
 /* Everything removed at one mounting site, as ONE solid.
@@ -2547,19 +2563,12 @@ <h2 id="drawersTitle">Your drawers</h2>
       ? cylinder(0, 0, magnetR, magZ0, magZ1, magnet.sides)
       : cylinder(0, 0, magnetR, -0.5, cfg.magnetH, magnet.sides));
   if (cfg.screws) {
-    /* A counterbore the magnet pocket from beneath holds whole is that pocket already: both
-       14 sides, corners on the same rays, no deeper. Since the bores stand their flats on
-       the sizes, the default 6 mm head's walls stand 0.022 mm inside the 6 mm magnet's,
-       and unioned, the test tile at 42 mm with magnets and screws left 6 edges open in
-       its underside. Left out, the pocket is the same solid, and closed. */
-    const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
-      head.r(cfg.screwHeadD) <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
-    const counterbore = head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet;
+    // the counterbore, unless the magnet pocket from beneath is that already (MOUNT_BORE.screw)
+    const { counterbore, turn: t } = MOUNT_BORE.screw(cfg);
     if (counterbore)
       add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
     // the shank, turned off the counterbore's corners where one would stand on a flat (#74)
     const shank = cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides);
-    const t = counterbore ? hole.turn(cfg.screwHoleD, cfg.screwHeadD, cfg.magnets ? magnetR : 0) : 0;
     const c = Math.cos(t), s = Math.sin(t), turn = (v) => [v[0]*c - v[1]*s, v[0]*s + v[1]*c, v[2]];
     add(t ? shank.map((p) => ({ verts: p.verts.map(turn), plane: { n: turn(p.plane.n), w: p.plane.w } }))
           : shank);
@@ -4070,16 +4079,17 @@ <h2 id="drawersTitle">Your drawers</h2>
 const MOUNT_LEVEL = 0.05, MOUNT_SEAM = 0.01;
 /* How far a mounting bore about (x, y) can grow before it meets any of `segs`, as the
    radius of the circle through its corners: the polygon cylinder() cuts, `sides` flats
-   with a corner at every 2πk/sides from +x. A point is in that polygon when it stands no
-   further out along any flat's normal than R cos(π/sides), so along one segment the
-   least R that takes a point of it in is at an end, or where the segment crosses the
-   line out through a corner, on which a point's R is its distance. */
-function boreReach(sides, segs, x, y) {
+   with a corner at every 2πk/sides from +x, or that turned `turn` about its axis, as
+   fastenerCutter turns a shank (MOUNT_BORE.screw). A point is in that polygon when it
+   stands no further out along any flat's normal than R cos(π/sides), so along one
+   segment the least R that takes a point of it in is at an end, or where the segment
+   crosses the line out through a corner, on which a point's R is its distance. */
+function boreReach(sides, segs, x, y, turn = 0) {
   const step = 2 * Math.PI / sides, h = Math.cos(step / 2);
   const cx = [], cy = [], nx = [], ny = [];
   for (let k = 0; k < sides; k++) {
-    cx.push(Math.cos(k * step)); cy.push(Math.sin(k * step));
-    nx.push(Math.cos((k + 0.5) * step)); ny.push(Math.sin((k + 0.5) * step));
+    cx.push(Math.cos(k * step + turn)); cy.push(Math.sin(k * step + turn));
+    nx.push(Math.cos((k + 0.5) * step + turn)); ny.push(Math.sin((k + 0.5) * step + turn));
   }
   const at = (dx, dy) => {
     let m = -Infinity;
@@ -4215,10 +4225,11 @@ <h2 id="drawersTitle">Your drawers</h2>
      magnet from beneath with a bowtie at 42 mm, which has 0.84 mm to spare and always
      built clean. */
   const pad = platePad(cfg), again = !!known && known.pad === pad;
-  /* Each cut as { top, sites }: its ceiling, and each site in reach of it as how far a
-     bore's corner circle (`room`) and the bores themselves (`bore`, by their sides) can
-     grow before they meet the cut, and a magnet or screw (`body`) before it meets the
-     part in it. */
+  /* Each cut as { top, segs, sites }: its ceiling, its footprint, and each site in reach
+     of it as how far a bore's corner circle (`room`) and the bores themselves (`bore`, by
+     their sides) can grow before they meet the cut, and a magnet or screw (`body`) before
+     it meets the part in it. Where the site stands from the cut's own origin (`x`, `y`)
+     is kept for a shank turned under its counterbore, measured for the sizes asked. */
   const jointCuts = again ? known.list : [];
   /* Room past the most the cell or the floor leaves cannot stop a size, so nothing
      further off than that is measured, and nothing at all where neither leaves any. A
@@ -4295,17 +4306,20 @@ <h2 id="drawersTitle">Your drawers</h2>
             const room = from(segs, x, y);
             if (room >= reach) continue;
             const bore = (n) => room > 0 ? boreReach(n, segs, x, y) : room;
-            sites.push({ room, body: from(part, x, y), bore: { 12: bore(12), 14: bore(14) } });
+            sites.push({ x, y, room, body: from(part, x, y), bore: { 12: bore(12), 14: bore(14) } });
           }
-        if (sites.length) jointCuts.push({ top: ceiling, sites });
+        if (sites.length) jointCuts.push({ top: ceiling, segs, sites });
       }
     }
   }
   /* The bores as fastenerCutter cuts them (MOUNT_BORE): how many sides, and the largest
      size whose corners stay inside a radius. Each stands its flats on its size, so its
      corners stand out past it, and a magnet's 0.1 mm over its radius where that is
-     further. */
+     further. The shank is turned where the cutter turns it, and measured so: its turn
+     goes by the sizes asked, the head's and the magnet's as well as its own, so it is
+     the shank of this design that is measured. */
   const BORE = { magnetD: MOUNT_BORE.magnet, screwHeadD: MOUNT_BORE.head, screwHoleD: MOUNT_BORE.hole };
+  const shankTurn = cfg.screws ? MOUNT_BORE.screw(cfg).turn : 0;
   // the room the cell, the floor or a boss leaves, and the hole beside
   const own = { magnetD: fit(cfg.magnetSide === 'top' ? top : under), screwHoleD: fit(top), screwHeadD: fit(under) };
   // a dovetail's notch takes a pocket from beneath that breaks into it; every other cut does not
@@ -4319,6 +4333,9 @@ <h2 id="drawersTitle">Your drawers</h2>
      into, but not stop just short of. */
   const jointFor = (f) => {
     const { sides, fits } = BORE[f];
+    // the room a bore has, measured again for a shank turned under its counterbore
+    const turn = f === 'screwHoleD' ? shankTurn : 0;
+    const reach = (c, s) => !turn ? s.bore[sides] : s.room > 0 ? boreReach(sides, c.segs, s.x, s.y, turn) : s.room;
     const above = f === 'magnetD' && cfg.magnetSide === 'top';
     // how high a pocket from beneath goes; a shank goes through
     const ceiling = f === 'magnetD' ? cfg.magnetH : f === 'screwHeadD' ? cfg.screwHeadDepth : Infinity;
@@ -4334,10 +4351,10 @@ <h2 id="drawersTitle">Your drawers</h2>
       const level = Math.round(Math.abs(ceiling - c.top) * 1e6) / 1e6 < MOUNT_LEVEL;
       const stop = above ? 'floor' : !notch ? 'cut' : level ? 'level' : 'part';
       for (const s of c.sites) {
-        const short = fits(s.bore[sides] - MOUNT_SEAM);
+        const bore = reach(c, s), short = fits(bore - MOUNT_SEAM);
         const size = stop === 'part' ? 2 * s.body : short;
         if (size < cap) { cap = size; why = stop; }
-        if (stop === 'part') near.push([short, fits(s.bore[sides])]);
+        if (stop === 'part') near.push([short, fits(bore)]);
       }
     }
     return { cap, why, near };
diff --git a/index.html b/index.html
index 5c60ffe..bb05ebb 100644
--- a/index.html
+++ b/index.html
@@ -2303,6 +2303,22 @@ <h2 id="drawersTitle">Your drawers</h2>
             }
             return most > clear(0) ? best : 0;
           } },
+  /* What fastenerCutter cuts for a design's screw, as { counterbore, turn }: whether the
+     counterbore is cut, and how far the shank is turned under it. Here so that mountLimits
+     measures the same shank the cutter cuts.
+     A counterbore the magnet pocket from beneath holds whole is that pocket already: both
+     14 sides, corners on the same rays, no deeper. Since the bores stand their flats on
+     the sizes, the default 6 mm head's walls stand 0.022 mm inside the 6 mm magnet's,
+     and unioned, the test tile at 42 mm with magnets and screws left 6 edges open in
+     its underside. Left out, the pocket is the same solid, and closed. */
+  screw: (cfg) => {
+    const { magnet, head, hole } = MOUNT_BORE, magnetR = magnet.r(cfg.magnetD);
+    const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
+      head.r(cfg.screwHeadD) <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
+    const counterbore = head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet;
+    return { counterbore,
+             turn: counterbore ? hole.turn(cfg.screwHoleD, cfg.screwHeadD, cfg.magnets ? magnetR : 0) : 0 };
+  },
 };
 
 /* Everything removed at one mounting site, as ONE solid.
@@ -2334,19 +2350,12 @@ <h2 id="drawersTitle">Your drawers</h2>
       ? cylinder(0, 0, magnetR, magZ0, magZ1, magnet.sides)
       : cylinder(0, 0, magnetR, -0.5, cfg.magnetH, magnet.sides));
   if (cfg.screws) {
-    /* A counterbore the magnet pocket from beneath holds whole is that pocket already: both
-       14 sides, corners on the same rays, no deeper. Since the bores stand their flats on
-       the sizes, the default 6 mm head's walls stand 0.022 mm inside the 6 mm magnet's,
-       and unioned, the test tile at 42 mm with magnets and screws left 6 edges open in
-       its underside. Left out, the pocket is the same solid, and closed. */
-    const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
-      head.r(cfg.screwHeadD) <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
-    const counterbore = head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet;
+    // the counterbore, unless the magnet pocket from beneath is that already (MOUNT_BORE.screw)
+    const { counterbore, turn: t } = MOUNT_BORE.screw(cfg);
     if (counterbore)
       add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
     // the shank, turned off the counterbore's corners where one would stand on a flat (#74)
     const shank = cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides);
-    const t = counterbore ? hole.turn(cfg.screwHoleD, cfg.screwHeadD, cfg.magnets ? magnetR : 0) : 0;
     const c = Math.cos(t), s = Math.sin(t), turn = (v) => [v[0]*c - v[1]*s, v[0]*s + v[1]*c, v[2]];
     add(t ? shank.map((p) => ({ verts: p.verts.map(turn), plane: { n: turn(p.plane.n), w: p.plane.w } }))
           : shank);
@@ -3857,16 +3866,17 @@ <h2 id="drawersTitle">Your drawers</h2>
 const MOUNT_LEVEL = 0.05, MOUNT_SEAM = 0.01;
 /* How far a mounting bore about (x, y) can grow before it meets any of `segs`, as the
    radius of the circle through its corners: the polygon cylinder() cuts, `sides` flats
-   with a corner at every 2πk/sides from +x. A point is in that polygon when it stands no
-   further out along any flat's normal than R cos(π/sides), so along one segment the
-   least R that takes a point of it in is at an end, or where the segment crosses the
-   line out through a corner, on which a point's R is its distance. */
-function boreReach(sides, segs, x, y) {
+   with a corner at every 2πk/sides from +x, or that turned `turn` about its axis, as
+   fastenerCutter turns a shank (MOUNT_BORE.screw). A point is in that polygon when it
+   stands no further out along any flat's normal than R cos(π/sides), so along one
+   segment the least R that takes a point of it in is at an end, or where the segment
+   crosses the line out through a corner, on which a point's R is its distance. */
+function boreReach(sides, segs, x, y, turn = 0) {
   const step = 2 * Math.PI / sides, h = Math.cos(step / 2);
   const cx = [], cy = [], nx = [], ny = [];
   for (let k = 0; k < sides; k++) {
-    cx.push(Math.cos(k * step)); cy.push(Math.sin(k * step));
-    nx.push(Math.cos((k + 0.5) * step)); ny.push(Math.sin((k + 0.5) * step));
+    cx.push(Math.cos(k * step + turn)); cy.push(Math.sin(k * step + turn));
+    nx.push(Math.cos((k + 0.5) * step + turn)); ny.push(Math.sin((k + 0.5) * step + turn));
   }
   const at = (dx, dy) => {
     let m = -Infinity;
@@ -4002,10 +4012,11 @@ <h2 id="drawersTitle">Your drawers</h2>
      magnet from beneath with a bowtie at 42 mm, which has 0.84 mm to spare and always
      built clean. */
   const pad = platePad(cfg), again = !!known && known.pad === pad;
-  /* Each cut as { top, sites }: its ceiling, and each site in reach of it as how far a
-     bore's corner circle (`room`) and the bores themselves (`bore`, by their sides) can
-     grow before they meet the cut, and a magnet or screw (`body`) before it meets the
-     part in it. */
+  /* Each cut as { top, segs, sites }: its ceiling, its footprint, and each site in reach
+     of it as how far a bore's corner circle (`room`) and the bores themselves (`bore`, by
+     their sides) can grow before they meet the cut, and a magnet or screw (`body`) before
+     it meets the part in it. Where the site stands from the cut's own origin (`x`, `y`)
+     is kept for a shank turned under its counterbore, measured for the sizes asked. */
   const jointCuts = again ? known.list : [];
   /* Room past the most the cell or the floor leaves cannot stop a size, so nothing
      further off than that is measured, and nothing at all where neither leaves any. A
@@ -4082,17 +4093,20 @@ <h2 id="drawersTitle">Your drawers</h2>
             const room = from(segs, x, y);
             if (room >= reach) continue;
             const bore = (n) => room > 0 ? boreReach(n, segs, x, y) : room;
-            sites.push({ room, body: from(part, x, y), bore: { 12: bore(12), 14: bore(14) } });
+            sites.push({ x, y, room, body: from(part, x, y), bore: { 12: bore(12), 14: bore(14) } });
           }
-        if (sites.length) jointCuts.push({ top: ceiling, sites });
+        if (sites.length) jointCuts.push({ top: ceiling, segs, sites });
       }
     }
   }
   /* The bores as fastenerCutter cuts them (MOUNT_BORE): how many sides, and the largest
      size whose corners stay inside a radius. Each stands its flats on its size, so its
      corners stand out past it, and a magnet's 0.1 mm over its radius where that is
-     further. */
+     further. The shank is turned where the cutter turns it, and measured so: its turn
+     goes by the sizes asked, the head's and the magnet's as well as its own, so it is
+     the shank of this design that is measured. */
   const BORE = { magnetD: MOUNT_BORE.magnet, screwHeadD: MOUNT_BORE.head, screwHoleD: MOUNT_BORE.hole };
+  const shankTurn = cfg.screws ? MOUNT_BORE.screw(cfg).turn : 0;
   // the room the cell, the floor or a boss leaves, and the hole beside
   const own = { magnetD: fit(cfg.magnetSide === 'top' ? top : under), screwHoleD: fit(top), screwHeadD: fit(under) };
   // a dovetail's notch takes a pocket from beneath that breaks into it; every other cut does not
@@ -4106,6 +4120,9 @@ <h2 id="drawersTitle">Your drawers</h2>
      into, but not stop just short of. */
   const jointFor = (f) => {
     const { sides, fits } = BORE[f];
+    // the room a bore has, measured again for a shank turned under its counterbore
+    const turn = f === 'screwHoleD' ? shankTurn : 0;
+    const reach = (c, s) => !turn ? s.bore[sides] : s.room > 0 ? boreReach(sides, c.segs, s.x, s.y, turn) : s.room;
     const above = f === 'magnetD' && cfg.magnetSide === 'top';
     // how high a pocket from beneath goes; a shank goes through
     const ceiling = f === 'magnetD' ? cfg.magnetH : f === 'screwHeadD' ? cfg.screwHeadDepth : Infinity;
@@ -4121,10 +4138,10 @@ <h2 id="drawersTitle">Your drawers</h2>
       const level = Math.round(Math.abs(ceiling - c.top) * 1e6) / 1e6 < MOUNT_LEVEL;
       const stop = above ? 'floor' : !notch ? 'cut' : level ? 'level' : 'part';
       for (const s of c.sites) {
-        const short = fits(s.bore[sides] - MOUNT_SEAM);
+        const bore = reach(c, s), short = fits(bore - MOUNT_SEAM);
         const size = stop === 'part' ? 2 * s.body : short;
         if (size < cap) { cap = size; why = stop; }
-        if (stop === 'part') near.push([short, fits(s.bore[sides])]);
+        if (stop === 'part') near.push([short, fits(bore)]);
       }
     }
     return { cap, why, near };
diff --git a/sw.js b/sw.js
index 68e0186..b74fa1d 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "79f2004a1eb1";
+const VERSION = "bdcd9d9789bf";
 const FILES = [
   "./",
   "bins/",

From 8d406b5a0d1ecdbe017c850fd084bfb8e65a474d Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 19:12:47 +0000
Subject: [PATCH 17/58] Turn the shank where a magnet pocket's corner stands on
 its flat, as for a counterbore's

MOUNT_BORE.hole.turn looked at the magnet pocket's corners only once the counterbore's
already called for a turn. So a shank no counterbore corner came near was cut unturned
even with a magnet's corner on a flat's plane, and the BSP split there: the review's
41.24 mm jigsaw link, a 3 mm shank under a 7.3 mm magnet from above whose corner stands
0.4 microns off a flat, built both pieces with 26 open edges and Download on, where main
fails to build. The magnet's corners now call for the turn as the counterbore's do.

The link, its 2.264 mm magnet and the 7.4 mm head beside it build whole, and #78's rows
keep their test, with the 7.4 mm head added. Heads 7.3 to 7.7, depths 3 to 3.25, magnets
2.15 to 2.35 thick and pitches 41.2 to 41.34 close, but for 7.31 mm, #77's coincidence.
The turn moves none of the 3,846 one-cell plates or 1,800 designs it was measured on, and
of 1,500 random designs it now turns, 54 close and 1 opens, at that one size.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md      | 22 ++++++++++++----------
 src/core.js         | 43 ++++++++++++++++++++++++++-----------------
 test/plate-audit.js | 13 +++++++++++--
 3 files changed, 49 insertions(+), 29 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index 2d4827b..3569308 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -708,16 +708,18 @@ currently installed):
   cuts' walls weave round the hole, and here and there a cell leaked by the hundred (#73:
   2.03 mm over 2 with the corners on the sizes, 2.046 over 2 and 1.034 over 1 with the
   flats). Such a head is cut as none, as one no wider than the hole always was. And the
-  shank is turned π/84 about its axis where one of the counterbore's corners would
-  otherwise stand within 0.005 mm of a flat's plane carried on past the shank
-  (`MOUNT_BORE.hole.turn`): the BSP splits a magnet pocket's floor or roof along that
-  whole plane, the weld pulled the corner onto the split, and the plate came out open by
-  the dozen round every site (#74: 136 edges a piece for 1.0353 mm under 1.0873 with a
-  magnet from above at 42 mm, on main). The magnet pocket's corners stand on the same
-  rays, so where π/84 would bring one of those within 0.005 mm of a flat instead, the
-  shank takes the step of the 24 across those 30/7° that keeps both furthest off. Turned,
-  no corner of either comes within 0.0039 mm of a flat, and a shank no corner of the
-  counterbore's came near is cut as before. `MOUNT_BORE.screw` says whether a design's
+  shank is turned π/84 about its axis where one of the counterbore's corners, or one of
+  the magnet pocket's, would otherwise stand within 0.005 mm of a flat's plane carried on
+  past the shank (`MOUNT_BORE.hole.turn`): the BSP splits a magnet pocket's floor or roof
+  along that whole plane, the weld pulled the corner onto the split, and the plate came
+  out open by the dozen round every site (#74: 136 edges a piece for 1.0353 mm under
+  1.0873 with a magnet from above at 42 mm, on main; and 26 a piece at 41.24 mm for a 3 mm
+  shank under a 7.3 mm magnet from above, whose corner stood 0.4 microns off a flat). The
+  two pockets' corners stand on the same rays, so where π/84 would bring one within 0.005
+  mm of a flat, the shank takes the step of the 24 across those 30/7° that keeps both
+  furthest off. Turned, no corner of either comes within 0.0039 mm of a flat where the
+  magnet stands 0.3 mm or more outside the shank's corners, and a shank no corner of
+  either came near is cut as before. `MOUNT_BORE.screw` says whether a design's
   counterbore is cut and how far its shank is turned, for the cutter and for
   `mountLimits`, which measures that shank turned.
 - **The socket's corner clearance is not uniform.** Known, documented, deliberately not
diff --git a/src/core.js b/src/core.js
index 15a5932..f6d8902 100644
--- a/src/core.js
+++ b/src/core.js
@@ -926,21 +926,30 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * it was. A magnet pocket's corners stand on the same rays as the counterbore's, and π/84
  * could bring one of those onto a flat instead: 4.85 mm under 7.246 with a 6 mm magnet
  * from above left 35 edges in the socket floor at 49.02 mm, and 5.773 under 12.053 25 at
- * 55 mm, where the flats unturned miss them by 0.07 and 0.04 (unturned shanks meet them at
- * other sizes: 4.9911 under 7.246 leaves 44 at 49.02 mm, with no turn). So where π/84
- * leaves a corner of either nearer than 0.005 mm, the turn is the one of 24 steps across
- * those 30/7° that keeps them furthest off. Wherever the counterbore's corners call for a
- * turn, no corner of either then comes within 0.0039 mm of a flat (6 and 8 mm magnets,
- * heads up to 2.2 times the shank). Half a facet, π/12, clears the corners as well, but
- * it squares two flats to the cell's edges, and at 37.67 mm those folded the socket floor
- * beside the pocket. Measured on 3,846 one-cell plates with a magnet from above, 37.67 to
- * 55 mm, shanks 1 to 5 mm and heads up to 1.15 times them, every 0.001 mm round these
- * sizes: 546 open before, and 1 now, a size the turn leaves alone; none came out worse.
- * On 1,800 random designs the turn moves, every kind of mount: 90 open before, 24 now. It
- * closed 83 and opened 17: 14 at 42 mm with a magnet from beneath under a deeper
- * counterbore, where one size in nine leaks unturned too, by the same slivers at the
- * magnet pocket's corners in the underside, and 3 in corner bosses, each at that one size
- * alone. */
+ * 55 mm, where the flats unturned miss them by 0.07 and 0.04. So where π/84 leaves a
+ * corner of either nearer than 0.005 mm, the turn is the one of 24 steps across those
+ * 30/7° that keeps them furthest off. Wherever the counterbore's corners call for a turn,
+ * no corner of either then comes within 0.0039 mm of a flat (6 and 8 mm magnets, heads up
+ * to 2.2 times the shank). And the magnet's corners call for one as the counterbore's do,
+ * since a shank no counterbore corner comes near can have a magnet's corner on a flat
+ * all the same: at 41.24 mm a 3 mm shank under a 7.3 mm magnet from above, a corner 0.4
+ * microns off a flat, left 26 edges a piece in the socket floor whatever the head, and
+ * 4.9911 under 7.246 with a 6 mm one left 44 at 49.02 mm. Wherever the magnet's
+ * corners stand 0.3 mm or more outside the shank's, none then comes within 0.0045 mm of
+ * a flat (magnets of 3 to 13 mm, heads up to 2.4 times the shank). Half a facet, π/12,
+ * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
+ * mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell plates
+ * with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times
+ * them, every 0.001 mm round these sizes: 546 open before, and 1 now, a size the turn
+ * leaves alone; none came out worse. On 1,800 random designs the turn moves, every kind
+ * of mount: 90 open before, 24 now. It closed 83 and opened 17: 14 at 42 mm with a magnet
+ * from beneath under a deeper counterbore, where one size in nine leaks unturned too, by
+ * the same slivers at the magnet pocket's corners in the underside, and 3 in corner
+ * bosses, each at that one size alone. The magnet's corners change the turn of none of
+ * those. On 1,500 random page designs that only a magnet's corner turns (34 to 56 mm;
+ * one cell, 2 x 2, and two pieces joined by dovetails or jigsaws; magnets of 3 to 12.7 mm
+ * either way up; a fifth on corner bosses): 66 bad before, 13 now. It closed 54 and
+ * opened 1, at that one size alone; of the 12 still bad, 10 are on corner bosses. */
 const MOUNT_BORE = {
   magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
             fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },
@@ -953,7 +962,8 @@ const MOUNT_BORE = {
           // how far to turn the shank under a counterbore headD across, in a magnet pocket
           // magnetR out at its corners or none (see above)
           turn: (d, headD, magnetR) => {
-            const { head, hole } = MOUNT_BORE, rs = [head.r(headD)];
+            // the magnet pocket's corners stand on the same rays as the counterbore's
+            const { head, hole } = MOUNT_BORE, rs = magnetR ? [head.r(headD), magnetR] : [head.r(headD)];
             const clear = (t) => {   // the nearest a corner comes to one of the flats' planes
               let g = Infinity;
               for (const R of rs) for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
@@ -961,7 +971,6 @@ const MOUNT_BORE = {
               return g;
             };
             if (clear(0) >= 0.005) return 0;
-            if (magnetR) rs.push(magnetR);   // the magnet pocket's corners stand on the same rays
             let best = Math.PI / 84, most = clear(best);
             if (most < 0.005) for (let j = 1; j < 24; j++) {
               const t = (Math.PI / 42) * j / 24, g = clear(t);
diff --git a/test/plate-audit.js b/test/plate-audit.js
index 7ce48f4..33f1d2d 100644
--- a/test/plate-audit.js
+++ b/test/plate-audit.js
@@ -1474,7 +1474,15 @@ function sectionArea(polys, z, dy) {
  * in the STL. A second run that comes out open throws now, so the plate fails to build, as
  * it did before, and the checks say so. These two rows are built as the page builds them
  * (its clearances and margins), and hold "threw in the seam repair, or watertight and
- * oriented": whatever builds them later has to build them whole. */
+ * oriented": whatever builds them later has to build them whole.
+ *
+ * With a bore's flats on its size, the same link cuts a counterbore 0.19 mm and a shank
+ * 0.1 mm wider, a cut the seam repair settles. It came out open instead, 26 edges a piece
+ * in the socket floor, and so did 38 of the 41 heads from 7.3 to 7.7 mm: a corner of the
+ * magnet's pocket stood 0.4 microns off the plane of a flat of the shank. The shank is
+ * turned for that now (MOUNT_BORE.hole.turn), so both rows build whole here, and so does
+ * the third, a 7.4 mm head, which main builds whole as well. Of those heads only 7.31 mm
+ * still leaks, its corners 0.001 mm inside the magnet's (#77). */
 console.log('\na counterbore whose ceiling three cut lines cross at one point (#76):');
 {
   const PLATE = { pitch: 39.07, drawerW: 170, drawerD: 90, bedW: 100, bedD: 400, marginMode: 'auto',
@@ -1508,7 +1516,8 @@ console.log('\na counterbore whose ceiling three cut lines cross at one point (#
                    connector: 'puzzle', clr: 0.2, screws: true, screwHoleD: 3, screwHeadDepth: 3.126,
                    screwHeadD: 7.504, magnets: true, magnetSide: 'top', magnetD: 7.3, magnetH: 2.25 };
   for (const [label, over] of [['41.24 mm jigsaw: 55 bad edges a piece', {}],
-                               ['2.264 mm magnet: folded twice', { magnetH: 2.264 }]]) {
+                               ['2.264 mm magnet: folded twice', { magnetH: 2.264 }],
+                               ['7.4 mm head', { screwHeadD: 7.4 }]]) {
     const b = build({ ...JIGSAW, ...over });
     const held = b.whole || /^healCsgSeams/.test(b.err || '');
     console.log(`  ${label.padEnd(38)} ${b.text}${held ? '' : '  NEITHER THREW NOR BUILT WHOLE'}`);

From 10f8cf8fcaacded25c1664b2578c9631333185c9 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 19:12:47 +0000
Subject: [PATCH 18/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html | 43 ++++++++++++++++++++++++++-----------------
 index.html      | 43 ++++++++++++++++++++++++++-----------------
 sw.js           |  2 +-
 3 files changed, 53 insertions(+), 35 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index 7a9155e..32e304b 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -2532,21 +2532,30 @@ <h2 id="drawersTitle">Your drawers</h2>
  * it was. A magnet pocket's corners stand on the same rays as the counterbore's, and π/84
  * could bring one of those onto a flat instead: 4.85 mm under 7.246 with a 6 mm magnet
  * from above left 35 edges in the socket floor at 49.02 mm, and 5.773 under 12.053 25 at
- * 55 mm, where the flats unturned miss them by 0.07 and 0.04 (unturned shanks meet them at
- * other sizes: 4.9911 under 7.246 leaves 44 at 49.02 mm, with no turn). So where π/84
- * leaves a corner of either nearer than 0.005 mm, the turn is the one of 24 steps across
- * those 30/7° that keeps them furthest off. Wherever the counterbore's corners call for a
- * turn, no corner of either then comes within 0.0039 mm of a flat (6 and 8 mm magnets,
- * heads up to 2.2 times the shank). Half a facet, π/12, clears the corners as well, but
- * it squares two flats to the cell's edges, and at 37.67 mm those folded the socket floor
- * beside the pocket. Measured on 3,846 one-cell plates with a magnet from above, 37.67 to
- * 55 mm, shanks 1 to 5 mm and heads up to 1.15 times them, every 0.001 mm round these
- * sizes: 546 open before, and 1 now, a size the turn leaves alone; none came out worse.
- * On 1,800 random designs the turn moves, every kind of mount: 90 open before, 24 now. It
- * closed 83 and opened 17: 14 at 42 mm with a magnet from beneath under a deeper
- * counterbore, where one size in nine leaks unturned too, by the same slivers at the
- * magnet pocket's corners in the underside, and 3 in corner bosses, each at that one size
- * alone. */
+ * 55 mm, where the flats unturned miss them by 0.07 and 0.04. So where π/84 leaves a
+ * corner of either nearer than 0.005 mm, the turn is the one of 24 steps across those
+ * 30/7° that keeps them furthest off. Wherever the counterbore's corners call for a turn,
+ * no corner of either then comes within 0.0039 mm of a flat (6 and 8 mm magnets, heads up
+ * to 2.2 times the shank). And the magnet's corners call for one as the counterbore's do,
+ * since a shank no counterbore corner comes near can have a magnet's corner on a flat
+ * all the same: at 41.24 mm a 3 mm shank under a 7.3 mm magnet from above, a corner 0.4
+ * microns off a flat, left 26 edges a piece in the socket floor whatever the head, and
+ * 4.9911 under 7.246 with a 6 mm one left 44 at 49.02 mm. Wherever the magnet's
+ * corners stand 0.3 mm or more outside the shank's, none then comes within 0.0045 mm of
+ * a flat (magnets of 3 to 13 mm, heads up to 2.4 times the shank). Half a facet, π/12,
+ * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
+ * mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell plates
+ * with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times
+ * them, every 0.001 mm round these sizes: 546 open before, and 1 now, a size the turn
+ * leaves alone; none came out worse. On 1,800 random designs the turn moves, every kind
+ * of mount: 90 open before, 24 now. It closed 83 and opened 17: 14 at 42 mm with a magnet
+ * from beneath under a deeper counterbore, where one size in nine leaks unturned too, by
+ * the same slivers at the magnet pocket's corners in the underside, and 3 in corner
+ * bosses, each at that one size alone. The magnet's corners change the turn of none of
+ * those. On 1,500 random page designs that only a magnet's corner turns (34 to 56 mm;
+ * one cell, 2 x 2, and two pieces joined by dovetails or jigsaws; magnets of 3 to 12.7 mm
+ * either way up; a fifth on corner bosses): 66 bad before, 13 now. It closed 54 and
+ * opened 1, at that one size alone; of the 12 still bad, 10 are on corner bosses. */
 const MOUNT_BORE = {
   magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
             fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },
@@ -2559,7 +2568,8 @@ <h2 id="drawersTitle">Your drawers</h2>
           // how far to turn the shank under a counterbore headD across, in a magnet pocket
           // magnetR out at its corners or none (see above)
           turn: (d, headD, magnetR) => {
-            const { head, hole } = MOUNT_BORE, rs = [head.r(headD)];
+            // the magnet pocket's corners stand on the same rays as the counterbore's
+            const { head, hole } = MOUNT_BORE, rs = magnetR ? [head.r(headD), magnetR] : [head.r(headD)];
             const clear = (t) => {   // the nearest a corner comes to one of the flats' planes
               let g = Infinity;
               for (const R of rs) for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
@@ -2567,7 +2577,6 @@ <h2 id="drawersTitle">Your drawers</h2>
               return g;
             };
             if (clear(0) >= 0.005) return 0;
-            if (magnetR) rs.push(magnetR);   // the magnet pocket's corners stand on the same rays
             let best = Math.PI / 84, most = clear(best);
             if (most < 0.005) for (let j = 1; j < 24; j++) {
               const t = (Math.PI / 42) * j / 24, g = clear(t);
diff --git a/index.html b/index.html
index c29a365..873668b 100644
--- a/index.html
+++ b/index.html
@@ -2319,21 +2319,30 @@ <h2 id="drawersTitle">Your drawers</h2>
  * it was. A magnet pocket's corners stand on the same rays as the counterbore's, and π/84
  * could bring one of those onto a flat instead: 4.85 mm under 7.246 with a 6 mm magnet
  * from above left 35 edges in the socket floor at 49.02 mm, and 5.773 under 12.053 25 at
- * 55 mm, where the flats unturned miss them by 0.07 and 0.04 (unturned shanks meet them at
- * other sizes: 4.9911 under 7.246 leaves 44 at 49.02 mm, with no turn). So where π/84
- * leaves a corner of either nearer than 0.005 mm, the turn is the one of 24 steps across
- * those 30/7° that keeps them furthest off. Wherever the counterbore's corners call for a
- * turn, no corner of either then comes within 0.0039 mm of a flat (6 and 8 mm magnets,
- * heads up to 2.2 times the shank). Half a facet, π/12, clears the corners as well, but
- * it squares two flats to the cell's edges, and at 37.67 mm those folded the socket floor
- * beside the pocket. Measured on 3,846 one-cell plates with a magnet from above, 37.67 to
- * 55 mm, shanks 1 to 5 mm and heads up to 1.15 times them, every 0.001 mm round these
- * sizes: 546 open before, and 1 now, a size the turn leaves alone; none came out worse.
- * On 1,800 random designs the turn moves, every kind of mount: 90 open before, 24 now. It
- * closed 83 and opened 17: 14 at 42 mm with a magnet from beneath under a deeper
- * counterbore, where one size in nine leaks unturned too, by the same slivers at the
- * magnet pocket's corners in the underside, and 3 in corner bosses, each at that one size
- * alone. */
+ * 55 mm, where the flats unturned miss them by 0.07 and 0.04. So where π/84 leaves a
+ * corner of either nearer than 0.005 mm, the turn is the one of 24 steps across those
+ * 30/7° that keeps them furthest off. Wherever the counterbore's corners call for a turn,
+ * no corner of either then comes within 0.0039 mm of a flat (6 and 8 mm magnets, heads up
+ * to 2.2 times the shank). And the magnet's corners call for one as the counterbore's do,
+ * since a shank no counterbore corner comes near can have a magnet's corner on a flat
+ * all the same: at 41.24 mm a 3 mm shank under a 7.3 mm magnet from above, a corner 0.4
+ * microns off a flat, left 26 edges a piece in the socket floor whatever the head, and
+ * 4.9911 under 7.246 with a 6 mm one left 44 at 49.02 mm. Wherever the magnet's
+ * corners stand 0.3 mm or more outside the shank's, none then comes within 0.0045 mm of
+ * a flat (magnets of 3 to 13 mm, heads up to 2.4 times the shank). Half a facet, π/12,
+ * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
+ * mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell plates
+ * with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times
+ * them, every 0.001 mm round these sizes: 546 open before, and 1 now, a size the turn
+ * leaves alone; none came out worse. On 1,800 random designs the turn moves, every kind
+ * of mount: 90 open before, 24 now. It closed 83 and opened 17: 14 at 42 mm with a magnet
+ * from beneath under a deeper counterbore, where one size in nine leaks unturned too, by
+ * the same slivers at the magnet pocket's corners in the underside, and 3 in corner
+ * bosses, each at that one size alone. The magnet's corners change the turn of none of
+ * those. On 1,500 random page designs that only a magnet's corner turns (34 to 56 mm;
+ * one cell, 2 x 2, and two pieces joined by dovetails or jigsaws; magnets of 3 to 12.7 mm
+ * either way up; a fifth on corner bosses): 66 bad before, 13 now. It closed 54 and
+ * opened 1, at that one size alone; of the 12 still bad, 10 are on corner bosses. */
 const MOUNT_BORE = {
   magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
             fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },
@@ -2346,7 +2355,8 @@ <h2 id="drawersTitle">Your drawers</h2>
           // how far to turn the shank under a counterbore headD across, in a magnet pocket
           // magnetR out at its corners or none (see above)
           turn: (d, headD, magnetR) => {
-            const { head, hole } = MOUNT_BORE, rs = [head.r(headD)];
+            // the magnet pocket's corners stand on the same rays as the counterbore's
+            const { head, hole } = MOUNT_BORE, rs = magnetR ? [head.r(headD), magnetR] : [head.r(headD)];
             const clear = (t) => {   // the nearest a corner comes to one of the flats' planes
               let g = Infinity;
               for (const R of rs) for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
@@ -2354,7 +2364,6 @@ <h2 id="drawersTitle">Your drawers</h2>
               return g;
             };
             if (clear(0) >= 0.005) return 0;
-            if (magnetR) rs.push(magnetR);   // the magnet pocket's corners stand on the same rays
             let best = Math.PI / 84, most = clear(best);
             if (most < 0.005) for (let j = 1; j < 24; j++) {
               const t = (Math.PI / 42) * j / 24, g = clear(t);
diff --git a/sw.js b/sw.js
index dd926af..d0d2e06 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "fcf7838578da";
+const VERSION = "418744ebfaa5";
 const FILES = [
   "./",
   "bins/",

From fdb25b1725fe1abe9e213f6538198a7bffbf105b Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 19:14:51 +0000
Subject: [PATCH 19/58] Keep the seam repair's guard tested with main's bores,
 now that the 41.24 mm link builds

With its shank turned, the review's 41.24 mm jigsaw link no longer runs out of passes
here, so #78's rows build whole and no longer reach the second run's guard. A fourth row
cuts main's bores for it, 7.504 cos(pi/14) and 3 cos(pi/12), which still run out of
passes and throw, here as on main. The comments that said the plate fails here now say
where it still does.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md                    | 5 +++--
 src/core.js                       | 4 +++-
 src/ui.js                         | 6 +++---
 test/plate-audit.js               | 9 +++++++--
 test/ui/plates-robustness.spec.js | 4 ++--
 5 files changed, 18 insertions(+), 10 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index 3569308..31cb56d 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -905,5 +905,6 @@ currently installed):
   counterbore's ceiling 2 microns from an edge of its own. Every piece with a seam on its
   left failed to build, for heads from 7.3 mm to the cap; 2.339 and 2.341 mm built. The
   second run is kept only if it comes out closed: a jigsaw plate at 41.24 mm with magnets
-  from above settles open after the merge, and fails to build as it did before rather
-  than going out with holes.
+  from above and main's bores (a 7.504 mm counterbore and a 3 mm shank, corners on the
+  sizes) settles open after the merge, and fails to build as it did before rather than
+  going out with holes.
diff --git a/src/core.js b/src/core.js
index f6d8902..094fb80 100644
--- a/src/core.js
+++ b/src/core.js
@@ -402,7 +402,9 @@ function healCsgSeams(polys, again) {
      every soup, but not every one. None of 1,100 random plates of every joint and mount
      ran out; the turned cutters of a cell cut again do on a few engine-only cells (see
      the fastener cut in buildPiece), and so does a jigsaw plate at 41.24 mm with magnets
-     from above and a 3.126 mm counterbore, on the first cut of both its pieces.
+     from above and a 3.126 mm counterbore, on the first cut of both its pieces, with
+     main's 7.504 mm head over a 3 mm shank (the bores 7.504 cos(π/14) and 3 cos(π/12) here,
+     where a bore's flats stand on its size).
 
      The second run is kept only if it comes out closed, and that jigsaw plate is why.
      The merge lets its repair settle, but open, and returned that was 55 bad edges on
diff --git a/src/ui.js b/src/ui.js
index 1c720c0..626b53a 100644
--- a/src/ui.js
+++ b/src/ui.js
@@ -531,9 +531,9 @@ function warningsList() {
      under the cut map. Drawn as an error but not flagged `err`, which would stop the next
      build as well, and the next build, on any change, is what clears it. It says Download
      is off, not that nothing can be downloaded: the pieces built before it keep their own
-     STL buttons in the piece table. And it promises no size that gets past it: the 41.24 mm
-     jigsaw plate in plate-audit.js fails with a 7.504 mm head and builds with holes at
-     7.502 mm, on main as well. */
+     STL buttons in the piece table. And it promises no size that gets past it: a size a
+     hundredth off one that fails can build with holes, as the 41.24 mm jigsaw plate in
+     plate-audit.js did at 7.502 mm on main, beside a 7.504 mm head that failed. */
   if (buildFailed)
     out.push({ failed: true, t: `Piece ${buildFailed} could not be built, so the build stopped ` +
       'there and Download is off. That is a fault in this tool, not in the design; moving a cut ' +
diff --git a/test/plate-audit.js b/test/plate-audit.js
index 33f1d2d..0d129ba 100644
--- a/test/plate-audit.js
+++ b/test/plate-audit.js
@@ -1482,7 +1482,10 @@ function sectionArea(polys, z, dy) {
  * magnet's pocket stood 0.4 microns off the plane of a flat of the shank. The shank is
  * turned for that now (MOUNT_BORE.hole.turn), so both rows build whole here, and so does
  * the third, a 7.4 mm head, which main builds whole as well. Of those heads only 7.31 mm
- * still leaks, its corners 0.001 mm inside the magnet's (#77). */
+ * still leaks, its corners 0.001 mm inside the magnet's (#77). The fourth cuts main's
+ * bores, the head and shank whose polygons are main's 7.504 and 3 mm ones, 7.504 cos(π/14)
+ * and 3 cos(π/12): it runs out of passes here as on main and throws, so the second run's
+ * guard is still tested. */
 console.log('\na counterbore whose ceiling three cut lines cross at one point (#76):');
 {
   const PLATE = { pitch: 39.07, drawerW: 170, drawerD: 90, bedW: 100, bedD: 400, marginMode: 'auto',
@@ -1517,7 +1520,9 @@ console.log('\na counterbore whose ceiling three cut lines cross at one point (#
                    screwHeadD: 7.504, magnets: true, magnetSide: 'top', magnetD: 7.3, magnetH: 2.25 };
   for (const [label, over] of [['41.24 mm jigsaw: 55 bad edges a piece', {}],
                                ['2.264 mm magnet: folded twice', { magnetH: 2.264 }],
-                               ['7.4 mm head', { screwHeadD: 7.4 }]]) {
+                               ['7.4 mm head', { screwHeadD: 7.4 }],
+                               ["main's bores", { screwHeadD: 7.504 * Math.cos(Math.PI / 14),
+                                                  screwHoleD: 3 * Math.cos(Math.PI / 12) }]]) {
     const b = build({ ...JIGSAW, ...over });
     const held = b.whole || /^healCsgSeams/.test(b.err || '');
     console.log(`  ${label.padEnd(38)} ${b.text}${held ? '' : '  NEITHER THREW NOR BUILT WHOLE'}`);
diff --git a/test/ui/plates-robustness.spec.js b/test/ui/plates-robustness.spec.js
index 7025f49..1f5455a 100644
--- a/test/ui/plates-robustness.spec.js
+++ b/test/ui/plates-robustness.spec.js
@@ -529,8 +529,8 @@ test.describe('a screw head that does not clear its shank is cut as none', () =>
    said so already, but the list under the cut map, where a design is read for what is
    wrong with it, was empty, so Download was off with no reason given there. The failure is
    forced rather than taken from a design that fails, which would tie this test to an engine
-   bug a later fix should remove: #76's plate builds now (below), and the 41.24 mm jigsaw
-   plate in plate-audit.js still fails in the seam repair, as it does on main. */
+   bug a later fix should remove: #76's plate builds now (below), and so does the 41.24 mm
+   jigsaw plate in plate-audit.js, which failed in the seam repair on main. */
 test('a failed build says so in the checks, the table and the dialog, and Download goes off',
   async ({ page }) => {
     const pageErrors = [];

From d617b5e334b8d371cc555a37352f577a95110b66 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 19:14:52 +0000
Subject: [PATCH 20/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html |  4 +++-
 index.html      | 10 ++++++----
 sw.js           |  2 +-
 3 files changed, 10 insertions(+), 6 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index 32e304b..73ab6fb 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -2008,7 +2008,9 @@ <h2 id="drawersTitle">Your drawers</h2>
      every soup, but not every one. None of 1,100 random plates of every joint and mount
      ran out; the turned cutters of a cell cut again do on a few engine-only cells (see
      the fastener cut in buildPiece), and so does a jigsaw plate at 41.24 mm with magnets
-     from above and a 3.126 mm counterbore, on the first cut of both its pieces.
+     from above and a 3.126 mm counterbore, on the first cut of both its pieces, with
+     main's 7.504 mm head over a 3 mm shank (the bores 7.504 cos(π/14) and 3 cos(π/12) here,
+     where a bore's flats stand on its size).
 
      The second run is kept only if it comes out closed, and that jigsaw plate is why.
      The merge lets its repair settle, but open, and returned that was 55 bad edges on
diff --git a/index.html b/index.html
index 873668b..fdf28b8 100644
--- a/index.html
+++ b/index.html
@@ -1795,7 +1795,9 @@ <h2 id="drawersTitle">Your drawers</h2>
      every soup, but not every one. None of 1,100 random plates of every joint and mount
      ran out; the turned cutters of a cell cut again do on a few engine-only cells (see
      the fastener cut in buildPiece), and so does a jigsaw plate at 41.24 mm with magnets
-     from above and a 3.126 mm counterbore, on the first cut of both its pieces.
+     from above and a 3.126 mm counterbore, on the first cut of both its pieces, with
+     main's 7.504 mm head over a 3 mm shank (the bores 7.504 cos(π/14) and 3 cos(π/12) here,
+     where a bore's flats stand on its size).
 
      The second run is kept only if it comes out closed, and that jigsaw plate is why.
      The merge lets its repair settle, but open, and returned that was 55 bad edges on
@@ -8228,9 +8230,9 @@ <h2 id="drawersTitle">Your drawers</h2>
      under the cut map. Drawn as an error but not flagged `err`, which would stop the next
      build as well, and the next build, on any change, is what clears it. It says Download
      is off, not that nothing can be downloaded: the pieces built before it keep their own
-     STL buttons in the piece table. And it promises no size that gets past it: the 41.24 mm
-     jigsaw plate in plate-audit.js fails with a 7.504 mm head and builds with holes at
-     7.502 mm, on main as well. */
+     STL buttons in the piece table. And it promises no size that gets past it: a size a
+     hundredth off one that fails can build with holes, as the 41.24 mm jigsaw plate in
+     plate-audit.js did at 7.502 mm on main, beside a 7.504 mm head that failed. */
   if (buildFailed)
     out.push({ failed: true, t: `Piece ${buildFailed} could not be built, so the build stopped ` +
       'there and Download is off. That is a fault in this tool, not in the design; moving a cut ' +
diff --git a/sw.js b/sw.js
index d0d2e06..e7ac401 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "418744ebfaa5";
+const VERSION = "624cd4380d11";
 const FILES = [
   "./",
   "bins/",

From 1e09bc54edf0d6bea86988341342560775f86e3c Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 20:30:34 +0000
Subject: [PATCH 21/58] Say at the screw head field when a head too narrow to
 clear its shank is cut as none

A head wider than the hole that does not clear the shank's corners has been
cut as no counterbore since #73, and only the README said so. A line under
the screw fields now says it, and from what size a counterbore is cut, while
neither size is refused. The README line reads the same helpers.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 src/template.html                 |  1 +
 src/ui.js                         | 23 ++++++++++++++++++-----
 test/ui/plates-robustness.spec.js | 14 ++++++++++----
 3 files changed, 29 insertions(+), 9 deletions(-)

diff --git a/src/template.html b/src/template.html
index bbe51a2..0ba249d 100644
--- a/src/template.html
+++ b/src/template.html
@@ -283,6 +283,7 @@ <h2 class="ph"><button type="button" aria-expanded="true" aria-controls="b-mag">
       <label class="f"><b>Head depth</b><input id="screwHeadDepth" type="number" step="0.1" min="0.5" max="10" value="2" aria-describedby="errScrew"></label>
     </div>
     <span class="hint" id="errScrew" style="color:var(--red)" hidden></span>
+    <span class="hint" id="screwHeadHint" hidden></span>
     <label class="f" id="baseModeRow" style="display:none"><b>Mounting base</b>
       <select id="baseMode">
         <option value="solid">Solid floor — at least 2.8 mm base under everything</option>
diff --git a/src/ui.js b/src/ui.js
index f725ff7..373fcd9 100644
--- a/src/ui.js
+++ b/src/ui.js
@@ -322,6 +322,12 @@ function showFieldErrors() {
   }
 }
 
+/* A head wider than the hole that does not clear its corners is cut as no counterbore
+   (MOUNT_BORE.head.cuts, #73); and the size one is cut from, to the hundredth above. */
+const headCutAsNone = () => state.screwHeadD > state.screwHoleD &&
+  !MOUNT_BORE.head.cuts(state.screwHeadD, state.screwHoleD);
+const headClearsFrom = (hole) => Math.ceil(MOUNT_BORE.head.over(hole) * 100 - 1e-9) / 100;
+
 function readControls() {
   fieldErrors.clear(); noRoom.clear();
   /* The switches before the numbers: which ranges apply, and how wide they are, depend
@@ -392,6 +398,15 @@ function readControls() {
   if (halfOpt && halfOpt.textContent !== halfText) halfOpt.textContent = halfText;
   $('magRow').style.display = state.magnets ? '' : 'none';
   $('screwRow').style.display = state.screws ? '' : 'none';
+  /* A head wider than the hole that does not clear its corners is cut as none (#73); the
+     README said so, and nothing at the field did. Not while either size is refused: the
+     red line under the fields says what to do first. */
+  const noBore = state.screws && headCutAsNone() &&
+    !['screwHoleD', 'screwHeadD'].some((id) => fieldErrors.has(id) || noRoom.has(id));
+  $('screwHeadHint').hidden = !noBore;
+  if (noBore) $('screwHeadHint').textContent = `A ${state.screwHeadD} mm head does not clear ` +
+    `the corners of a ${state.screwHoleD} mm hole, so no counterbore is cut. One is from ` +
+    `${headClearsFrom(state.screwHoleD)} mm.`;
   $('connHintDove').style.display = state.connector === 'dovetail' ? '' : 'none';
   $('connHintPuzzle').style.display = state.connector === 'puzzle' ? '' : 'none';
   // Bowtie and puzzle key shared one hint, so picking between them meant reading the
@@ -1844,12 +1859,10 @@ function readmeText() {
   /* A head that does not clear the hole's corners is cut as none (MOUNT_BORE in core.js),
      and one no wider than the hole always was; the README says so, and for a head that
      was meant as a counterbore, the size that would be one. */
-  const { head } = MOUNT_BORE;
   if (state.screws) lines.push(`Screws: ${state.screwHoleD} mm holes, ` +
-    (head.cuts(state.screwHeadD, state.screwHoleD) ? `${state.screwHeadD} mm counterbore`
-      : 'no counterbore' + (state.screwHeadD <= state.screwHoleD ? ''
-        : ` (a head clears a ${state.screwHoleD} mm hole from ` +
-          `${Math.ceil(head.over(state.screwHoleD) * 100 - 1e-9) / 100} mm)`)));
+    (MOUNT_BORE.head.cuts(state.screwHeadD, state.screwHoleD) ? `${state.screwHeadD} mm counterbore`
+      : 'no counterbore' + (headCutAsNone()
+        ? ` (a head clears a ${state.screwHoleD} mm hole from ${headClearsFrom(state.screwHoleD)} mm)` : '')));
   /* The figure the dialog quotes, said the way it says it, with the price it was worked
      out at: the README is read away from the page. The ZIP is only made once every piece
      exists, so there is always a total to give. */
diff --git a/test/ui/plates-robustness.spec.js b/test/ui/plates-robustness.spec.js
index 0c62f46..62a996a 100644
--- a/test/ui/plates-robustness.spec.js
+++ b/test/ui/plates-robustness.spec.js
@@ -561,13 +561,17 @@ test.describe('the clearance ceiling is the joint\'s and the pitch\'s', () => {
    corners is cut as none now, as one no wider than the hole always was (MOUNT_BORE in
    core.js): within 3.5% of the hole it is no seat for a screw head. So the link builds
    with Download on and nothing in Checks, and the README says there is no counterbore
-   and from what size there would be one. 2.1 mm clears a 2 mm hole and is cut. */
+   and from what size there would be one, as does a line under the fields. 2.1 mm clears a
+   2 mm hole and is cut; 2 mm is no wider than the hole, and needs no word. */
 test.describe('a screw head that does not clear its shank is cut as none', () => {
   const AT = '#pi=37.67&w=150.68&d=75.34&mm=custom&ml=0&mr=0&mf=0&mb=0&bw=91.34&bd=400' +
     '&sc=1&sh=2&cn=none';
-  for (const [sd, says] of [
-    ['2.03', 'Screws: 2 mm holes, no counterbore (a head clears a 2 mm hole from 2.09 mm)'],
-    ['2.1', 'Screws: 2 mm holes, 2.1 mm counterbore'],
+  for (const [sd, says, hint] of [
+    ['2.03', 'Screws: 2 mm holes, no counterbore (a head clears a 2 mm hole from 2.09 mm)',
+      'A 2.03 mm head does not clear the corners of a 2 mm hole, so no counterbore is cut. ' +
+      'One is from 2.09 mm.'],
+    ['2.1', 'Screws: 2 mm holes, 2.1 mm counterbore', null],
+    ['2', 'Screws: 2 mm holes, no counterbore', null],
   ])
     test(`a ${sd} mm head over a 2 mm shank builds, and the README says what was cut`,
       async ({ page }) => {
@@ -577,6 +581,8 @@ test.describe('a screw head that does not clear its shank is cut as none', () =>
         expect(await exportOff(page)).toBe(false);
         const readme = (await page.evaluate(() => readmeText())).split('\n');
         expect(readme).toContain(says);
+        expect(await shown(page, 'screwHeadHint')).toBe(!!hint);
+        if (hint) expect(await text(page, 'screwHeadHint')).toBe(hint);
         expect(errors).toEqual([]);
       });
 });

From 749bc57abb1e70bccdb006f999d713c79c14b8f0 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 20:30:59 +0000
Subject: [PATCH 22/58] Refuse a screw hole the magnet pocket it runs through
 does not clear

A shank has to clear the magnet pocket on its axis as it would a counterbore,
its corners 0.005 mm inside the pocket's flats. Any wider, the 14 flats cross
the 12 corners and the walls weave, and no turn of the shank kept them closed:
5 mm under a 5.1 mm magnet and a 5.4 mm head left 47 open edges at 42 mm
turned for the magnet's corners, and turning for the shank's corners on the
pocket's flats as well, which closed it, opened 3.0177 under a 3 mm magnet at
43.43 mm (58 edges). So mountLimits caps the shank there (throughMagnet), the
field says why, and the turn stays as it was: the magnet pocket's corners and
the counterbore's call for it alike. That also takes the shanks the turn's
clearance did not hold for (a magnet narrower than the shank) and #77's
5.85 mm shanks under a 6 mm magnet at 55 mm.

The page reads the shank again after the head and the magnet, whose sizes its
turn and that cap go by; read before them only, a magnet pasted in was
measured against the one before it. A turned shank's reach is kept on each
site, so the second read on the same cuts is quick (3.6 ms to 0.7 on a
30 x 30 puzzle plate).

The figures in MOUNT_BORE's comment are re-measured on the merged tree: 3,846
one-cell plates 546 open to 1, none worse; 1,800 designs a counterbore's
corner turns 85 to 10 (80 closed, 5 opened); 1,500 that only a magnet's corner
turns 41 open or folded to 6 (40 closed, 5 opened, each for a size or two).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md                    |  14 ++--
 src/core.js                       | 125 ++++++++++++++++++------------
 src/ui.js                         |  14 +++-
 test/plate-audit.js               |  33 +++++++-
 test/ui/plates-robustness.spec.js |  30 +++++++
 5 files changed, 159 insertions(+), 57 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index de16f16..bb72db8 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -767,11 +767,15 @@ currently installed):
   shank under a 7.3 mm magnet from above, whose corner stood 0.4 microns off a flat). The
   two pockets' corners stand on the same rays, so where π/84 would bring one within 0.005
   mm of a flat, the shank takes the step of the 24 across those 30/7° that keeps both
-  furthest off. Turned, no corner of either comes within 0.0039 mm of a flat where the
-  magnet stands 0.3 mm or more outside the shank's corners, and a shank no corner of
-  either came near is cut as before. `MOUNT_BORE.screw` says whether a design's
-  counterbore is cut and how far its shank is turned, for the cutter and for
-  `mountLimits`, which measures that shank turned.
+  furthest off. A shank has to clear the magnet pocket it runs through as it would a
+  counterbore, and `mountLimits` refuses a wider one, which the field says
+  (`throughMagnet`): the pocket's flats cross the shank's corners, the walls weave, and
+  no turn kept them closed (5 mm under a 5.1 mm magnet and a 5.4 head at 42 mm left 47
+  edges turned for the magnet's corners). Turned, no corner of either comes within
+  0.0039 mm of a flat, and a shank no corner came near is cut as before. The page reads
+  the shank again after the head and the magnet, since its turn and that cap go by both.
+  `MOUNT_BORE.screw` says whether a design's counterbore is cut and how far its shank is
+  turned, for the cutter and for `mountLimits`, which measures that shank turned.
 - **The socket's corner clearance is not uniform.** Known, documented, deliberately not
   fixed — see [socket-clearance.md](socket-clearance.md).
 - **The plate's outer corner radius has a ceiling, and it is the socket's.** Both the
diff --git a/src/core.js b/src/core.js
index 6a33946..804af71 100644
--- a/src/core.js
+++ b/src/core.js
@@ -911,47 +911,50 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * always was: within 3.5% of the hole it is no seat for a screw head, and all it would
  * add is slivers between the shank's corners.
  *
- * Under a counterbore the shank is turned a little about its axis (`turn`, #74) where one
- * of the counterbore's corners would stand on one of its flats carried on past the shank.
- * The BSP splits what it meets along a flat's whole plane, not just the flat: the floor
- * of a magnet pocket from above, which is a ring round the counterbore, or the roof of one
- * from beneath round a counterbore deeper than it. A split a micron or two from the
- * corner was welded onto it (healCsgSeams), which bent the counterbore's wall off its
- * plane, and the plate came out open by the dozen round every site: 136 edges a piece at
- * 42 mm for main's 1.0353 mm shank under a 1.0873 head with a 6 x 2 magnet from above, 36
- * a cell for 1.06 over 1 here, 62 for 3.305 over 3, 55 for 5.4959 over 3 under an 8 x 3
- * magnet. Such sizes come every few hundredths at any ratio of head to shank. A corner
- * meets a flat's plane at an odd multiple of 15/7° off the flat's normal; turned π/84,
- * 15/7°, it meets them at the even ones, so a size that put a corner on a flat puts it
- * midway between two. The turn is taken where a corner comes nearer than 0.005 mm
- * unturned and the turn leaves it further off, and a shank no corner came near is cut as
- * it was. A magnet pocket's corners stand on the same rays as the counterbore's, and π/84
- * could bring one of those onto a flat instead: 4.85 mm under 7.246 with a 6 mm magnet
- * from above left 35 edges in the socket floor at 49.02 mm, and 5.773 under 12.053 25 at
- * 55 mm, where the flats unturned miss them by 0.07 and 0.04. So where π/84 leaves a
- * corner of either nearer than 0.005 mm, the turn is the one of 24 steps across those
- * 30/7° that keeps them furthest off. Wherever the counterbore's corners call for a turn,
- * no corner of either then comes within 0.0039 mm of a flat (6 and 8 mm magnets, heads up
- * to 2.2 times the shank). And the magnet's corners call for one as the counterbore's do,
- * since a shank no counterbore corner comes near can have a magnet's corner on a flat
- * all the same: at 41.24 mm a 3 mm shank under a 7.3 mm magnet from above, a corner 0.4
- * microns off a flat, left 26 edges a piece in the socket floor whatever the head, and
- * 4.9911 under 7.246 with a 6 mm one left 44 at 49.02 mm. Wherever the magnet's
- * corners stand 0.3 mm or more outside the shank's, none then comes within 0.0045 mm of
- * a flat (magnets of 3 to 13 mm, heads up to 2.4 times the shank). Half a facet, π/12,
- * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
- * mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell plates
- * with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times
- * them, every 0.001 mm round these sizes: 546 open before, and 1 now, a size the turn
- * leaves alone; none came out worse. On 1,800 random designs the turn moves, every kind
- * of mount: 90 open before, 24 now. It closed 83 and opened 17: 14 at 42 mm with a magnet
- * from beneath under a deeper counterbore, where one size in nine leaks unturned too, by
- * the same slivers at the magnet pocket's corners in the underside, and 3 in corner
- * bosses, each at that one size alone. The magnet's corners change the turn of none of
- * those. On 1,500 random page designs that only a magnet's corner turns (34 to 56 mm;
- * one cell, 2 x 2, and two pieces joined by dovetails or jigsaws; magnets of 3 to 12.7 mm
- * either way up; a fifth on corner bosses): 66 bad before, 13 now. It closed 54 and
- * opened 1, at that one size alone; of the 12 still bad, 10 are on corner bosses. */
+ * Under a counterbore the shank is turned a little about its axis (`turn`, #74) where a
+ * corner of the counterbore or of the magnet pocket would stand on one of its flats
+ * carried on past the shank. The BSP splits what it meets along a flat's whole plane, not
+ * just the flat: the floor of a magnet pocket from above, which is a ring round the
+ * counterbore, or the roof of one from beneath round a counterbore deeper than it. A
+ * split a micron or two from the corner was welded onto it (healCsgSeams), which bent the
+ * counterbore's wall off its plane, and the plate came out open by the dozen round every
+ * site: 136 edges a piece at 42 mm for main's 1.0353 mm shank under a 1.0873 head with a
+ * 6 x 2 magnet from above, 36 a cell for 1.06 over 1 here, 62 for 3.305 over 3, 55 for
+ * 5.4959 over 3 under an 8 x 3 magnet. Such sizes come every few hundredths at any ratio
+ * of head to shank. A corner meets a flat's plane at an odd multiple of 15/7° off the
+ * flat's normal; turned π/84, 15/7°, it meets them at the even ones, so a size that put a
+ * corner on a flat puts it midway between two. The turn is taken where a corner comes
+ * nearer than 0.005 mm unturned and the turn leaves it further off, and a shank no corner
+ * came near is cut as it was. The magnet pocket's corners stand on the same rays as the
+ * counterbore's, and π/84 could bring one of those onto a flat instead: 4.85 mm under
+ * 7.246 with a 6 mm magnet from above left 35 edges in the socket floor at 49.02 mm, and
+ * 5.773 under 12.053 25 at 55 mm, where the flats unturned miss them by 0.07 and 0.04. So
+ * where π/84 leaves a corner of either nearer than 0.005 mm, the turn is the one of 24
+ * steps across those 30/7° that keeps them furthest off. And a magnet's corner calls for
+ * a turn as a counterbore's does, since a shank no counterbore corner comes near can have
+ * a magnet's corner on a flat all the same: at 41.24 mm a 3 mm shank under a 7.3 mm
+ * magnet from above, a corner 0.4 microns off a flat, left 26 edges a piece in the socket
+ * floor whatever the head, and 4.9911 under 7.246 with a 6 mm one left 44 at 49.02 mm. A
+ * shank the magnet pocket does not clear as it would a counterbore is refused
+ * (mountLimits): the two walls weave, and no turn kept them closed. On every shank taken,
+ * no corner of either then comes within 0.0039 mm of a flat, whichever called the turn
+ * (magnets of 3 to 13 mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every
+ * 0.001 mm round the sizes that put a corner on a flat). Half a facet, π/12, clears the
+ * corners as well, but it squares two flats to the cell's edges, and at 37.67 mm those
+ * folded the socket floor beside the pocket. Measured on 3,846 one-cell plates with a
+ * magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times them,
+ * every 0.001 mm round these sizes: 546 open before, and 1 now, a size the turn leaves
+ * alone; none came out worse. On 1,800 random designs a counterbore's corner turns, every
+ * kind of mount: 85 open before, 10 now. It closed 80 and opened 5: 3 at 42 mm with a
+ * magnet from beneath under a deeper counterbore, where one size in nine leaks unturned
+ * too, by the same slivers at the magnet pocket's corners in the underside; 1 in a corner
+ * boss, at that one size alone; and 1 at 42 mm under a magnet from above, open for a few
+ * thousandths round 2.114 under 2.253. The magnet's corners change the turn of none of
+ * the 1,800. On 1,500 random page designs that only a magnet's corner turns (34 to 56
+ * mm; one cell, 2 x 2, and two pieces joined by dovetails or jigsaws; magnets of 3 to
+ * 12.7 mm either way up; a fifth on corner bosses): 41 open or folded before, 6 now. It
+ * closed 40 and opened 5, each for a size or two (2 patches 0.002 mm wide, 2 single
+ * sizes, and 1 whose neighbours fold unturned too); the sixth folds the same unturned. */
 const MOUNT_BORE = {
   magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
             fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },
@@ -1031,7 +1034,8 @@ function fastenerCutter(cfg, magZ0, magZ1, shankTop) {
     const { counterbore, turn: t } = MOUNT_BORE.screw(cfg);
     if (counterbore)
       add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
-    // the shank, turned off the counterbore's corners where one would stand on a flat (#74)
+    // the shank, turned where a corner of the counterbore or the magnet pocket would stand
+    // on one of its flats (#74)
     const shank = cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides);
     const c = Math.cos(t), s = Math.sin(t), turn = (v) => [v[0]*c - v[1]*s, v[0]*s + v[1]*c, v[2]];
     add(t ? shank.map((p) => ({ verts: p.verts.map(turn), plane: { n: turn(p.plane.n), w: p.plane.w } }))
@@ -2813,6 +2817,18 @@ function mountLimits(cfg, layout, known) {
   const shankTurn = cfg.screws ? MOUNT_BORE.screw(cfg).turn : 0;
   // the room the cell, the floor or a boss leaves, and the hole beside
   const own = { magnetD: fit(cfg.magnetSide === 'top' ? top : under), screwHoleD: fit(top), screwHeadD: fit(under) };
+  /* A shank runs up the magnet pocket's axis, and has to clear it as it would a
+     counterbore (MOUNT_BORE.head.over): its corners 0.005 mm inside the pocket's flats.
+     Any wider, and the pocket's 14 flats cross the shank's 12 corners, the walls weave
+     round each other as a counterbore's under the line would, and the magnet has no
+     ledge to stop against. No turn of the shank kept such a pair closed: 5 mm under a
+     5.1 mm magnet from above and a 5.4 mm head, closed unturned at 42 mm, left 47 open
+     edges turned for the magnet's corners; turned for the shank's corners on the
+     pocket's flats as well it closed, but 3.0177 under a 3 mm magnet and a 6.557 head at
+     43.43 mm, closed the other two ways, then left 58. */
+  const ledge = cfg.magnets
+    ? MOUNT_BORE.hole.fits(MOUNT_BORE.magnet.r(cfg.magnetD) * Math.cos(Math.PI / MOUNT_BORE.magnet.sides) - 0.005)
+    : Infinity;
   // a dovetail's notch takes a pocket from beneath that breaks into it; every other cut does not
   const notch = cfg.connector === 'dovetail';
   /* The cuts are measured where they stand in the cells, and a corner boss's stands two
@@ -2835,9 +2851,17 @@ function mountLimits(cfg, layout, known) {
      into, but not stop just short of. */
   const jointFor = (f) => {
     const { sides, fits } = BORE[f];
-    // the room a bore has, measured again for a shank turned under its counterbore
+    /* the room a bore has, measured again for a shank turned under its counterbore, and
+       kept on the site by its turn: the page asks again on the same cuts (`known`) once
+       the head and the magnet are read, and on a 30 x 30 puzzle plate that took 3.6 ms */
     const turn = f === 'screwHoleD' ? shankTurn : 0;
-    const reach = (c, s) => !turn ? s.bore[sides] : s.room > 0 ? boreReach(sides, c.segs, s.x, s.y, turn) : s.room;
+    const reach = (c, s) => {
+      if (!turn) return s.bore[sides];
+      if (!(s.room > 0)) return s.room;
+      const kept = s.turned || (s.turned = new Map());
+      if (!kept.has(turn)) kept.set(turn, boreReach(sides, c.segs, s.x, s.y, turn));
+      return kept.get(turn);
+    };
     const above = f === 'magnetD' && cfg.magnetSide === 'top';
     // how high a pocket from beneath goes; a shank goes through
     const ceiling = f === 'magnetD' ? cfg.magnetH : f === 'screwHeadD' ? cfg.screwHeadDepth : Infinity;
@@ -2863,10 +2887,13 @@ function mountLimits(cfg, layout, known) {
     return { cap, why, near };
   };
   const sizes = {}, joint = {}, gaps = {};
+  let byMagnet = false;
   for (const f of ['magnetD', 'screwHoleD', 'screwHeadD']) {
     const cell = BORE[f].fits(own[f]), J = jointFor(f);
-    let size = r10(Math.min(cell, J.cap));
-    joint[f] = J.cap < cell && J.why;
+    const most = f === 'screwHoleD' ? Math.min(cell, ledge) : cell;
+    let size = r10(Math.min(most, J.cap));
+    joint[f] = J.cap < most && J.why;
+    if (f === 'screwHoleD') byMagnet = ledge < cell && !joint[f];
     /* The sizes `near` refuses, out to the hundredths either side, since the field takes
        hundredths: each gap is [from, to], both taken. A window is about 0.02 mm wide, so
        rounded out to the tenths as the cap is, it refused up to a tenth that builds clean
@@ -2881,7 +2908,7 @@ function mountLimits(cfg, layout, known) {
     gaps[f] = [];
     for (const [from, to] of out) {
       if (from >= size) break;
-      if (to > size) { size = from; joint[f] = 'near'; break; }
+      if (to > size) { size = from; joint[f] = 'near'; if (f === 'screwHoleD') byMagnet = false; break; }
       gaps[f].push([from, to]);
     }
     sizes[f] = size;
@@ -2894,8 +2921,10 @@ function mountLimits(cfg, layout, known) {
     depth: bosses ? r10(BOSS_H - MOUNT_SKIN) : Infinity,
     // which of the sizes the cut beside it stops, rather than the floor, cell or boss
     beside: { magnetD: own.magnetD === beside && !joint.magnetD,
-              screwHoleD: own.screwHoleD === beside && !joint.screwHoleD,
+              screwHoleD: own.screwHoleD === beside && !joint.screwHoleD && !byMagnet,
               screwHeadD: own.screwHeadD === beside && !joint.screwHeadD },
+    // whether the magnet pocket the shank runs through stops it, before all of those
+    throughMagnet: byMagnet,
     // and which a joint's cut stops, before any of those, and how (jointFor)
     joint,
     // sizes under the largest refused all the same, as [from, to] with both ends taken
diff --git a/src/ui.js b/src/ui.js
index 373fcd9..1049816 100644
--- a/src/ui.js
+++ b/src/ui.js
@@ -106,8 +106,11 @@ const cutsNamed = () => `${['dovetail', 'puzzle'].includes(state.connector) ? 'n
    stands into a boss's pocket (#75). Nor where the bosses are buried in the floor a
    joint needs (cornerBosses): a key put in from above, in the walls, needs none, so
    taking the hint would stand them up again, and the cup in their pockets. Only a floor
-   asked for (bottomPad) keeps them buried whatever the joint. */
+   asked for (bottomPad) keeps them buried whatever the joint. A screw hole the magnet
+   pocket stops is stopped whatever the pitch, so that is all it says. */
 const mountWhy = (opens, field) => {
+  if (field === 'screwHoleD' && mount().throughMagnet)
+    return `— it runs through the ${state.magnetD} mm magnet's pocket, and has to be narrower than the pocket`;
   const joint = mount().joint[field];
   const cuts = cutsNamed();
   return `${atPitch()} — mounting holes sit ` +
@@ -380,6 +383,15 @@ function readControls() {
     if (id === 'magnetD' && mountNow) mountNow = mountLimits(state, mountLayout, mountNow.cuts);
     state[id] = readNumber(id);
   }
+  /* And the shank once more, on the sizes just read: how far it is turned goes by the head
+     and the magnet (MOUNT_BORE.screw), and the magnet pocket it runs through caps it
+     (mountLimits' throughMagnet), both read after it. Read before them only, a 5 mm hole
+     stood under a 5.1 mm magnet typed in after it, refused only at the next keystroke. */
+  if (state.screws && mountNow) {
+    mountNow = mountLimits(state, mountLayout, mountNow.cuts);
+    fieldErrors.delete('screwHoleD'); noRoom.delete('screwHoleD');
+    state.screwHoleD = readNumber('screwHoleD');
+  }
   // and Checks says what is wrong in the panel's order, not the order it was read in
   for (const m of [fieldErrors, noRoom]) {
     const read = new Map(m);
diff --git a/test/plate-audit.js b/test/plate-audit.js
index 5d7b159..a7d3053 100644
--- a/test/plate-audit.js
+++ b/test/plate-audit.js
@@ -2140,10 +2140,11 @@ console.log('\nthe other limits, built at their ends:');
      flats on the sizes, are a 1 mm shank under 1.06 (36 a cell). 4.25 over 4 left 26 and
      3.305 over 3 62; 5.4959 over 3 under an 8 x 3 magnet, a head nearly twice the shank,
      55; and from beneath, the magnet's roof round a counterbore deeper than it, 1.06 over
-     1 left 12. The shank is turned off the corners now (MOUNT_BORE.hole.turn). The last
+     1 left 12. The shank is turned off the corners now (MOUNT_BORE.hole.turn). The next
      two are where π/84 alone put a corner of the magnet pocket's on a flat instead (35 and
-     25 edges in the socket floor), so the turn keeps those clear too. Each has to build
-     closed, with no folds. */
+     25 edges in the socket floor), so the turn keeps those clear too. A magnet's corner on
+     a flat calls for the turn as a counterbore's does: 4.9911 under 7.246 at 49.02 mm, no
+     counterbore corner near, left 44 unturned. Each has to build closed, with no folds. */
   for (const [nm, o] of [
     ['main\'s 1.0353 under 1.0873, 42', { pitch: 42, drawerW: 168, drawerD: 84, bedW: 100, bedD: 400,
       screwHoleD: 1.0353 * Math.cos(Math.PI / 12), screwHeadD: 1.0873 * Math.cos(Math.PI / 14) }],
@@ -2154,6 +2155,7 @@ console.log('\nthe other limits, built at their ends:');
     ['1.06 over 1, from beneath', { screwHoleD: 1, screwHeadD: 1.06, magnetSide: 'bottom', screwHeadDepth: 3 }],
     ['4.85 under 7.246, 49.02', { pitch: 49.02, drawerW: 49.02, drawerD: 49.02, screwHoleD: 4.85, screwHeadD: 7.246 }],
     ['5.773 under 12.053, 55', { pitch: 55, drawerW: 55, drawerD: 55, screwHoleD: 5.773, screwHeadD: 12.053 }],
+    ['4.9911 under 7.246, 49.02', { pitch: 49.02, drawerW: 49.02, drawerD: 49.02, screwHoleD: 4.9911, screwHeadD: 7.246 }],
   ]) {
     const r = buildAll({ pitch: 42, drawerW: 42, drawerD: 42, connector: 'none', magnets: true,
                          magnetSide: 'top', screws: true, ...o });
@@ -2161,6 +2163,31 @@ console.log('\nthe other limits, built at their ends:');
     console.log(`  ${nm.padEnd(30)} ${leakText(r)}${folds ? `, ${folds} FOLDS` : ''}`);
     if (r.bad || folds) bad++;
   }
+  /* A shank the magnet pocket does not clear as a counterbore has to, its corners at the
+     pocket's flats or through them, is refused (mountLimits' throughMagnet): the walls
+     weave, and no turn kept them closed. 5 mm under a 5.4 mm head and a 5.1 mm magnet, its
+     corners 4.6 microns outside the pocket's flats, built closed unturned and left 47
+     edges turned for the magnet's corners; 3.0177 under 6.557 with a 3 mm magnet at
+     43.43 mm, two pieces with a dovetail, left 58 turned for the shank's corners on the
+     pocket's flats as well; and 5.8561 under 12.053 with a 6 mm magnet at 55 mm left 116
+     unturned (#77). Each is refused, by the magnet's pocket, and builds closed at the
+     widest shank taken. */
+  for (const [nm, o] of [
+    ['5 under 5.4, 5.1 mm magnet', { screwHoleD: 5, screwHeadD: 5.4, magnetD: 5.1 }],
+    ['3.0177 under 6.557, 43.43', { pitch: 43.43, drawerW: 86.86, drawerD: 43.43, bedW: 55.43, bedD: 400,
+      connector: 'dovetail', screwHoleD: 3.0177, screwHeadD: 6.557, screwHeadDepth: 1.5, magnetD: 3, magnetH: 1.5 }],
+    ['5.8561 under 12.053, 55', { pitch: 55, drawerW: 55, drawerD: 55, screwHoleD: 5.8561, screwHeadD: 12.053 }],
+  ]) {
+    const at = { pitch: 42, drawerW: 42, drawerD: 42, connector: 'none', magnets: true, magnetSide: 'top',
+                 screws: true, ...o };
+    const cfg = designCfg(at), lim = G.mountLimits(cfg, G.computeLayout(cfg));
+    const refused = at.screwHoleD > lim.screwHoleD && lim.throughMagnet;
+    const r = buildAll({ ...at, screwHoleD: lim.screwHoleD });
+    const folds = r.pieces.reduce((s, pp) => s + checkOrientation(pp).folds, 0);
+    console.log(`  ${nm.padEnd(30)} ${refused ? `refused, by the magnet's pocket, over ${lim.screwHoleD} mm`
+      : `TAKEN up to ${lim.screwHoleD} mm`}; at that, ${leakText(r)}${folds ? `, ${folds} FOLDS` : ''}`);
+    if (!refused || r.bad || folds) bad++;
+  }
   /* A pocket against a joint's cut in the floor (#64). A bowtie housed in the floor at
      42 mm, with magnets from beneath, built 12 bad edges at 7.9 mm and 19 at 10 with
      Download on: the pocket reached the key's recess, and with both ceilings 2 mm up the
diff --git a/test/ui/plates-robustness.spec.js b/test/ui/plates-robustness.spec.js
index 62a996a..c0a0c41 100644
--- a/test/ui/plates-robustness.spec.js
+++ b/test/ui/plates-robustness.spec.js
@@ -136,6 +136,11 @@ test.describe('ranges on the geometry fields', () => {
     ['#pi=36.13&w=144.52&d=72.26&mm=custom&ml=0&mr=0&mf=0&mb=0&bw=88.26&bd=400&cn=bowtie&km=wall&ki=bottom' +
       '&bm=bosses&mg=1&md=7.9', 'errMagnet',
       /Magnet Ø must be 6\.1 mm or less at a 36\.13 mm pitch — .* the recesses the bowtie keys fit into/],
+    /* #81: a shank has to clear the magnet pocket it runs up the middle of, as it would a
+       counterbore. 5 mm under a 5.1 mm magnet and a 5.4 mm head built 47 open edges at
+       42 mm. */
+    ['#cn=none&mg=1&md=5.1&ms=top&sc=1&sh=5&sd=5.4', 'errScrew',
+      /Screw hole Ø must be 4\.9 mm or less — it runs through the 5\.1 mm magnet's pocket, and has to be narrower than the pocket\./],
   ];
   for (const [hash, errId, msg] of CASES) {
     test(`${hash} is refused at the field`, async ({ page }) => {
@@ -177,6 +182,31 @@ test.describe('ranges on the geometry fields', () => {
       expect(errors).toEqual([]);
     });
 
+  /* The shank's cap moves with the magnet typed after it, on the one read: the shank is
+     read again after the head and the magnet (readControls). Pasted in, one input event
+     and no change, 5.1 was measured against the 6 mm magnet before it, and built. */
+  test('a screw hole is held inside the magnet pocket typed after it', async ({ page }) => {
+    const errors = await openAt(page, '#cn=none&mg=1&ms=top&sc=1&sh=5&sd=5.4');
+    expect(await shown(page, 'errScrew')).toBe(false);
+    expect(await text(page, 'pieceTail')).toMatch(/ready/);
+    await page.evaluate(() => {
+      const e = document.getElementById('magnetD');
+      e.value = '5.1';
+      e.dispatchEvent(new Event('input', { bubbles: true }));
+    });
+    await page.waitForTimeout(250);
+    expect(await text(page, 'errScrew'))
+      .toMatch(/Screw hole Ø must be 4\.9 mm or less — it runs through the 5\.1 mm magnet's pocket/);
+    expect(await text(page, 'pieceTail')).toMatch(/not building/);
+    expect(await exportOff(page)).toBe(true);
+    await H.setField(page, 'magnetD', '6');
+    await page.waitForFunction(() => /ready/.test(document.getElementById('pieceTail').textContent),
+                               null, { timeout: 30000 });
+    expect(await shown(page, 'errScrew')).toBe(false);
+    expect(await exportOff(page)).toBe(false);
+    expect(errors).toEqual([]);
+  });
+
   /* #70: corner pockets over a floor. A bowtie housed in the floor stood its 2.8 mm floor
      round the 2.6 mm bosses and sealed their pockets in it, with Download on, and an extra
      floor did the same. Such a plate is built as a solid floor builds it now, and Checks

From fc3f2d8b6d70c907074d45a8578cadb40f324579 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 20:31:01 +0000
Subject: [PATCH 23/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html | 125 +++++++++++++++++++++++--------------
 index.html      | 163 ++++++++++++++++++++++++++++++++----------------
 sw.js           |   2 +-
 3 files changed, 187 insertions(+), 103 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index 2fe3978..17f47ac 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -2517,47 +2517,50 @@ <h2 id="drawersTitle">Your drawers</h2>
  * always was: within 3.5% of the hole it is no seat for a screw head, and all it would
  * add is slivers between the shank's corners.
  *
- * Under a counterbore the shank is turned a little about its axis (`turn`, #74) where one
- * of the counterbore's corners would stand on one of its flats carried on past the shank.
- * The BSP splits what it meets along a flat's whole plane, not just the flat: the floor
- * of a magnet pocket from above, which is a ring round the counterbore, or the roof of one
- * from beneath round a counterbore deeper than it. A split a micron or two from the
- * corner was welded onto it (healCsgSeams), which bent the counterbore's wall off its
- * plane, and the plate came out open by the dozen round every site: 136 edges a piece at
- * 42 mm for main's 1.0353 mm shank under a 1.0873 head with a 6 x 2 magnet from above, 36
- * a cell for 1.06 over 1 here, 62 for 3.305 over 3, 55 for 5.4959 over 3 under an 8 x 3
- * magnet. Such sizes come every few hundredths at any ratio of head to shank. A corner
- * meets a flat's plane at an odd multiple of 15/7° off the flat's normal; turned π/84,
- * 15/7°, it meets them at the even ones, so a size that put a corner on a flat puts it
- * midway between two. The turn is taken where a corner comes nearer than 0.005 mm
- * unturned and the turn leaves it further off, and a shank no corner came near is cut as
- * it was. A magnet pocket's corners stand on the same rays as the counterbore's, and π/84
- * could bring one of those onto a flat instead: 4.85 mm under 7.246 with a 6 mm magnet
- * from above left 35 edges in the socket floor at 49.02 mm, and 5.773 under 12.053 25 at
- * 55 mm, where the flats unturned miss them by 0.07 and 0.04. So where π/84 leaves a
- * corner of either nearer than 0.005 mm, the turn is the one of 24 steps across those
- * 30/7° that keeps them furthest off. Wherever the counterbore's corners call for a turn,
- * no corner of either then comes within 0.0039 mm of a flat (6 and 8 mm magnets, heads up
- * to 2.2 times the shank). And the magnet's corners call for one as the counterbore's do,
- * since a shank no counterbore corner comes near can have a magnet's corner on a flat
- * all the same: at 41.24 mm a 3 mm shank under a 7.3 mm magnet from above, a corner 0.4
- * microns off a flat, left 26 edges a piece in the socket floor whatever the head, and
- * 4.9911 under 7.246 with a 6 mm one left 44 at 49.02 mm. Wherever the magnet's
- * corners stand 0.3 mm or more outside the shank's, none then comes within 0.0045 mm of
- * a flat (magnets of 3 to 13 mm, heads up to 2.4 times the shank). Half a facet, π/12,
- * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
- * mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell plates
- * with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times
- * them, every 0.001 mm round these sizes: 546 open before, and 1 now, a size the turn
- * leaves alone; none came out worse. On 1,800 random designs the turn moves, every kind
- * of mount: 90 open before, 24 now. It closed 83 and opened 17: 14 at 42 mm with a magnet
- * from beneath under a deeper counterbore, where one size in nine leaks unturned too, by
- * the same slivers at the magnet pocket's corners in the underside, and 3 in corner
- * bosses, each at that one size alone. The magnet's corners change the turn of none of
- * those. On 1,500 random page designs that only a magnet's corner turns (34 to 56 mm;
- * one cell, 2 x 2, and two pieces joined by dovetails or jigsaws; magnets of 3 to 12.7 mm
- * either way up; a fifth on corner bosses): 66 bad before, 13 now. It closed 54 and
- * opened 1, at that one size alone; of the 12 still bad, 10 are on corner bosses. */
+ * Under a counterbore the shank is turned a little about its axis (`turn`, #74) where a
+ * corner of the counterbore or of the magnet pocket would stand on one of its flats
+ * carried on past the shank. The BSP splits what it meets along a flat's whole plane, not
+ * just the flat: the floor of a magnet pocket from above, which is a ring round the
+ * counterbore, or the roof of one from beneath round a counterbore deeper than it. A
+ * split a micron or two from the corner was welded onto it (healCsgSeams), which bent the
+ * counterbore's wall off its plane, and the plate came out open by the dozen round every
+ * site: 136 edges a piece at 42 mm for main's 1.0353 mm shank under a 1.0873 head with a
+ * 6 x 2 magnet from above, 36 a cell for 1.06 over 1 here, 62 for 3.305 over 3, 55 for
+ * 5.4959 over 3 under an 8 x 3 magnet. Such sizes come every few hundredths at any ratio
+ * of head to shank. A corner meets a flat's plane at an odd multiple of 15/7° off the
+ * flat's normal; turned π/84, 15/7°, it meets them at the even ones, so a size that put a
+ * corner on a flat puts it midway between two. The turn is taken where a corner comes
+ * nearer than 0.005 mm unturned and the turn leaves it further off, and a shank no corner
+ * came near is cut as it was. The magnet pocket's corners stand on the same rays as the
+ * counterbore's, and π/84 could bring one of those onto a flat instead: 4.85 mm under
+ * 7.246 with a 6 mm magnet from above left 35 edges in the socket floor at 49.02 mm, and
+ * 5.773 under 12.053 25 at 55 mm, where the flats unturned miss them by 0.07 and 0.04. So
+ * where π/84 leaves a corner of either nearer than 0.005 mm, the turn is the one of 24
+ * steps across those 30/7° that keeps them furthest off. And a magnet's corner calls for
+ * a turn as a counterbore's does, since a shank no counterbore corner comes near can have
+ * a magnet's corner on a flat all the same: at 41.24 mm a 3 mm shank under a 7.3 mm
+ * magnet from above, a corner 0.4 microns off a flat, left 26 edges a piece in the socket
+ * floor whatever the head, and 4.9911 under 7.246 with a 6 mm one left 44 at 49.02 mm. A
+ * shank the magnet pocket does not clear as it would a counterbore is refused
+ * (mountLimits): the two walls weave, and no turn kept them closed. On every shank taken,
+ * no corner of either then comes within 0.0039 mm of a flat, whichever called the turn
+ * (magnets of 3 to 13 mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every
+ * 0.001 mm round the sizes that put a corner on a flat). Half a facet, π/12, clears the
+ * corners as well, but it squares two flats to the cell's edges, and at 37.67 mm those
+ * folded the socket floor beside the pocket. Measured on 3,846 one-cell plates with a
+ * magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times them,
+ * every 0.001 mm round these sizes: 546 open before, and 1 now, a size the turn leaves
+ * alone; none came out worse. On 1,800 random designs a counterbore's corner turns, every
+ * kind of mount: 85 open before, 10 now. It closed 80 and opened 5: 3 at 42 mm with a
+ * magnet from beneath under a deeper counterbore, where one size in nine leaks unturned
+ * too, by the same slivers at the magnet pocket's corners in the underside; 1 in a corner
+ * boss, at that one size alone; and 1 at 42 mm under a magnet from above, open for a few
+ * thousandths round 2.114 under 2.253. The magnet's corners change the turn of none of
+ * the 1,800. On 1,500 random page designs that only a magnet's corner turns (34 to 56
+ * mm; one cell, 2 x 2, and two pieces joined by dovetails or jigsaws; magnets of 3 to
+ * 12.7 mm either way up; a fifth on corner bosses): 41 open or folded before, 6 now. It
+ * closed 40 and opened 5, each for a size or two (2 patches 0.002 mm wide, 2 single
+ * sizes, and 1 whose neighbours fold unturned too); the sixth folds the same unturned. */
 const MOUNT_BORE = {
   magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
             fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },
@@ -2637,7 +2640,8 @@ <h2 id="drawersTitle">Your drawers</h2>
     const { counterbore, turn: t } = MOUNT_BORE.screw(cfg);
     if (counterbore)
       add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
-    // the shank, turned off the counterbore's corners where one would stand on a flat (#74)
+    // the shank, turned where a corner of the counterbore or the magnet pocket would stand
+    // on one of its flats (#74)
     const shank = cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides);
     const c = Math.cos(t), s = Math.sin(t), turn = (v) => [v[0]*c - v[1]*s, v[0]*s + v[1]*c, v[2]];
     add(t ? shank.map((p) => ({ verts: p.verts.map(turn), plane: { n: turn(p.plane.n), w: p.plane.w } }))
@@ -4419,6 +4423,18 @@ <h2 id="drawersTitle">Your drawers</h2>
   const shankTurn = cfg.screws ? MOUNT_BORE.screw(cfg).turn : 0;
   // the room the cell, the floor or a boss leaves, and the hole beside
   const own = { magnetD: fit(cfg.magnetSide === 'top' ? top : under), screwHoleD: fit(top), screwHeadD: fit(under) };
+  /* A shank runs up the magnet pocket's axis, and has to clear it as it would a
+     counterbore (MOUNT_BORE.head.over): its corners 0.005 mm inside the pocket's flats.
+     Any wider, and the pocket's 14 flats cross the shank's 12 corners, the walls weave
+     round each other as a counterbore's under the line would, and the magnet has no
+     ledge to stop against. No turn of the shank kept such a pair closed: 5 mm under a
+     5.1 mm magnet from above and a 5.4 mm head, closed unturned at 42 mm, left 47 open
+     edges turned for the magnet's corners; turned for the shank's corners on the
+     pocket's flats as well it closed, but 3.0177 under a 3 mm magnet and a 6.557 head at
+     43.43 mm, closed the other two ways, then left 58. */
+  const ledge = cfg.magnets
+    ? MOUNT_BORE.hole.fits(MOUNT_BORE.magnet.r(cfg.magnetD) * Math.cos(Math.PI / MOUNT_BORE.magnet.sides) - 0.005)
+    : Infinity;
   // a dovetail's notch takes a pocket from beneath that breaks into it; every other cut does not
   const notch = cfg.connector === 'dovetail';
   /* The cuts are measured where they stand in the cells, and a corner boss's stands two
@@ -4441,9 +4457,17 @@ <h2 id="drawersTitle">Your drawers</h2>
      into, but not stop just short of. */
   const jointFor = (f) => {
     const { sides, fits } = BORE[f];
-    // the room a bore has, measured again for a shank turned under its counterbore
+    /* the room a bore has, measured again for a shank turned under its counterbore, and
+       kept on the site by its turn: the page asks again on the same cuts (`known`) once
+       the head and the magnet are read, and on a 30 x 30 puzzle plate that took 3.6 ms */
     const turn = f === 'screwHoleD' ? shankTurn : 0;
-    const reach = (c, s) => !turn ? s.bore[sides] : s.room > 0 ? boreReach(sides, c.segs, s.x, s.y, turn) : s.room;
+    const reach = (c, s) => {
+      if (!turn) return s.bore[sides];
+      if (!(s.room > 0)) return s.room;
+      const kept = s.turned || (s.turned = new Map());
+      if (!kept.has(turn)) kept.set(turn, boreReach(sides, c.segs, s.x, s.y, turn));
+      return kept.get(turn);
+    };
     const above = f === 'magnetD' && cfg.magnetSide === 'top';
     // how high a pocket from beneath goes; a shank goes through
     const ceiling = f === 'magnetD' ? cfg.magnetH : f === 'screwHeadD' ? cfg.screwHeadDepth : Infinity;
@@ -4469,10 +4493,13 @@ <h2 id="drawersTitle">Your drawers</h2>
     return { cap, why, near };
   };
   const sizes = {}, joint = {}, gaps = {};
+  let byMagnet = false;
   for (const f of ['magnetD', 'screwHoleD', 'screwHeadD']) {
     const cell = BORE[f].fits(own[f]), J = jointFor(f);
-    let size = r10(Math.min(cell, J.cap));
-    joint[f] = J.cap < cell && J.why;
+    const most = f === 'screwHoleD' ? Math.min(cell, ledge) : cell;
+    let size = r10(Math.min(most, J.cap));
+    joint[f] = J.cap < most && J.why;
+    if (f === 'screwHoleD') byMagnet = ledge < cell && !joint[f];
     /* The sizes `near` refuses, out to the hundredths either side, since the field takes
        hundredths: each gap is [from, to], both taken. A window is about 0.02 mm wide, so
        rounded out to the tenths as the cap is, it refused up to a tenth that builds clean
@@ -4487,7 +4514,7 @@ <h2 id="drawersTitle">Your drawers</h2>
     gaps[f] = [];
     for (const [from, to] of out) {
       if (from >= size) break;
-      if (to > size) { size = from; joint[f] = 'near'; break; }
+      if (to > size) { size = from; joint[f] = 'near'; if (f === 'screwHoleD') byMagnet = false; break; }
       gaps[f].push([from, to]);
     }
     sizes[f] = size;
@@ -4500,8 +4527,10 @@ <h2 id="drawersTitle">Your drawers</h2>
     depth: bosses ? r10(BOSS_H - MOUNT_SKIN) : Infinity,
     // which of the sizes the cut beside it stops, rather than the floor, cell or boss
     beside: { magnetD: own.magnetD === beside && !joint.magnetD,
-              screwHoleD: own.screwHoleD === beside && !joint.screwHoleD,
+              screwHoleD: own.screwHoleD === beside && !joint.screwHoleD && !byMagnet,
               screwHeadD: own.screwHeadD === beside && !joint.screwHeadD },
+    // whether the magnet pocket the shank runs through stops it, before all of those
+    throughMagnet: byMagnet,
     // and which a joint's cut stops, before any of those, and how (jointFor)
     joint,
     // sizes under the largest refused all the same, as [from, to] with both ends taken
diff --git a/index.html b/index.html
index 447d689..6eca2bb 100644
--- a/index.html
+++ b/index.html
@@ -1234,6 +1234,7 @@ <h2 class="ph"><button type="button" aria-expanded="true" aria-controls="b-mag">
       <label class="f"><b>Head depth</b><input id="screwHeadDepth" type="number" step="0.1" min="0.5" max="10" value="2" aria-describedby="errScrew"></label>
     </div>
     <span class="hint" id="errScrew" style="color:var(--red)" hidden></span>
+    <span class="hint" id="screwHeadHint" hidden></span>
     <label class="f" id="baseModeRow" style="display:none"><b>Mounting base</b>
       <select id="baseMode">
         <option value="solid">Solid floor — at least 2.8 mm base under everything</option>
@@ -2304,47 +2305,50 @@ <h2 id="drawersTitle">Your drawers</h2>
  * always was: within 3.5% of the hole it is no seat for a screw head, and all it would
  * add is slivers between the shank's corners.
  *
- * Under a counterbore the shank is turned a little about its axis (`turn`, #74) where one
- * of the counterbore's corners would stand on one of its flats carried on past the shank.
- * The BSP splits what it meets along a flat's whole plane, not just the flat: the floor
- * of a magnet pocket from above, which is a ring round the counterbore, or the roof of one
- * from beneath round a counterbore deeper than it. A split a micron or two from the
- * corner was welded onto it (healCsgSeams), which bent the counterbore's wall off its
- * plane, and the plate came out open by the dozen round every site: 136 edges a piece at
- * 42 mm for main's 1.0353 mm shank under a 1.0873 head with a 6 x 2 magnet from above, 36
- * a cell for 1.06 over 1 here, 62 for 3.305 over 3, 55 for 5.4959 over 3 under an 8 x 3
- * magnet. Such sizes come every few hundredths at any ratio of head to shank. A corner
- * meets a flat's plane at an odd multiple of 15/7° off the flat's normal; turned π/84,
- * 15/7°, it meets them at the even ones, so a size that put a corner on a flat puts it
- * midway between two. The turn is taken where a corner comes nearer than 0.005 mm
- * unturned and the turn leaves it further off, and a shank no corner came near is cut as
- * it was. A magnet pocket's corners stand on the same rays as the counterbore's, and π/84
- * could bring one of those onto a flat instead: 4.85 mm under 7.246 with a 6 mm magnet
- * from above left 35 edges in the socket floor at 49.02 mm, and 5.773 under 12.053 25 at
- * 55 mm, where the flats unturned miss them by 0.07 and 0.04. So where π/84 leaves a
- * corner of either nearer than 0.005 mm, the turn is the one of 24 steps across those
- * 30/7° that keeps them furthest off. Wherever the counterbore's corners call for a turn,
- * no corner of either then comes within 0.0039 mm of a flat (6 and 8 mm magnets, heads up
- * to 2.2 times the shank). And the magnet's corners call for one as the counterbore's do,
- * since a shank no counterbore corner comes near can have a magnet's corner on a flat
- * all the same: at 41.24 mm a 3 mm shank under a 7.3 mm magnet from above, a corner 0.4
- * microns off a flat, left 26 edges a piece in the socket floor whatever the head, and
- * 4.9911 under 7.246 with a 6 mm one left 44 at 49.02 mm. Wherever the magnet's
- * corners stand 0.3 mm or more outside the shank's, none then comes within 0.0045 mm of
- * a flat (magnets of 3 to 13 mm, heads up to 2.4 times the shank). Half a facet, π/12,
- * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
- * mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell plates
- * with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times
- * them, every 0.001 mm round these sizes: 546 open before, and 1 now, a size the turn
- * leaves alone; none came out worse. On 1,800 random designs the turn moves, every kind
- * of mount: 90 open before, 24 now. It closed 83 and opened 17: 14 at 42 mm with a magnet
- * from beneath under a deeper counterbore, where one size in nine leaks unturned too, by
- * the same slivers at the magnet pocket's corners in the underside, and 3 in corner
- * bosses, each at that one size alone. The magnet's corners change the turn of none of
- * those. On 1,500 random page designs that only a magnet's corner turns (34 to 56 mm;
- * one cell, 2 x 2, and two pieces joined by dovetails or jigsaws; magnets of 3 to 12.7 mm
- * either way up; a fifth on corner bosses): 66 bad before, 13 now. It closed 54 and
- * opened 1, at that one size alone; of the 12 still bad, 10 are on corner bosses. */
+ * Under a counterbore the shank is turned a little about its axis (`turn`, #74) where a
+ * corner of the counterbore or of the magnet pocket would stand on one of its flats
+ * carried on past the shank. The BSP splits what it meets along a flat's whole plane, not
+ * just the flat: the floor of a magnet pocket from above, which is a ring round the
+ * counterbore, or the roof of one from beneath round a counterbore deeper than it. A
+ * split a micron or two from the corner was welded onto it (healCsgSeams), which bent the
+ * counterbore's wall off its plane, and the plate came out open by the dozen round every
+ * site: 136 edges a piece at 42 mm for main's 1.0353 mm shank under a 1.0873 head with a
+ * 6 x 2 magnet from above, 36 a cell for 1.06 over 1 here, 62 for 3.305 over 3, 55 for
+ * 5.4959 over 3 under an 8 x 3 magnet. Such sizes come every few hundredths at any ratio
+ * of head to shank. A corner meets a flat's plane at an odd multiple of 15/7° off the
+ * flat's normal; turned π/84, 15/7°, it meets them at the even ones, so a size that put a
+ * corner on a flat puts it midway between two. The turn is taken where a corner comes
+ * nearer than 0.005 mm unturned and the turn leaves it further off, and a shank no corner
+ * came near is cut as it was. The magnet pocket's corners stand on the same rays as the
+ * counterbore's, and π/84 could bring one of those onto a flat instead: 4.85 mm under
+ * 7.246 with a 6 mm magnet from above left 35 edges in the socket floor at 49.02 mm, and
+ * 5.773 under 12.053 25 at 55 mm, where the flats unturned miss them by 0.07 and 0.04. So
+ * where π/84 leaves a corner of either nearer than 0.005 mm, the turn is the one of 24
+ * steps across those 30/7° that keeps them furthest off. And a magnet's corner calls for
+ * a turn as a counterbore's does, since a shank no counterbore corner comes near can have
+ * a magnet's corner on a flat all the same: at 41.24 mm a 3 mm shank under a 7.3 mm
+ * magnet from above, a corner 0.4 microns off a flat, left 26 edges a piece in the socket
+ * floor whatever the head, and 4.9911 under 7.246 with a 6 mm one left 44 at 49.02 mm. A
+ * shank the magnet pocket does not clear as it would a counterbore is refused
+ * (mountLimits): the two walls weave, and no turn kept them closed. On every shank taken,
+ * no corner of either then comes within 0.0039 mm of a flat, whichever called the turn
+ * (magnets of 3 to 13 mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every
+ * 0.001 mm round the sizes that put a corner on a flat). Half a facet, π/12, clears the
+ * corners as well, but it squares two flats to the cell's edges, and at 37.67 mm those
+ * folded the socket floor beside the pocket. Measured on 3,846 one-cell plates with a
+ * magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times them,
+ * every 0.001 mm round these sizes: 546 open before, and 1 now, a size the turn leaves
+ * alone; none came out worse. On 1,800 random designs a counterbore's corner turns, every
+ * kind of mount: 85 open before, 10 now. It closed 80 and opened 5: 3 at 42 mm with a
+ * magnet from beneath under a deeper counterbore, where one size in nine leaks unturned
+ * too, by the same slivers at the magnet pocket's corners in the underside; 1 in a corner
+ * boss, at that one size alone; and 1 at 42 mm under a magnet from above, open for a few
+ * thousandths round 2.114 under 2.253. The magnet's corners change the turn of none of
+ * the 1,800. On 1,500 random page designs that only a magnet's corner turns (34 to 56
+ * mm; one cell, 2 x 2, and two pieces joined by dovetails or jigsaws; magnets of 3 to
+ * 12.7 mm either way up; a fifth on corner bosses): 41 open or folded before, 6 now. It
+ * closed 40 and opened 5, each for a size or two (2 patches 0.002 mm wide, 2 single
+ * sizes, and 1 whose neighbours fold unturned too); the sixth folds the same unturned. */
 const MOUNT_BORE = {
   magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
             fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },
@@ -2424,7 +2428,8 @@ <h2 id="drawersTitle">Your drawers</h2>
     const { counterbore, turn: t } = MOUNT_BORE.screw(cfg);
     if (counterbore)
       add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
-    // the shank, turned off the counterbore's corners where one would stand on a flat (#74)
+    // the shank, turned where a corner of the counterbore or the magnet pocket would stand
+    // on one of its flats (#74)
     const shank = cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides);
     const c = Math.cos(t), s = Math.sin(t), turn = (v) => [v[0]*c - v[1]*s, v[0]*s + v[1]*c, v[2]];
     add(t ? shank.map((p) => ({ verts: p.verts.map(turn), plane: { n: turn(p.plane.n), w: p.plane.w } }))
@@ -4206,6 +4211,18 @@ <h2 id="drawersTitle">Your drawers</h2>
   const shankTurn = cfg.screws ? MOUNT_BORE.screw(cfg).turn : 0;
   // the room the cell, the floor or a boss leaves, and the hole beside
   const own = { magnetD: fit(cfg.magnetSide === 'top' ? top : under), screwHoleD: fit(top), screwHeadD: fit(under) };
+  /* A shank runs up the magnet pocket's axis, and has to clear it as it would a
+     counterbore (MOUNT_BORE.head.over): its corners 0.005 mm inside the pocket's flats.
+     Any wider, and the pocket's 14 flats cross the shank's 12 corners, the walls weave
+     round each other as a counterbore's under the line would, and the magnet has no
+     ledge to stop against. No turn of the shank kept such a pair closed: 5 mm under a
+     5.1 mm magnet from above and a 5.4 mm head, closed unturned at 42 mm, left 47 open
+     edges turned for the magnet's corners; turned for the shank's corners on the
+     pocket's flats as well it closed, but 3.0177 under a 3 mm magnet and a 6.557 head at
+     43.43 mm, closed the other two ways, then left 58. */
+  const ledge = cfg.magnets
+    ? MOUNT_BORE.hole.fits(MOUNT_BORE.magnet.r(cfg.magnetD) * Math.cos(Math.PI / MOUNT_BORE.magnet.sides) - 0.005)
+    : Infinity;
   // a dovetail's notch takes a pocket from beneath that breaks into it; every other cut does not
   const notch = cfg.connector === 'dovetail';
   /* The cuts are measured where they stand in the cells, and a corner boss's stands two
@@ -4228,9 +4245,17 @@ <h2 id="drawersTitle">Your drawers</h2>
      into, but not stop just short of. */
   const jointFor = (f) => {
     const { sides, fits } = BORE[f];
-    // the room a bore has, measured again for a shank turned under its counterbore
+    /* the room a bore has, measured again for a shank turned under its counterbore, and
+       kept on the site by its turn: the page asks again on the same cuts (`known`) once
+       the head and the magnet are read, and on a 30 x 30 puzzle plate that took 3.6 ms */
     const turn = f === 'screwHoleD' ? shankTurn : 0;
-    const reach = (c, s) => !turn ? s.bore[sides] : s.room > 0 ? boreReach(sides, c.segs, s.x, s.y, turn) : s.room;
+    const reach = (c, s) => {
+      if (!turn) return s.bore[sides];
+      if (!(s.room > 0)) return s.room;
+      const kept = s.turned || (s.turned = new Map());
+      if (!kept.has(turn)) kept.set(turn, boreReach(sides, c.segs, s.x, s.y, turn));
+      return kept.get(turn);
+    };
     const above = f === 'magnetD' && cfg.magnetSide === 'top';
     // how high a pocket from beneath goes; a shank goes through
     const ceiling = f === 'magnetD' ? cfg.magnetH : f === 'screwHeadD' ? cfg.screwHeadDepth : Infinity;
@@ -4256,10 +4281,13 @@ <h2 id="drawersTitle">Your drawers</h2>
     return { cap, why, near };
   };
   const sizes = {}, joint = {}, gaps = {};
+  let byMagnet = false;
   for (const f of ['magnetD', 'screwHoleD', 'screwHeadD']) {
     const cell = BORE[f].fits(own[f]), J = jointFor(f);
-    let size = r10(Math.min(cell, J.cap));
-    joint[f] = J.cap < cell && J.why;
+    const most = f === 'screwHoleD' ? Math.min(cell, ledge) : cell;
+    let size = r10(Math.min(most, J.cap));
+    joint[f] = J.cap < most && J.why;
+    if (f === 'screwHoleD') byMagnet = ledge < cell && !joint[f];
     /* The sizes `near` refuses, out to the hundredths either side, since the field takes
        hundredths: each gap is [from, to], both taken. A window is about 0.02 mm wide, so
        rounded out to the tenths as the cap is, it refused up to a tenth that builds clean
@@ -4274,7 +4302,7 @@ <h2 id="drawersTitle">Your drawers</h2>
     gaps[f] = [];
     for (const [from, to] of out) {
       if (from >= size) break;
-      if (to > size) { size = from; joint[f] = 'near'; break; }
+      if (to > size) { size = from; joint[f] = 'near'; if (f === 'screwHoleD') byMagnet = false; break; }
       gaps[f].push([from, to]);
     }
     sizes[f] = size;
@@ -4287,8 +4315,10 @@ <h2 id="drawersTitle">Your drawers</h2>
     depth: bosses ? r10(BOSS_H - MOUNT_SKIN) : Infinity,
     // which of the sizes the cut beside it stops, rather than the floor, cell or boss
     beside: { magnetD: own.magnetD === beside && !joint.magnetD,
-              screwHoleD: own.screwHoleD === beside && !joint.screwHoleD,
+              screwHoleD: own.screwHoleD === beside && !joint.screwHoleD && !byMagnet,
               screwHeadD: own.screwHeadD === beside && !joint.screwHeadD },
+    // whether the magnet pocket the shank runs through stops it, before all of those
+    throughMagnet: byMagnet,
     // and which a joint's cut stops, before any of those, and how (jointFor)
     joint,
     // sizes under the largest refused all the same, as [from, to] with both ends taken
@@ -8007,8 +8037,11 @@ <h2 id="drawersTitle">Your drawers</h2>
    stands into a boss's pocket (#75). Nor where the bosses are buried in the floor a
    joint needs (cornerBosses): a key put in from above, in the walls, needs none, so
    taking the hint would stand them up again, and the cup in their pockets. Only a floor
-   asked for (bottomPad) keeps them buried whatever the joint. */
+   asked for (bottomPad) keeps them buried whatever the joint. A screw hole the magnet
+   pocket stops is stopped whatever the pitch, so that is all it says. */
 const mountWhy = (opens, field) => {
+  if (field === 'screwHoleD' && mount().throughMagnet)
+    return `— it runs through the ${state.magnetD} mm magnet's pocket, and has to be narrower than the pocket`;
   const joint = mount().joint[field];
   const cuts = cutsNamed();
   return `${atPitch()} — mounting holes sit ` +
@@ -8223,6 +8256,12 @@ <h2 id="drawersTitle">Your drawers</h2>
   }
 }
 
+/* A head wider than the hole that does not clear its corners is cut as no counterbore
+   (MOUNT_BORE.head.cuts, #73); and the size one is cut from, to the hundredth above. */
+const headCutAsNone = () => state.screwHeadD > state.screwHoleD &&
+  !MOUNT_BORE.head.cuts(state.screwHeadD, state.screwHoleD);
+const headClearsFrom = (hole) => Math.ceil(MOUNT_BORE.head.over(hole) * 100 - 1e-9) / 100;
+
 function readControls() {
   fieldErrors.clear(); noRoom.clear();
   /* The switches before the numbers: which ranges apply, and how wide they are, depend
@@ -8275,6 +8314,15 @@ <h2 id="drawersTitle">Your drawers</h2>
     if (id === 'magnetD' && mountNow) mountNow = mountLimits(state, mountLayout, mountNow.cuts);
     state[id] = readNumber(id);
   }
+  /* And the shank once more, on the sizes just read: how far it is turned goes by the head
+     and the magnet (MOUNT_BORE.screw), and the magnet pocket it runs through caps it
+     (mountLimits' throughMagnet), both read after it. Read before them only, a 5 mm hole
+     stood under a 5.1 mm magnet typed in after it, refused only at the next keystroke. */
+  if (state.screws && mountNow) {
+    mountNow = mountLimits(state, mountLayout, mountNow.cuts);
+    fieldErrors.delete('screwHoleD'); noRoom.delete('screwHoleD');
+    state.screwHoleD = readNumber('screwHoleD');
+  }
   // and Checks says what is wrong in the panel's order, not the order it was read in
   for (const m of [fieldErrors, noRoom]) {
     const read = new Map(m);
@@ -8293,6 +8341,15 @@ <h2 id="drawersTitle">Your drawers</h2>
   if (halfOpt && halfOpt.textContent !== halfText) halfOpt.textContent = halfText;
   $('magRow').style.display = state.magnets ? '' : 'none';
   $('screwRow').style.display = state.screws ? '' : 'none';
+  /* A head wider than the hole that does not clear its corners is cut as none (#73); the
+     README said so, and nothing at the field did. Not while either size is refused: the
+     red line under the fields says what to do first. */
+  const noBore = state.screws && headCutAsNone() &&
+    !['screwHoleD', 'screwHeadD'].some((id) => fieldErrors.has(id) || noRoom.has(id));
+  $('screwHeadHint').hidden = !noBore;
+  if (noBore) $('screwHeadHint').textContent = `A ${state.screwHeadD} mm head does not clear ` +
+    `the corners of a ${state.screwHoleD} mm hole, so no counterbore is cut. One is from ` +
+    `${headClearsFrom(state.screwHoleD)} mm.`;
   $('connHintDove').style.display = state.connector === 'dovetail' ? '' : 'none';
   $('connHintPuzzle').style.display = state.connector === 'puzzle' ? '' : 'none';
   // Bowtie and puzzle key shared one hint, so picking between them meant reading the
@@ -9745,12 +9802,10 @@ <h2 id="drawersTitle">Your drawers</h2>
   /* A head that does not clear the hole's corners is cut as none (MOUNT_BORE in core.js),
      and one no wider than the hole always was; the README says so, and for a head that
      was meant as a counterbore, the size that would be one. */
-  const { head } = MOUNT_BORE;
   if (state.screws) lines.push(`Screws: ${state.screwHoleD} mm holes, ` +
-    (head.cuts(state.screwHeadD, state.screwHoleD) ? `${state.screwHeadD} mm counterbore`
-      : 'no counterbore' + (state.screwHeadD <= state.screwHoleD ? ''
-        : ` (a head clears a ${state.screwHoleD} mm hole from ` +
-          `${Math.ceil(head.over(state.screwHoleD) * 100 - 1e-9) / 100} mm)`)));
+    (MOUNT_BORE.head.cuts(state.screwHeadD, state.screwHoleD) ? `${state.screwHeadD} mm counterbore`
+      : 'no counterbore' + (headCutAsNone()
+        ? ` (a head clears a ${state.screwHoleD} mm hole from ${headClearsFrom(state.screwHoleD)} mm)` : '')));
   /* The figure the dialog quotes, said the way it says it, with the price it was worked
      out at: the README is read away from the page. The ZIP is only made once every piece
      exists, so there is always a total to give. */
diff --git a/sw.js b/sw.js
index 0dc8a8a..2f4db41 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "e4838b216ae5";
+const VERSION = "b4df602d4c9e";
 const FILES = [
   "./",
   "bins/",

From 2a58bd7bd9e32d942fc61f52264babced63693f8 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 21:21:10 +0000
Subject: [PATCH 24/58] Say how near a turned shank's flats come to a corner on
 every shank taken, as measured

The turn's comment said no corner comes within 0.0039 mm of a flat on every shank
mountLimits takes. Searched again (every 0.001 mm round the sizes that put a corner
on a flat, 6.7 million sizes drawn at random round them, and a local search for the
least), the nearest is 0.0032 mm, at 1.0197 under 1.0748 with a 3.72 mm magnet; under
0.0039 only with a magnet and a shank under 1.2 mm, and with no magnet 0.00399. The
nearest ten build closed at 42 and 49.02 mm, the magnet either way up. MOUNT_BORE's
comment and ENGINE.md say 0.003, and where the 0.0039 holds.

The sweeps the comment quotes are run again on the merged tree, the 1,800 and 1,500
on new draws: 3,846 one-cell plates 546 open to 1, none worse, as before; 1,800
designs a counterbore's corner turns 75 open or folded to 15 (72 closed, 12 opened,
11 of them the known 6 x 2 from beneath under a 3 mm counterbore); 1,500 that only a
magnet's corner turns 47 to 5 (43 closed, 1 opened).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md |  5 +++--
 src/core.js    | 42 ++++++++++++++++++++++++------------------
 2 files changed, 27 insertions(+), 20 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index bb72db8..88299a5 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -771,8 +771,9 @@ currently installed):
   counterbore, and `mountLimits` refuses a wider one, which the field says
   (`throughMagnet`): the pocket's flats cross the shank's corners, the walls weave, and
   no turn kept them closed (5 mm under a 5.1 mm magnet and a 5.4 head at 42 mm left 47
-  edges turned for the magnet's corners). Turned, no corner of either comes within
-  0.0039 mm of a flat, and a shank no corner came near is cut as before. The page reads
+  edges turned for the magnet's corners). On every shank taken, turned, no corner of
+  either comes within 0.003 mm of a flat, and none within 0.0039 but under a magnet on a
+  shank under 1.2 mm; a shank no corner came near is cut as before. The page reads
   the shank again after the head and the magnet, since its turn and that cap go by both.
   `MOUNT_BORE.screw` says whether a design's counterbore is cut and how far its shank is
   turned, for the cutter and for `mountLimits`, which measures that shank turned.
diff --git a/src/core.js b/src/core.js
index 804af71..ed2558e 100644
--- a/src/core.js
+++ b/src/core.js
@@ -937,24 +937,30 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * floor whatever the head, and 4.9911 under 7.246 with a 6 mm one left 44 at 49.02 mm. A
  * shank the magnet pocket does not clear as it would a counterbore is refused
  * (mountLimits): the two walls weave, and no turn kept them closed. On every shank taken,
- * no corner of either then comes within 0.0039 mm of a flat, whichever called the turn
- * (magnets of 3 to 13 mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every
- * 0.001 mm round the sizes that put a corner on a flat). Half a facet, π/12, clears the
- * corners as well, but it squares two flats to the cell's edges, and at 37.67 mm those
- * folded the socket floor beside the pocket. Measured on 3,846 one-cell plates with a
- * magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times them,
- * every 0.001 mm round these sizes: 546 open before, and 1 now, a size the turn leaves
- * alone; none came out worse. On 1,800 random designs a counterbore's corner turns, every
- * kind of mount: 85 open before, 10 now. It closed 80 and opened 5: 3 at 42 mm with a
- * magnet from beneath under a deeper counterbore, where one size in nine leaks unturned
- * too, by the same slivers at the magnet pocket's corners in the underside; 1 in a corner
- * boss, at that one size alone; and 1 at 42 mm under a magnet from above, open for a few
- * thousandths round 2.114 under 2.253. The magnet's corners change the turn of none of
- * the 1,800. On 1,500 random page designs that only a magnet's corner turns (34 to 56
- * mm; one cell, 2 x 2, and two pieces joined by dovetails or jigsaws; magnets of 3 to
- * 12.7 mm either way up; a fifth on corner bosses): 41 open or folded before, 6 now. It
- * closed 40 and opened 5, each for a size or two (2 patches 0.002 mm wide, 2 single
- * sizes, and 1 whose neighbours fold unturned too); the sixth folds the same unturned. */
+ * whichever called the turn, no corner of either then comes within 0.003 mm of a flat,
+ * and none within 0.0039 but under a magnet on a shank under 1.2 mm (magnets of 3 to 13
+ * mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every 0.001 mm round the sizes
+ * that put a corner on a flat, and 6.7 million sizes drawn at random round them). The
+ * nearest, 0.0032 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
+ * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. Half a facet, π/12,
+ * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
+ * mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell plates
+ * with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times
+ * them, every 0.001 mm round these sizes: 546 open before, and 1 now, a size the turn
+ * leaves alone; none came out worse. On 1,800 random designs a counterbore's corner
+ * turns, every kind of mount: 75 open or folded before, 15 now. It closed 72 and opened
+ * 12: 11 with a 6 x 2 magnet from beneath under a 3 mm counterbore, all at 42 mm but one,
+ * where about one size in ten leaks unturned too, by the same slivers at the magnet
+ * pocket's corners in the underside; and 1 at 55 mm under an 8 x 3 magnet from above,
+ * 1.723 under 1.89, among sizes that leak turned or not (of 26 turned round it, 6 leak
+ * turned and 4 unturned). The magnet's corners change the turn of none of the 1,800. On
+ * 1,500 random page designs that only a magnet's corner turns (34 to 56 mm; one cell,
+ * 2 x 2, and two pieces joined by dovetails or jigsaws; magnets of 3 to 12.7 mm either
+ * way up; 115 on corner bosses): 47 open or folded before, 5 now. It closed 43 and opened
+ * 1, two pieces with a jigsaw at 44.46 mm and a 4 mm magnet from above: 3 open edges a
+ * piece 2.8 mm up and 2.2 mm off the site, for every shank from 2.487 under a 2.895 head,
+ * which builds closed unturned (the counterbore's corners turn it, and open it, from
+ * 2.508); the other 4 fold the same unturned. */
 const MOUNT_BORE = {
   magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
             fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },

From 6bdb7f4465551579c57e421bbf4f109f07ea8f71 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 21:21:10 +0000
Subject: [PATCH 25/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html | 42 ++++++++++++++++++++++++------------------
 index.html      | 42 ++++++++++++++++++++++++------------------
 sw.js           |  2 +-
 3 files changed, 49 insertions(+), 37 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index 17f47ac..1634797 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -2543,24 +2543,30 @@ <h2 id="drawersTitle">Your drawers</h2>
  * floor whatever the head, and 4.9911 under 7.246 with a 6 mm one left 44 at 49.02 mm. A
  * shank the magnet pocket does not clear as it would a counterbore is refused
  * (mountLimits): the two walls weave, and no turn kept them closed. On every shank taken,
- * no corner of either then comes within 0.0039 mm of a flat, whichever called the turn
- * (magnets of 3 to 13 mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every
- * 0.001 mm round the sizes that put a corner on a flat). Half a facet, π/12, clears the
- * corners as well, but it squares two flats to the cell's edges, and at 37.67 mm those
- * folded the socket floor beside the pocket. Measured on 3,846 one-cell plates with a
- * magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times them,
- * every 0.001 mm round these sizes: 546 open before, and 1 now, a size the turn leaves
- * alone; none came out worse. On 1,800 random designs a counterbore's corner turns, every
- * kind of mount: 85 open before, 10 now. It closed 80 and opened 5: 3 at 42 mm with a
- * magnet from beneath under a deeper counterbore, where one size in nine leaks unturned
- * too, by the same slivers at the magnet pocket's corners in the underside; 1 in a corner
- * boss, at that one size alone; and 1 at 42 mm under a magnet from above, open for a few
- * thousandths round 2.114 under 2.253. The magnet's corners change the turn of none of
- * the 1,800. On 1,500 random page designs that only a magnet's corner turns (34 to 56
- * mm; one cell, 2 x 2, and two pieces joined by dovetails or jigsaws; magnets of 3 to
- * 12.7 mm either way up; a fifth on corner bosses): 41 open or folded before, 6 now. It
- * closed 40 and opened 5, each for a size or two (2 patches 0.002 mm wide, 2 single
- * sizes, and 1 whose neighbours fold unturned too); the sixth folds the same unturned. */
+ * whichever called the turn, no corner of either then comes within 0.003 mm of a flat,
+ * and none within 0.0039 but under a magnet on a shank under 1.2 mm (magnets of 3 to 13
+ * mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every 0.001 mm round the sizes
+ * that put a corner on a flat, and 6.7 million sizes drawn at random round them). The
+ * nearest, 0.0032 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
+ * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. Half a facet, π/12,
+ * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
+ * mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell plates
+ * with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times
+ * them, every 0.001 mm round these sizes: 546 open before, and 1 now, a size the turn
+ * leaves alone; none came out worse. On 1,800 random designs a counterbore's corner
+ * turns, every kind of mount: 75 open or folded before, 15 now. It closed 72 and opened
+ * 12: 11 with a 6 x 2 magnet from beneath under a 3 mm counterbore, all at 42 mm but one,
+ * where about one size in ten leaks unturned too, by the same slivers at the magnet
+ * pocket's corners in the underside; and 1 at 55 mm under an 8 x 3 magnet from above,
+ * 1.723 under 1.89, among sizes that leak turned or not (of 26 turned round it, 6 leak
+ * turned and 4 unturned). The magnet's corners change the turn of none of the 1,800. On
+ * 1,500 random page designs that only a magnet's corner turns (34 to 56 mm; one cell,
+ * 2 x 2, and two pieces joined by dovetails or jigsaws; magnets of 3 to 12.7 mm either
+ * way up; 115 on corner bosses): 47 open or folded before, 5 now. It closed 43 and opened
+ * 1, two pieces with a jigsaw at 44.46 mm and a 4 mm magnet from above: 3 open edges a
+ * piece 2.8 mm up and 2.2 mm off the site, for every shank from 2.487 under a 2.895 head,
+ * which builds closed unturned (the counterbore's corners turn it, and open it, from
+ * 2.508); the other 4 fold the same unturned. */
 const MOUNT_BORE = {
   magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
             fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },
diff --git a/index.html b/index.html
index 6eca2bb..08e2ea6 100644
--- a/index.html
+++ b/index.html
@@ -2331,24 +2331,30 @@ <h2 id="drawersTitle">Your drawers</h2>
  * floor whatever the head, and 4.9911 under 7.246 with a 6 mm one left 44 at 49.02 mm. A
  * shank the magnet pocket does not clear as it would a counterbore is refused
  * (mountLimits): the two walls weave, and no turn kept them closed. On every shank taken,
- * no corner of either then comes within 0.0039 mm of a flat, whichever called the turn
- * (magnets of 3 to 13 mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every
- * 0.001 mm round the sizes that put a corner on a flat). Half a facet, π/12, clears the
- * corners as well, but it squares two flats to the cell's edges, and at 37.67 mm those
- * folded the socket floor beside the pocket. Measured on 3,846 one-cell plates with a
- * magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times them,
- * every 0.001 mm round these sizes: 546 open before, and 1 now, a size the turn leaves
- * alone; none came out worse. On 1,800 random designs a counterbore's corner turns, every
- * kind of mount: 85 open before, 10 now. It closed 80 and opened 5: 3 at 42 mm with a
- * magnet from beneath under a deeper counterbore, where one size in nine leaks unturned
- * too, by the same slivers at the magnet pocket's corners in the underside; 1 in a corner
- * boss, at that one size alone; and 1 at 42 mm under a magnet from above, open for a few
- * thousandths round 2.114 under 2.253. The magnet's corners change the turn of none of
- * the 1,800. On 1,500 random page designs that only a magnet's corner turns (34 to 56
- * mm; one cell, 2 x 2, and two pieces joined by dovetails or jigsaws; magnets of 3 to
- * 12.7 mm either way up; a fifth on corner bosses): 41 open or folded before, 6 now. It
- * closed 40 and opened 5, each for a size or two (2 patches 0.002 mm wide, 2 single
- * sizes, and 1 whose neighbours fold unturned too); the sixth folds the same unturned. */
+ * whichever called the turn, no corner of either then comes within 0.003 mm of a flat,
+ * and none within 0.0039 but under a magnet on a shank under 1.2 mm (magnets of 3 to 13
+ * mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every 0.001 mm round the sizes
+ * that put a corner on a flat, and 6.7 million sizes drawn at random round them). The
+ * nearest, 0.0032 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
+ * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. Half a facet, π/12,
+ * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
+ * mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell plates
+ * with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times
+ * them, every 0.001 mm round these sizes: 546 open before, and 1 now, a size the turn
+ * leaves alone; none came out worse. On 1,800 random designs a counterbore's corner
+ * turns, every kind of mount: 75 open or folded before, 15 now. It closed 72 and opened
+ * 12: 11 with a 6 x 2 magnet from beneath under a 3 mm counterbore, all at 42 mm but one,
+ * where about one size in ten leaks unturned too, by the same slivers at the magnet
+ * pocket's corners in the underside; and 1 at 55 mm under an 8 x 3 magnet from above,
+ * 1.723 under 1.89, among sizes that leak turned or not (of 26 turned round it, 6 leak
+ * turned and 4 unturned). The magnet's corners change the turn of none of the 1,800. On
+ * 1,500 random page designs that only a magnet's corner turns (34 to 56 mm; one cell,
+ * 2 x 2, and two pieces joined by dovetails or jigsaws; magnets of 3 to 12.7 mm either
+ * way up; 115 on corner bosses): 47 open or folded before, 5 now. It closed 43 and opened
+ * 1, two pieces with a jigsaw at 44.46 mm and a 4 mm magnet from above: 3 open edges a
+ * piece 2.8 mm up and 2.2 mm off the site, for every shank from 2.487 under a 2.895 head,
+ * which builds closed unturned (the counterbore's corners turn it, and open it, from
+ * 2.508); the other 4 fold the same unturned. */
 const MOUNT_BORE = {
   magnet: { sides: 14, r: (d) => Math.max(d/2 + 0.1, d/2 / Math.cos(Math.PI/14)),
             fits: (room) => 2 * Math.min(room - 0.1, room * Math.cos(Math.PI / 14)) },
diff --git a/sw.js b/sw.js
index 2f4db41..0f69737 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "b4df602d4c9e";
+const VERSION = "2187bb259559";
 const FILES = [
   "./",
   "bins/",

From cac5ccbda0c16e5f08dcd48eb3723777b76d9bae Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 23:33:18 +0000
Subject: [PATCH 26/58] Cut a counterbore that nearly matches the magnet pocket
 at the pocket's corners

The default 6 mm counterbore 3 mm deep under the default 6 x 2 magnet from
beneath shipped open at 42 mm (6 edges, the test tile too, at any depth past
the magnet's): its corners stood 0.022 mm inside the pocket's, on the same rays.
A counterbore within 0.05 mm of the pocket's corners is now cut at the pocket's,
and where it reaches the pocket the two are one prism. The shank's turn and
mountLimits go by the counterbore as cut. The comments also say the shank turns
only where a counterbore is cut, and give the nearest corner as 0.0033 mm.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md      |  23 ++++++--
 src/core.js         | 132 ++++++++++++++++++++++++++++++++------------
 test/plate-audit.js |  36 +++++++++++-
 3 files changed, 150 insertions(+), 41 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index 88299a5..eab68ff 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -757,10 +757,20 @@ currently installed):
   cos(π/12), and 0.01 mm more. Narrower, the 14 flats cross the 12 corners and the two
   cuts' walls weave round the hole, and here and there a cell leaked by the hundred (#73:
   2.03 mm over 2 with the corners on the sizes, 2.046 over 2 and 1.034 over 1 with the
-  flats). Such a head is cut as none, as one no wider than the hole always was. And the
-  shank is turned π/84 about its axis where one of the counterbore's corners, or one of
-  the magnet pocket's, would otherwise stand within 0.005 mm of a flat's plane carried on
-  past the shank (`MOUNT_BORE.hole.turn`): the BSP splits a magnet pocket's floor or roof
+  flats). Such a head is cut as none, as one no wider than the hole always was. A
+  counterbore whose corners come within 0.05 mm of the magnet pocket's is cut at the
+  pocket's (`MOUNT_BORE.head.cut`), and where it reaches the pocket the two are cut as
+  one prism: both are 14-gons on the same rays, and a hair apart, where one stopped
+  inside the other, they left a ring that thin. Standing its flats on the size put the
+  default 6 mm head's corners 0.022 mm inside the 6 mm magnet's, and 3 mm deep under the
+  6 × 2 magnet from beneath it left 6 edges open a cell at 42 mm, the test tile among
+  them; main's head, its corners on the size, stood 0.1 off and built closed. A head in
+  the band is cut up to 0.1 mm wider or narrower across its flats than typed, and
+  `mountLimits` reads it back as cut (`head.fitsCut`). Where a counterbore is cut, and
+  only there, the shank is turned π/84 about its axis where one of the counterbore's
+  corners, or one of the magnet pocket's, would otherwise stand within 0.005 mm of a
+  flat's plane carried on past the shank (`MOUNT_BORE.hole.turn`, which goes by the
+  counterbore as cut): the BSP splits a magnet pocket's floor or roof
   along that whole plane, the weld pulled the corner onto the split, and the plate came
   out open by the dozen round every site (#74: 136 edges a piece for 1.0353 mm under
   1.0873 with a magnet from above at 42 mm, on main; and 26 a piece at 41.24 mm for a 3 mm
@@ -775,8 +785,9 @@ currently installed):
   either comes within 0.003 mm of a flat, and none within 0.0039 but under a magnet on a
   shank under 1.2 mm; a shank no corner came near is cut as before. The page reads
   the shank again after the head and the magnet, since its turn and that cap go by both.
-  `MOUNT_BORE.screw` says whether a design's counterbore is cut and how far its shank is
-  turned, for the cutter and for `mountLimits`, which measures that shank turned.
+  `MOUNT_BORE.screw` says whether a design's counterbore is cut, how far out its corners
+  stand and how far its shank is turned, for the cutter and for `mountLimits`, which
+  measures that counterbore and that shank turned.
 - **The socket's corner clearance is not uniform.** Known, documented, deliberately not
   fixed — see [socket-clearance.md](socket-clearance.md).
 - **The plate's outer corner radius has a ceiling, and it is the socket's.** Both the
diff --git a/src/core.js b/src/core.js
index ed2558e..107cd09 100644
--- a/src/core.js
+++ b/src/core.js
@@ -911,9 +911,40 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * always was: within 3.5% of the hole it is no seat for a screw head, and all it would
  * add is slivers between the shank's corners.
  *
- * Under a counterbore the shank is turned a little about its axis (`turn`, #74) where a
- * corner of the counterbore or of the magnet pocket would stand on one of its flats
- * carried on past the shank. The BSP splits what it meets along a flat's whole plane, not
+ * A counterbore whose corners come within 0.05 mm of the magnet pocket's (head.snap) is
+ * cut at the pocket's (head.cut), and where it reaches the pocket the two are cut as one
+ * prism (fastenerCutter). Both are 14-gons on the same rays, so a hair apart their walls
+ * stand a hair off each other, and where one stops inside the other it leaves a ring that
+ * thin: the roof of a pocket from beneath round a counterbore deeper than it, the floor
+ * of one from above that a counterbore breaks into, or the counterbore's own roof in the
+ * pocket. Standing its flats on the size put the default 6 mm head's corners 0.022 mm
+ * inside the 6 mm magnet's, where main's, on the size, stood 0.1 inside. Deeper than the
+ * 2 mm magnet from beneath it left 6 edges open a cell at 42 mm, the test tile with
+ * magnets and screws among them, at every depth from 2.25 to 4, and 39 of 49 shanks from
+ * 1 to 5.8 mm under it 3 deep left 3 to 6. A 6.39 head 2 deep over a 4.24 shank broke
+ * into a 6.35 x 2 magnet pocket from above at 44.46 mm, its corners 0.0018 mm out, and
+ * left 131 a cell. Main builds every one of these closed. Cut at the pocket's corners
+ * but unioned with it, the counterbore still split their shared walls at the pocket's
+ * roof, and a jigsaw at 41.76 mm folded there; as one prism it is the pocket made deeper.
+ * A head in the band is cut up to 0.1 mm wider or narrower across its flats than typed,
+ * mountLimits measures it as cut (head.fitsCut), and one the pocket from beneath then
+ * holds whole is not cut, as before. The shank's turn goes by the counterbore as cut: one
+ * turned for a 6.02 mm head's corners while it was cut at the 6 mm magnet's left 3.66
+ * under it open at 42 mm. Measured on 240 random designs whose counterbore's corners are
+ * in the band and reach the pocket (two in three a 6 x 2 magnet, either way up; half at
+ * 42 mm, the rest 34 to 56; one cell, the test tile, 2 x 2, two pieces with dovetails or
+ * jigsaws): of the 223 taken, 12 were open, folded or turned before, with 380 open edges,
+ * and 2 now: one tile at 36.43 mm with a face turned on main as well, and 5.376 under
+ * 6.006 at 42 mm, 12 open edges, a shank that leaks as many under the bare pocket with
+ * no counterbore at all. Main leaves 7 of its 225 bad. A design whose counterbore is not
+ * in the band builds the same bytes as before.
+ *
+ * Where a counterbore is cut, and only there, the shank is turned a little about its
+ * axis (`turn`, #74) where a corner of the counterbore or of the magnet pocket would
+ * stand on one of its flats carried on past the shank. With no counterbore a magnet
+ * pocket's corners alone do not turn it: at 41.24 mm a 3 mm shank under a 7.3 mm magnet
+ * from above, a corner on a flat, builds closed unturned with no counterbore over it.
+ * The BSP splits what it meets along a flat's whole plane, not
  * just the flat: the floor of a magnet pocket from above, which is a ring round the
  * counterbore, or the roof of one from beneath round a counterbore deeper than it. A
  * split a micron or two from the corner was welded onto it (healCsgSeams), which bent the
@@ -941,22 +972,25 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * and none within 0.0039 but under a magnet on a shank under 1.2 mm (magnets of 3 to 13
  * mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every 0.001 mm round the sizes
  * that put a corner on a flat, and 6.7 million sizes drawn at random round them). The
- * nearest, 0.0032 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
+ * nearest, 0.0033 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
  * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. Half a facet, π/12,
  * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
  * mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell plates
  * with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times
  * them, every 0.001 mm round these sizes: 546 open before, and 1 now, a size the turn
  * leaves alone; none came out worse. On 1,800 random designs a counterbore's corner
- * turns, every kind of mount: 75 open or folded before, 15 now. It closed 72 and opened
- * 12: 11 with a 6 x 2 magnet from beneath under a 3 mm counterbore, all at 42 mm but one,
- * where about one size in ten leaks unturned too, by the same slivers at the magnet
- * pocket's corners in the underside; and 1 at 55 mm under an 8 x 3 magnet from above,
- * 1.723 under 1.89, among sizes that leak turned or not (of 26 turned round it, 6 leak
- * turned and 4 unturned). The magnet's corners change the turn of none of the 1,800. On
+ * turns, every kind of mount: 74 open or folded before, 14 now. It closed 71 and opened
+ * 11: 10 with a 6 x 2 magnet from beneath under a 3 mm counterbore, all at 42 mm but one,
+ * by slivers at the magnet pocket's corners in the underside, sizes main builds closed
+ * but one; and 1 at 55 mm under an 8 x 3 magnet from above, 1.723 under 1.89, among sizes
+ * that leak turned or not (of 26 turned round it, 6 leak turned and 4 unturned). That
+ * mount at 42 mm is the one where the turn does more harm than good: 5 closed against 9
+ * opened, and on 300 random sizes there 5 opened of the 27 it turns and none closed. The
+ * mount leaks by itself as well: of the 273 sizes it leaves unturned, 21 here, 17 on main.
+ * The magnet's corners change the turn of none of the 1,800. On
  * 1,500 random page designs that only a magnet's corner turns (34 to 56 mm; one cell,
  * 2 x 2, and two pieces joined by dovetails or jigsaws; magnets of 3 to 12.7 mm either
- * way up; 115 on corner bosses): 47 open or folded before, 5 now. It closed 43 and opened
+ * way up; 115 on corner bosses): 45 open or folded before, 5 now. It closed 41 and opened
  * 1, two pieces with a jigsaw at 44.46 mm and a 4 mm magnet from above: 3 open edges a
  * piece 2.8 mm up and 2.2 mm off the site, for every shank from 2.487 under a 2.895 head,
  * which builds closed unturned (the counterbore's corners turn it, and open it, from
@@ -967,14 +1001,32 @@ const MOUNT_BORE = {
   head: { sides: 14, r: (d) => d/2 / Math.cos(Math.PI/14),
           fits: (room) => 2 * room * Math.cos(Math.PI / 14),
           over: (hole) => 2 * MOUNT_BORE.hole.r(hole) + 0.01,
-          cuts: (d, hole) => d >= MOUNT_BORE.head.over(hole) },
+          cuts: (d, hole) => d >= MOUNT_BORE.head.over(hole),
+          // how far out a counterbore headD across is cut at its corners, beside a magnet
+          // pocket magnetR out at its corners or none: within `snap` of the pocket's, at
+          // the pocket's (see above)
+          cut: (d, magnetR) => {
+            const r = MOUNT_BORE.head.r(d);
+            return magnetR && Math.abs(r - magnetR) < MOUNT_BORE.head.snap ? magnetR : r;
+          },
+          /* and back the other way, the largest size cut inside a room. `cut` never goes
+             down as the size goes up, so that is a size: below the band, `fits`; for a
+             room the pocket's corners fit but the band's top does not, the band's top,
+             since every size in the band is cut at the pocket's; for one the band's
+             bottom fits but the pocket does not, the band's bottom. */
+          fitsCut: (room, magnetR) => {
+            const { head } = MOUNT_BORE, s = head.snap;
+            if (!magnetR || room >= magnetR + s || room < magnetR - s) return head.fits(room);
+            return head.fits(room >= magnetR ? magnetR + s : magnetR - s) - 1e-6;
+          },
+          snap: 0.05 },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12),
-          // how far to turn the shank under a counterbore headD across, in a magnet pocket
-          // magnetR out at its corners or none (see above)
-          turn: (d, headD, magnetR) => {
+          // how far to turn the shank under a counterbore cut headR out at its corners
+          // (head.cut), in a magnet pocket magnetR out at its corners or none (see above)
+          turn: (d, headR, magnetR) => {
             // the magnet pocket's corners stand on the same rays as the counterbore's
-            const { head, hole } = MOUNT_BORE, rs = magnetR ? [head.r(headD), magnetR] : [head.r(headD)];
+            const { head, hole } = MOUNT_BORE, rs = magnetR ? [headR, magnetR] : [headR];
             const clear = (t) => {   // the nearest a corner comes to one of the flats' planes
               let g = Infinity;
               for (const R of rs) for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
@@ -989,21 +1041,22 @@ const MOUNT_BORE = {
             }
             return most > clear(0) ? best : 0;
           } },
-  /* What fastenerCutter cuts for a design's screw, as { counterbore, turn }: whether the
-     counterbore is cut, and how far the shank is turned under it. Here so that mountLimits
-     measures the same shank the cutter cuts.
+  /* What fastenerCutter cuts for a design's screw, as { counterbore, headR, turn }:
+     whether the counterbore is cut, how far out its corners stand (head.cut), and how far
+     the shank is turned under it. Here so that mountLimits measures the same counterbore
+     and shank the cutter cuts.
      A counterbore the magnet pocket from beneath holds whole is that pocket already: both
-     14 sides, corners on the same rays, no deeper. Since the bores stand their flats on
-     the sizes, the default 6 mm head's walls stand 0.022 mm inside the 6 mm magnet's,
-     and unioned, the test tile at 42 mm with magnets and screws left 6 edges open in
-     its underside. Left out, the pocket is the same solid, and closed. */
+     14 sides, corners on the same rays, no deeper. Left out, the pocket is the same
+     solid. That is the default 6 mm head under the 6 mm magnet 2 deep, cut at the
+     pocket's corners (head.cut), and the test tile at 42 mm with magnets and screws. */
   screw: (cfg) => {
-    const { magnet, head, hole } = MOUNT_BORE, magnetR = magnet.r(cfg.magnetD);
+    const { magnet, head, hole } = MOUNT_BORE, magnetR = cfg.magnets ? magnet.r(cfg.magnetD) : 0;
+    const headR = head.cut(cfg.screwHeadD, magnetR);
     const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
-      head.r(cfg.screwHeadD) <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
+      headR <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
     const counterbore = head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet;
-    return { counterbore,
-             turn: counterbore ? hole.turn(cfg.screwHoleD, cfg.screwHeadD, cfg.magnets ? magnetR : 0) : 0 };
+    return { counterbore, headR,
+             turn: counterbore ? hole.turn(cfg.screwHoleD, headR, magnetR) : 0 };
   },
 };
 
@@ -1031,15 +1084,21 @@ function fastenerCutter(cfg, magZ0, magZ1, shankTop) {
   // each bore as MOUNT_BORE shapes it
   const { magnet, head, hole } = MOUNT_BORE;
   const magnetR = magnet.r(cfg.magnetD);
+  const { counterbore, headR, turn: t } = cfg.screws ? MOUNT_BORE.screw(cfg) : { counterbore: false };
+  const above = cfg.magnetSide === 'top';
+  // a counterbore cut at the magnet pocket's corners (MOUNT_BORE.head.cut) that reaches the
+  // pocket is one prism with it, from the underside to the top of whichever ends higher:
+  // unioned, their shared walls came out split at the pocket's roof (see MOUNT_BORE)
+  const one = cfg.magnets && counterbore && headR === magnetR && (!above || cfg.screwHeadDepth >= magZ0);
   if (cfg.magnets)
-    add(cfg.magnetSide === 'top'
-      ? cylinder(0, 0, magnetR, magZ0, magZ1, magnet.sides)
+    add(one ? cylinder(0, 0, magnetR, -0.5, Math.max(above ? magZ1 : cfg.magnetH, cfg.screwHeadDepth), magnet.sides)
+      : above ? cylinder(0, 0, magnetR, magZ0, magZ1, magnet.sides)
       : cylinder(0, 0, magnetR, -0.5, cfg.magnetH, magnet.sides));
   if (cfg.screws) {
     // the counterbore, unless the magnet pocket from beneath is that already (MOUNT_BORE.screw)
-    const { counterbore, turn: t } = MOUNT_BORE.screw(cfg);
-    if (counterbore)
-      add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
+    // or it is cut as one with the pocket
+    if (counterbore && !one)
+      add(cylinder(0, 0, headR, -0.5, cfg.screwHeadDepth, head.sides));
     // the shank, turned where a corner of the counterbore or the magnet pocket would stand
     // on one of its flats (#74)
     const shank = cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides);
@@ -2818,8 +2877,13 @@ function mountLimits(cfg, layout, known) {
      corners stand out past it, and a magnet's 0.1 mm over its radius where that is
      further. The shank is turned where the cutter turns it, and measured so: its turn
      goes by the sizes asked, the head's and the magnet's as well as its own, so it is
-     the shank of this design that is measured. */
-  const BORE = { magnetD: MOUNT_BORE.magnet, screwHeadD: MOUNT_BORE.head, screwHoleD: MOUNT_BORE.hole };
+     the shank of this design that is measured. A counterbore within MOUNT_BORE.head.snap
+     of the magnet pocket's corners is cut at the pocket's, up to 0.05 mm further out or
+     in, so its sizes are read back through that (head.fitsCut), which goes by the room
+     alone: the cap does not move with the head typed. */
+  const magnetR = cfg.magnets ? MOUNT_BORE.magnet.r(cfg.magnetD) : 0;
+  const BORE = { magnetD: MOUNT_BORE.magnet, screwHoleD: MOUNT_BORE.hole,
+                 screwHeadD: { sides: MOUNT_BORE.head.sides, fits: (room) => MOUNT_BORE.head.fitsCut(room, magnetR) } };
   const shankTurn = cfg.screws ? MOUNT_BORE.screw(cfg).turn : 0;
   // the room the cell, the floor or a boss leaves, and the hole beside
   const own = { magnetD: fit(cfg.magnetSide === 'top' ? top : under), screwHoleD: fit(top), screwHeadD: fit(under) };
diff --git a/test/plate-audit.js b/test/plate-audit.js
index a7d3053..809adaa 100644
--- a/test/plate-audit.js
+++ b/test/plate-audit.js
@@ -1046,10 +1046,15 @@ console.log('\nloose parts and samples, watertight and oriented:');
      their flats on the sizes, the 6 mm counterbore's walls stood 0.022 mm inside the 6 mm
      magnet pocket's from beneath, and the tile left 6 edges open in its underside; a
      counterbore the magnet pocket holds whole is not cut now (fastenerCutter). A magnet
-     from above is cut from the other face, and that tile is built too. */
+     from above is cut from the other face, and that tile is built too. A counterbore
+     deeper than the 2 mm magnet left the same 6 at every depth from 2.25 to 4: it is cut
+     at the pocket's corners now, one prism with it (MOUNT_BORE.head.cut). */
   for (const side of ['bottom', 'top'])
     report(`tile, magnets ${side === 'top' ? 'above' : 'below'}, screws`,
       G.buildTestTile({ ...tileCfg, magnets: true, magnetSide: side, screws: true }).polys);
+  for (const depth of [2.5, 3])
+    report(`tile, below, ${depth} deep`,
+      G.buildTestTile({ ...tileCfg, magnets: true, screws: true, screwHeadDepth: depth }).polys);
 
   for (const conn of CONNECTORS)
     for (const keyInsert of ['bottom', 'top']) {
@@ -2188,6 +2193,35 @@ console.log('\nthe other limits, built at their ends:');
       : `TAKEN up to ${lim.screwHoleD} mm`}; at that, ${leakText(r)}${folds ? `, ${folds} FOLDS` : ''}`);
     if (!refused || r.bad || folds) bad++;
   }
+  /* A counterbore whose corners come within 0.05 mm of the magnet pocket's, and that
+     reaches the pocket. Both are 14-gons on the same rays, and where one stopped inside
+     the other a hair off it they left a ring that thin. The default 6 mm head's corners
+     stand 0.022 mm inside the 6 mm magnet's, and 3 mm deep under the 6 x 2 magnet from
+     beneath it left 6 edges open at 42 mm; a 6.39 mm head 2 deep broke into a 6.35 x 2
+     magnet pocket from above at 44.46 mm, its corners 0.0018 mm out, and left 248 over
+     two pieces. Main built both closed. Such a counterbore is cut at the pocket's corners
+     now, one prism with it (MOUNT_BORE.head.cut). The shank's turn goes by the counterbore
+     as cut: turned for the 6.02 mm head's corners while it was cut at the magnet's, 3.66
+     under it left 9. And unioned rather than one prism, the two split their shared walls
+     at the pocket's roof, and the jigsaw at 41.76 mm folded twice there. Each is a size
+     the page takes, and has to build closed, with no folds. */
+  for (const [nm, o] of [
+    ['3 under 6, 3 deep, 42', { screwHeadDepth: 3 }],
+    ['4.24 under 6.39, above, 44.46', { pitch: 44.46, drawerW: 88.92, drawerD: 44.46, bedW: 56.46, connector: 'dovetail',
+      magnetD: 6.35, magnetSide: 'top', screwHoleD: 4.24, screwHeadD: 6.39 }],
+    ['3.66 under 6.02, 3 deep, 42', { screwHoleD: 3.66, screwHeadD: 6.02, screwHeadDepth: 3 }],
+    ['41.76 mm jigsaw, 3.742 deep', { pitch: 41.76, drawerW: 83.52, drawerD: 41.76, bedW: 53.76, connector: 'puzzle',
+      screwHoleD: 3.32, screwHeadD: 5.973, screwHeadDepth: 3.742 }],
+  ]) {
+    const at = { pitch: 42, drawerW: 42, drawerD: 42, connector: 'none', magnets: true, screws: true, ...o };
+    const cfg = designCfg(at), lim = G.mountLimits(cfg, G.computeLayout(cfg));
+    const taken = ['magnetD', 'screwHoleD', 'screwHeadD'].every((f) => cfg[f] <= lim[f] + 1e-9 &&
+      !lim.gaps[f].some(([a, b]) => cfg[f] >= a - 1e-9 && cfg[f] <= b + 1e-9));
+    const r = buildAll(at);
+    const folds = r.pieces.reduce((s, pp) => s + checkOrientation(pp).folds, 0);
+    console.log(`  ${nm.padEnd(30)} ${taken ? '' : 'REFUSED, '}${leakText(r)}${folds ? `, ${folds} FOLDS` : ''}`);
+    if (!taken || r.bad || folds) bad++;
+  }
   /* A pocket against a joint's cut in the floor (#64). A bowtie housed in the floor at
      42 mm, with magnets from beneath, built 12 bad edges at 7.9 mm and 19 at 10 with
      Download on: the pocket reached the key's recess, and with both ceilings 2 mm up the

From bfdc5a0c8055984f42c2468af979abbafe70a895 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 23:33:36 +0000
Subject: [PATCH 27/58] Drop screwCutter, which nothing calls since
 fastenerCutter cuts every screw

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 src/core.js | 18 ++----------------
 1 file changed, 2 insertions(+), 16 deletions(-)

diff --git a/src/core.js b/src/core.js
index 107cd09..8822168 100644
--- a/src/core.js
+++ b/src/core.js
@@ -876,8 +876,8 @@ function cylinder(cx, cy, r, z0, z1, seg) {
 
 /* The polygon each mounting bore is cut as: how many sides, and how far out its corners
  * stand for a size typed (`r`), and back the other way, the largest size whose corners
- * stay inside a room (`fits`). fastenerCutter and screwCutter cut these and mountLimits
- * holds the sizes to them, so a bore's shape is decided here and nowhere else. Each is
+ * stay inside a room (`fits`). fastenerCutter cuts these and mountLimits holds the sizes
+ * to them, so a bore's shape is decided here and nowhere else. Each is
  * cylinder's polygon about the site, a corner at every 2πk/sides from +x, but for a shank
  * that `turn` moves (below).
  *
@@ -1120,20 +1120,6 @@ function movePolys(polys, dx, dy) {
   }));
 }
 
-// counterbore: hole cylinder full height + wider recess from chosen face, each bore as
-// MOUNT_BORE shapes it
-function screwCutter(cx, cy, holeD, headD, z0, z1, headDepth, fromTop) {
-  const { head, hole } = MOUNT_BORE;
-  let polys = cylinder(cx, cy, hole.r(holeD), z0 - 0.5, z1 + 0.5, hole.sides);
-  if (head.cuts(headD, holeD)) {
-    const rec = fromTop
-      ? cylinder(cx, cy, head.r(headD), z1 - headDepth, z1 + 0.5, head.sides)
-      : cylinder(cx, cy, head.r(headD), z0 - 0.5, z0 + headDepth, head.sides);
-    polys = csgUnion(polys, rec);
-  }
-  return polys;
-}
-
 // dovetail tab footprint (2D); edge: '+x'|'-x'|'+y'|'-y', e = edge coordinate, s = centre along edge
 function tabFootprint(edge, e, s, wr, wt, dp, back) {
   let pts;

From 97decc4037dc4ba04b27c436708c29ecd244993e Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 23:34:01 +0000
Subject: [PATCH 28/58] Say a screw hole has to stay inside the magnet pocket's
 sides, not just narrower

A 5 mm hole is narrower than a 5.1 mm magnet's pocket and is still refused, since
the magnet needs a ledge to sit on; the message now says that.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 src/ui.js                         | 3 ++-
 test/ui/plates-robustness.spec.js | 2 +-
 2 files changed, 3 insertions(+), 2 deletions(-)

diff --git a/src/ui.js b/src/ui.js
index 1049816..f0c18ce 100644
--- a/src/ui.js
+++ b/src/ui.js
@@ -110,7 +110,8 @@ const cutsNamed = () => `${['dovetail', 'puzzle'].includes(state.connector) ? 'n
    pocket stops is stopped whatever the pitch, so that is all it says. */
 const mountWhy = (opens, field) => {
   if (field === 'screwHoleD' && mount().throughMagnet)
-    return `— it runs through the ${state.magnetD} mm magnet's pocket, and has to be narrower than the pocket`;
+    return `— it runs through the ${state.magnetD} mm magnet's pocket, and has to stay inside the pocket's sides ` +
+      'to leave the magnet a ledge to sit on';
   const joint = mount().joint[field];
   const cuts = cutsNamed();
   return `${atPitch()} — mounting holes sit ` +
diff --git a/test/ui/plates-robustness.spec.js b/test/ui/plates-robustness.spec.js
index c0a0c41..e5ed0aa 100644
--- a/test/ui/plates-robustness.spec.js
+++ b/test/ui/plates-robustness.spec.js
@@ -140,7 +140,7 @@ test.describe('ranges on the geometry fields', () => {
        counterbore. 5 mm under a 5.1 mm magnet and a 5.4 mm head built 47 open edges at
        42 mm. */
     ['#cn=none&mg=1&md=5.1&ms=top&sc=1&sh=5&sd=5.4', 'errScrew',
-      /Screw hole Ø must be 4\.9 mm or less — it runs through the 5\.1 mm magnet's pocket, and has to be narrower than the pocket\./],
+      /Screw hole Ø must be 4\.9 mm or less — it runs through the 5\.1 mm magnet's pocket, and has to stay inside the pocket's sides to leave the magnet a ledge to sit on\./],
   ];
   for (const [hash, errId, msg] of CASES) {
     test(`${hash} is refused at the field`, async ({ page }) => {

From 0b2b98d9dcd97751f2cafb0323e12eef9583952c Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 23:35:33 +0000
Subject: [PATCH 29/58] Say no counterbore fits where the size one needs is
 past the head's limit

The line under the screw fields named the size a counterbore is cut from even
where the field refuses it: a bowtie in the floor at 42 mm said "from 7.78 mm"
over a 7.5 mm hole, with the head held to 7.6. It says none fits there now, and
the head field is described by the line as well as by the error.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 src/template.html                 |  2 +-
 src/ui.js                         | 16 ++++++++++++----
 test/ui/plates-robustness.spec.js | 13 +++++++++++++
 3 files changed, 26 insertions(+), 5 deletions(-)

diff --git a/src/template.html b/src/template.html
index 0ba249d..77fab93 100644
--- a/src/template.html
+++ b/src/template.html
@@ -279,7 +279,7 @@ <h2 class="ph"><button type="button" aria-expanded="true" aria-controls="b-mag">
     <label class="tog"><input id="screws" type="checkbox"> Screw holes (counterbored, 4 per cell)</label>
     <div class="row3" id="screwRow" style="display:none">
       <label class="f"><b>Hole Ø</b><input id="screwHoleD" type="number" step="0.5" min="1" value="3" aria-describedby="errScrew"></label>
-      <label class="f"><b>Head Ø</b><input id="screwHeadD" type="number" step="0.5" min="1" value="6" aria-describedby="errScrew"></label>
+      <label class="f"><b>Head Ø</b><input id="screwHeadD" type="number" step="0.5" min="1" value="6" aria-describedby="errScrew screwHeadHint"></label>
       <label class="f"><b>Head depth</b><input id="screwHeadDepth" type="number" step="0.1" min="0.5" max="10" value="2" aria-describedby="errScrew"></label>
     </div>
     <span class="hint" id="errScrew" style="color:var(--red)" hidden></span>
diff --git a/src/ui.js b/src/ui.js
index f0c18ce..6d032bc 100644
--- a/src/ui.js
+++ b/src/ui.js
@@ -413,13 +413,21 @@ function readControls() {
   $('screwRow').style.display = state.screws ? '' : 'none';
   /* A head wider than the hole that does not clear its corners is cut as none (#73); the
      README said so, and nothing at the field did. Not while either size is refused: the
-     red line under the fields says what to do first. */
+     red line under the fields says what to do first. And the size one is cut from only
+     where the field takes it, past any sizes it refuses: a bowtie in the floor at 42 mm
+     holds the head to 7.6 mm, and over a 7.5 mm hole one is cut only from 7.78. */
   const noBore = state.screws && headCutAsNone() &&
     !['screwHoleD', 'screwHeadD'].some((id) => fieldErrors.has(id) || noRoom.has(id));
   $('screwHeadHint').hidden = !noBore;
-  if (noBore) $('screwHeadHint').textContent = `A ${state.screwHeadD} mm head does not clear ` +
-    `the corners of a ${state.screwHoleD} mm hole, so no counterbore is cut. One is from ` +
-    `${headClearsFrom(state.screwHoleD)} mm.`;
+  if (noBore) {
+    const from = headClearsFrom(state.screwHoleD), m = mount();
+    let at = from;
+    for (const [a, b] of m.gaps.screwHeadD) if (at >= a - 1e-9 && at <= b + 1e-9) at = Math.round(b * 100 + 1) / 100;
+    $('screwHeadHint').textContent = `A ${state.screwHeadD} mm head does not clear ` +
+      `the corners of a ${state.screwHoleD} mm hole, so no counterbore is cut. ` +
+      (at <= m.screwHeadD + 1e-9 ? `One is from ${at} mm.`
+        : `None fits here: one is from ${from} mm, and the head stops at ${m.screwHeadD} mm.`);
+  }
   $('connHintDove').style.display = state.connector === 'dovetail' ? '' : 'none';
   $('connHintPuzzle').style.display = state.connector === 'puzzle' ? '' : 'none';
   // Bowtie and puzzle key shared one hint, so picking between them meant reading the
diff --git a/test/ui/plates-robustness.spec.js b/test/ui/plates-robustness.spec.js
index e5ed0aa..9318914 100644
--- a/test/ui/plates-robustness.spec.js
+++ b/test/ui/plates-robustness.spec.js
@@ -615,6 +615,19 @@ test.describe('a screw head that does not clear its shank is cut as none', () =>
         if (hint) expect(await text(page, 'screwHeadHint')).toBe(hint);
         expect(errors).toEqual([]);
       });
+  /* The line names a size the field takes, or says none fits: a bowtie in the floor at
+     42 mm holds the head to 7.6 mm, and over a 7.5 mm hole a counterbore is cut only
+     from 7.78. It is read with the field. */
+  test('where no counterbore fits, the line says so rather than naming one the field refuses',
+    async ({ page }) => {
+      const errors = await openAt(page, '#cn=bowtie&sc=1&sh=7.5&sd=7.55');
+      expect(await shown(page, 'errScrew')).toBe(false);
+      expect(await text(page, 'screwHeadHint')).toBe('A 7.55 mm head does not clear the corners of ' +
+        'a 7.5 mm hole, so no counterbore is cut. None fits here: one is from 7.78 mm, and the ' +
+        'head stops at 7.6 mm.');
+      expect(await page.getAttribute('#screwHeadD', 'aria-describedby')).toContain('screwHeadHint');
+      expect(errors).toEqual([]);
+    });
 });
 
 /* The checks name the piece as well (#76). The table, the preview and Download's tooltip

From d38cec0b03f787798b8eb4ac1e0b7f361157904d Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 23:35:51 +0000
Subject: [PATCH 30/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html | 150 ++++++++++++++++++++++++++++--------------
 index.html      | 171 ++++++++++++++++++++++++++++++++----------------
 sw.js           |   2 +-
 3 files changed, 216 insertions(+), 107 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index 1634797..ab5bbdb 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -2482,8 +2482,8 @@ <h2 id="drawersTitle">Your drawers</h2>
 
 /* The polygon each mounting bore is cut as: how many sides, and how far out its corners
  * stand for a size typed (`r`), and back the other way, the largest size whose corners
- * stay inside a room (`fits`). fastenerCutter and screwCutter cut these and mountLimits
- * holds the sizes to them, so a bore's shape is decided here and nowhere else. Each is
+ * stay inside a room (`fits`). fastenerCutter cuts these and mountLimits holds the sizes
+ * to them, so a bore's shape is decided here and nowhere else. Each is
  * cylinder's polygon about the site, a corner at every 2πk/sides from +x, but for a shank
  * that `turn` moves (below).
  *
@@ -2517,9 +2517,40 @@ <h2 id="drawersTitle">Your drawers</h2>
  * always was: within 3.5% of the hole it is no seat for a screw head, and all it would
  * add is slivers between the shank's corners.
  *
- * Under a counterbore the shank is turned a little about its axis (`turn`, #74) where a
- * corner of the counterbore or of the magnet pocket would stand on one of its flats
- * carried on past the shank. The BSP splits what it meets along a flat's whole plane, not
+ * A counterbore whose corners come within 0.05 mm of the magnet pocket's (head.snap) is
+ * cut at the pocket's (head.cut), and where it reaches the pocket the two are cut as one
+ * prism (fastenerCutter). Both are 14-gons on the same rays, so a hair apart their walls
+ * stand a hair off each other, and where one stops inside the other it leaves a ring that
+ * thin: the roof of a pocket from beneath round a counterbore deeper than it, the floor
+ * of one from above that a counterbore breaks into, or the counterbore's own roof in the
+ * pocket. Standing its flats on the size put the default 6 mm head's corners 0.022 mm
+ * inside the 6 mm magnet's, where main's, on the size, stood 0.1 inside. Deeper than the
+ * 2 mm magnet from beneath it left 6 edges open a cell at 42 mm, the test tile with
+ * magnets and screws among them, at every depth from 2.25 to 4, and 39 of 49 shanks from
+ * 1 to 5.8 mm under it 3 deep left 3 to 6. A 6.39 head 2 deep over a 4.24 shank broke
+ * into a 6.35 x 2 magnet pocket from above at 44.46 mm, its corners 0.0018 mm out, and
+ * left 131 a cell. Main builds every one of these closed. Cut at the pocket's corners
+ * but unioned with it, the counterbore still split their shared walls at the pocket's
+ * roof, and a jigsaw at 41.76 mm folded there; as one prism it is the pocket made deeper.
+ * A head in the band is cut up to 0.1 mm wider or narrower across its flats than typed,
+ * mountLimits measures it as cut (head.fitsCut), and one the pocket from beneath then
+ * holds whole is not cut, as before. The shank's turn goes by the counterbore as cut: one
+ * turned for a 6.02 mm head's corners while it was cut at the 6 mm magnet's left 3.66
+ * under it open at 42 mm. Measured on 240 random designs whose counterbore's corners are
+ * in the band and reach the pocket (two in three a 6 x 2 magnet, either way up; half at
+ * 42 mm, the rest 34 to 56; one cell, the test tile, 2 x 2, two pieces with dovetails or
+ * jigsaws): of the 223 taken, 12 were open, folded or turned before, with 380 open edges,
+ * and 2 now: one tile at 36.43 mm with a face turned on main as well, and 5.376 under
+ * 6.006 at 42 mm, 12 open edges, a shank that leaks as many under the bare pocket with
+ * no counterbore at all. Main leaves 7 of its 225 bad. A design whose counterbore is not
+ * in the band builds the same bytes as before.
+ *
+ * Where a counterbore is cut, and only there, the shank is turned a little about its
+ * axis (`turn`, #74) where a corner of the counterbore or of the magnet pocket would
+ * stand on one of its flats carried on past the shank. With no counterbore a magnet
+ * pocket's corners alone do not turn it: at 41.24 mm a 3 mm shank under a 7.3 mm magnet
+ * from above, a corner on a flat, builds closed unturned with no counterbore over it.
+ * The BSP splits what it meets along a flat's whole plane, not
  * just the flat: the floor of a magnet pocket from above, which is a ring round the
  * counterbore, or the roof of one from beneath round a counterbore deeper than it. A
  * split a micron or two from the corner was welded onto it (healCsgSeams), which bent the
@@ -2547,22 +2578,25 @@ <h2 id="drawersTitle">Your drawers</h2>
  * and none within 0.0039 but under a magnet on a shank under 1.2 mm (magnets of 3 to 13
  * mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every 0.001 mm round the sizes
  * that put a corner on a flat, and 6.7 million sizes drawn at random round them). The
- * nearest, 0.0032 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
+ * nearest, 0.0033 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
  * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. Half a facet, π/12,
  * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
  * mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell plates
  * with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times
  * them, every 0.001 mm round these sizes: 546 open before, and 1 now, a size the turn
  * leaves alone; none came out worse. On 1,800 random designs a counterbore's corner
- * turns, every kind of mount: 75 open or folded before, 15 now. It closed 72 and opened
- * 12: 11 with a 6 x 2 magnet from beneath under a 3 mm counterbore, all at 42 mm but one,
- * where about one size in ten leaks unturned too, by the same slivers at the magnet
- * pocket's corners in the underside; and 1 at 55 mm under an 8 x 3 magnet from above,
- * 1.723 under 1.89, among sizes that leak turned or not (of 26 turned round it, 6 leak
- * turned and 4 unturned). The magnet's corners change the turn of none of the 1,800. On
+ * turns, every kind of mount: 74 open or folded before, 14 now. It closed 71 and opened
+ * 11: 10 with a 6 x 2 magnet from beneath under a 3 mm counterbore, all at 42 mm but one,
+ * by slivers at the magnet pocket's corners in the underside, sizes main builds closed
+ * but one; and 1 at 55 mm under an 8 x 3 magnet from above, 1.723 under 1.89, among sizes
+ * that leak turned or not (of 26 turned round it, 6 leak turned and 4 unturned). That
+ * mount at 42 mm is the one where the turn does more harm than good: 5 closed against 9
+ * opened, and on 300 random sizes there 5 opened of the 27 it turns and none closed. The
+ * mount leaks by itself as well: of the 273 sizes it leaves unturned, 21 here, 17 on main.
+ * The magnet's corners change the turn of none of the 1,800. On
  * 1,500 random page designs that only a magnet's corner turns (34 to 56 mm; one cell,
  * 2 x 2, and two pieces joined by dovetails or jigsaws; magnets of 3 to 12.7 mm either
- * way up; 115 on corner bosses): 47 open or folded before, 5 now. It closed 43 and opened
+ * way up; 115 on corner bosses): 45 open or folded before, 5 now. It closed 41 and opened
  * 1, two pieces with a jigsaw at 44.46 mm and a 4 mm magnet from above: 3 open edges a
  * piece 2.8 mm up and 2.2 mm off the site, for every shank from 2.487 under a 2.895 head,
  * which builds closed unturned (the counterbore's corners turn it, and open it, from
@@ -2573,14 +2607,32 @@ <h2 id="drawersTitle">Your drawers</h2>
   head: { sides: 14, r: (d) => d/2 / Math.cos(Math.PI/14),
           fits: (room) => 2 * room * Math.cos(Math.PI / 14),
           over: (hole) => 2 * MOUNT_BORE.hole.r(hole) + 0.01,
-          cuts: (d, hole) => d >= MOUNT_BORE.head.over(hole) },
+          cuts: (d, hole) => d >= MOUNT_BORE.head.over(hole),
+          // how far out a counterbore headD across is cut at its corners, beside a magnet
+          // pocket magnetR out at its corners or none: within `snap` of the pocket's, at
+          // the pocket's (see above)
+          cut: (d, magnetR) => {
+            const r = MOUNT_BORE.head.r(d);
+            return magnetR && Math.abs(r - magnetR) < MOUNT_BORE.head.snap ? magnetR : r;
+          },
+          /* and back the other way, the largest size cut inside a room. `cut` never goes
+             down as the size goes up, so that is a size: below the band, `fits`; for a
+             room the pocket's corners fit but the band's top does not, the band's top,
+             since every size in the band is cut at the pocket's; for one the band's
+             bottom fits but the pocket does not, the band's bottom. */
+          fitsCut: (room, magnetR) => {
+            const { head } = MOUNT_BORE, s = head.snap;
+            if (!magnetR || room >= magnetR + s || room < magnetR - s) return head.fits(room);
+            return head.fits(room >= magnetR ? magnetR + s : magnetR - s) - 1e-6;
+          },
+          snap: 0.05 },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12),
-          // how far to turn the shank under a counterbore headD across, in a magnet pocket
-          // magnetR out at its corners or none (see above)
-          turn: (d, headD, magnetR) => {
+          // how far to turn the shank under a counterbore cut headR out at its corners
+          // (head.cut), in a magnet pocket magnetR out at its corners or none (see above)
+          turn: (d, headR, magnetR) => {
             // the magnet pocket's corners stand on the same rays as the counterbore's
-            const { head, hole } = MOUNT_BORE, rs = magnetR ? [head.r(headD), magnetR] : [head.r(headD)];
+            const { head, hole } = MOUNT_BORE, rs = magnetR ? [headR, magnetR] : [headR];
             const clear = (t) => {   // the nearest a corner comes to one of the flats' planes
               let g = Infinity;
               for (const R of rs) for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
@@ -2595,21 +2647,22 @@ <h2 id="drawersTitle">Your drawers</h2>
             }
             return most > clear(0) ? best : 0;
           } },
-  /* What fastenerCutter cuts for a design's screw, as { counterbore, turn }: whether the
-     counterbore is cut, and how far the shank is turned under it. Here so that mountLimits
-     measures the same shank the cutter cuts.
+  /* What fastenerCutter cuts for a design's screw, as { counterbore, headR, turn }:
+     whether the counterbore is cut, how far out its corners stand (head.cut), and how far
+     the shank is turned under it. Here so that mountLimits measures the same counterbore
+     and shank the cutter cuts.
      A counterbore the magnet pocket from beneath holds whole is that pocket already: both
-     14 sides, corners on the same rays, no deeper. Since the bores stand their flats on
-     the sizes, the default 6 mm head's walls stand 0.022 mm inside the 6 mm magnet's,
-     and unioned, the test tile at 42 mm with magnets and screws left 6 edges open in
-     its underside. Left out, the pocket is the same solid, and closed. */
+     14 sides, corners on the same rays, no deeper. Left out, the pocket is the same
+     solid. That is the default 6 mm head under the 6 mm magnet 2 deep, cut at the
+     pocket's corners (head.cut), and the test tile at 42 mm with magnets and screws. */
   screw: (cfg) => {
-    const { magnet, head, hole } = MOUNT_BORE, magnetR = magnet.r(cfg.magnetD);
+    const { magnet, head, hole } = MOUNT_BORE, magnetR = cfg.magnets ? magnet.r(cfg.magnetD) : 0;
+    const headR = head.cut(cfg.screwHeadD, magnetR);
     const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
-      head.r(cfg.screwHeadD) <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
+      headR <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
     const counterbore = head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet;
-    return { counterbore,
-             turn: counterbore ? hole.turn(cfg.screwHoleD, cfg.screwHeadD, cfg.magnets ? magnetR : 0) : 0 };
+    return { counterbore, headR,
+             turn: counterbore ? hole.turn(cfg.screwHoleD, headR, magnetR) : 0 };
   },
 };
 
@@ -2637,15 +2690,21 @@ <h2 id="drawersTitle">Your drawers</h2>
   // each bore as MOUNT_BORE shapes it
   const { magnet, head, hole } = MOUNT_BORE;
   const magnetR = magnet.r(cfg.magnetD);
+  const { counterbore, headR, turn: t } = cfg.screws ? MOUNT_BORE.screw(cfg) : { counterbore: false };
+  const above = cfg.magnetSide === 'top';
+  // a counterbore cut at the magnet pocket's corners (MOUNT_BORE.head.cut) that reaches the
+  // pocket is one prism with it, from the underside to the top of whichever ends higher:
+  // unioned, their shared walls came out split at the pocket's roof (see MOUNT_BORE)
+  const one = cfg.magnets && counterbore && headR === magnetR && (!above || cfg.screwHeadDepth >= magZ0);
   if (cfg.magnets)
-    add(cfg.magnetSide === 'top'
-      ? cylinder(0, 0, magnetR, magZ0, magZ1, magnet.sides)
+    add(one ? cylinder(0, 0, magnetR, -0.5, Math.max(above ? magZ1 : cfg.magnetH, cfg.screwHeadDepth), magnet.sides)
+      : above ? cylinder(0, 0, magnetR, magZ0, magZ1, magnet.sides)
       : cylinder(0, 0, magnetR, -0.5, cfg.magnetH, magnet.sides));
   if (cfg.screws) {
     // the counterbore, unless the magnet pocket from beneath is that already (MOUNT_BORE.screw)
-    const { counterbore, turn: t } = MOUNT_BORE.screw(cfg);
-    if (counterbore)
-      add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
+    // or it is cut as one with the pocket
+    if (counterbore && !one)
+      add(cylinder(0, 0, headR, -0.5, cfg.screwHeadDepth, head.sides));
     // the shank, turned where a corner of the counterbore or the magnet pocket would stand
     // on one of its flats (#74)
     const shank = cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides);
@@ -2667,20 +2726,6 @@ <h2 id="drawersTitle">Your drawers</h2>
   }));
 }
 
-// counterbore: hole cylinder full height + wider recess from chosen face, each bore as
-// MOUNT_BORE shapes it
-function screwCutter(cx, cy, holeD, headD, z0, z1, headDepth, fromTop) {
-  const { head, hole } = MOUNT_BORE;
-  let polys = cylinder(cx, cy, hole.r(holeD), z0 - 0.5, z1 + 0.5, hole.sides);
-  if (head.cuts(headD, holeD)) {
-    const rec = fromTop
-      ? cylinder(cx, cy, head.r(headD), z1 - headDepth, z1 + 0.5, head.sides)
-      : cylinder(cx, cy, head.r(headD), z0 - 0.5, z0 + headDepth, head.sides);
-    polys = csgUnion(polys, rec);
-  }
-  return polys;
-}
-
 // dovetail tab footprint (2D); edge: '+x'|'-x'|'+y'|'-y', e = edge coordinate, s = centre along edge
 function tabFootprint(edge, e, s, wr, wt, dp, back) {
   let pts;
@@ -4424,8 +4469,13 @@ <h2 id="drawersTitle">Your drawers</h2>
      corners stand out past it, and a magnet's 0.1 mm over its radius where that is
      further. The shank is turned where the cutter turns it, and measured so: its turn
      goes by the sizes asked, the head's and the magnet's as well as its own, so it is
-     the shank of this design that is measured. */
-  const BORE = { magnetD: MOUNT_BORE.magnet, screwHeadD: MOUNT_BORE.head, screwHoleD: MOUNT_BORE.hole };
+     the shank of this design that is measured. A counterbore within MOUNT_BORE.head.snap
+     of the magnet pocket's corners is cut at the pocket's, up to 0.05 mm further out or
+     in, so its sizes are read back through that (head.fitsCut), which goes by the room
+     alone: the cap does not move with the head typed. */
+  const magnetR = cfg.magnets ? MOUNT_BORE.magnet.r(cfg.magnetD) : 0;
+  const BORE = { magnetD: MOUNT_BORE.magnet, screwHoleD: MOUNT_BORE.hole,
+                 screwHeadD: { sides: MOUNT_BORE.head.sides, fits: (room) => MOUNT_BORE.head.fitsCut(room, magnetR) } };
   const shankTurn = cfg.screws ? MOUNT_BORE.screw(cfg).turn : 0;
   // the room the cell, the floor or a boss leaves, and the hole beside
   const own = { magnetD: fit(cfg.magnetSide === 'top' ? top : under), screwHoleD: fit(top), screwHeadD: fit(under) };
diff --git a/index.html b/index.html
index 08e2ea6..350796d 100644
--- a/index.html
+++ b/index.html
@@ -1230,7 +1230,7 @@ <h2 class="ph"><button type="button" aria-expanded="true" aria-controls="b-mag">
     <label class="tog"><input id="screws" type="checkbox"> Screw holes (counterbored, 4 per cell)</label>
     <div class="row3" id="screwRow" style="display:none">
       <label class="f"><b>Hole Ø</b><input id="screwHoleD" type="number" step="0.5" min="1" value="3" aria-describedby="errScrew"></label>
-      <label class="f"><b>Head Ø</b><input id="screwHeadD" type="number" step="0.5" min="1" value="6" aria-describedby="errScrew"></label>
+      <label class="f"><b>Head Ø</b><input id="screwHeadD" type="number" step="0.5" min="1" value="6" aria-describedby="errScrew screwHeadHint"></label>
       <label class="f"><b>Head depth</b><input id="screwHeadDepth" type="number" step="0.1" min="0.5" max="10" value="2" aria-describedby="errScrew"></label>
     </div>
     <span class="hint" id="errScrew" style="color:var(--red)" hidden></span>
@@ -2270,8 +2270,8 @@ <h2 id="drawersTitle">Your drawers</h2>
 
 /* The polygon each mounting bore is cut as: how many sides, and how far out its corners
  * stand for a size typed (`r`), and back the other way, the largest size whose corners
- * stay inside a room (`fits`). fastenerCutter and screwCutter cut these and mountLimits
- * holds the sizes to them, so a bore's shape is decided here and nowhere else. Each is
+ * stay inside a room (`fits`). fastenerCutter cuts these and mountLimits holds the sizes
+ * to them, so a bore's shape is decided here and nowhere else. Each is
  * cylinder's polygon about the site, a corner at every 2πk/sides from +x, but for a shank
  * that `turn` moves (below).
  *
@@ -2305,9 +2305,40 @@ <h2 id="drawersTitle">Your drawers</h2>
  * always was: within 3.5% of the hole it is no seat for a screw head, and all it would
  * add is slivers between the shank's corners.
  *
- * Under a counterbore the shank is turned a little about its axis (`turn`, #74) where a
- * corner of the counterbore or of the magnet pocket would stand on one of its flats
- * carried on past the shank. The BSP splits what it meets along a flat's whole plane, not
+ * A counterbore whose corners come within 0.05 mm of the magnet pocket's (head.snap) is
+ * cut at the pocket's (head.cut), and where it reaches the pocket the two are cut as one
+ * prism (fastenerCutter). Both are 14-gons on the same rays, so a hair apart their walls
+ * stand a hair off each other, and where one stops inside the other it leaves a ring that
+ * thin: the roof of a pocket from beneath round a counterbore deeper than it, the floor
+ * of one from above that a counterbore breaks into, or the counterbore's own roof in the
+ * pocket. Standing its flats on the size put the default 6 mm head's corners 0.022 mm
+ * inside the 6 mm magnet's, where main's, on the size, stood 0.1 inside. Deeper than the
+ * 2 mm magnet from beneath it left 6 edges open a cell at 42 mm, the test tile with
+ * magnets and screws among them, at every depth from 2.25 to 4, and 39 of 49 shanks from
+ * 1 to 5.8 mm under it 3 deep left 3 to 6. A 6.39 head 2 deep over a 4.24 shank broke
+ * into a 6.35 x 2 magnet pocket from above at 44.46 mm, its corners 0.0018 mm out, and
+ * left 131 a cell. Main builds every one of these closed. Cut at the pocket's corners
+ * but unioned with it, the counterbore still split their shared walls at the pocket's
+ * roof, and a jigsaw at 41.76 mm folded there; as one prism it is the pocket made deeper.
+ * A head in the band is cut up to 0.1 mm wider or narrower across its flats than typed,
+ * mountLimits measures it as cut (head.fitsCut), and one the pocket from beneath then
+ * holds whole is not cut, as before. The shank's turn goes by the counterbore as cut: one
+ * turned for a 6.02 mm head's corners while it was cut at the 6 mm magnet's left 3.66
+ * under it open at 42 mm. Measured on 240 random designs whose counterbore's corners are
+ * in the band and reach the pocket (two in three a 6 x 2 magnet, either way up; half at
+ * 42 mm, the rest 34 to 56; one cell, the test tile, 2 x 2, two pieces with dovetails or
+ * jigsaws): of the 223 taken, 12 were open, folded or turned before, with 380 open edges,
+ * and 2 now: one tile at 36.43 mm with a face turned on main as well, and 5.376 under
+ * 6.006 at 42 mm, 12 open edges, a shank that leaks as many under the bare pocket with
+ * no counterbore at all. Main leaves 7 of its 225 bad. A design whose counterbore is not
+ * in the band builds the same bytes as before.
+ *
+ * Where a counterbore is cut, and only there, the shank is turned a little about its
+ * axis (`turn`, #74) where a corner of the counterbore or of the magnet pocket would
+ * stand on one of its flats carried on past the shank. With no counterbore a magnet
+ * pocket's corners alone do not turn it: at 41.24 mm a 3 mm shank under a 7.3 mm magnet
+ * from above, a corner on a flat, builds closed unturned with no counterbore over it.
+ * The BSP splits what it meets along a flat's whole plane, not
  * just the flat: the floor of a magnet pocket from above, which is a ring round the
  * counterbore, or the roof of one from beneath round a counterbore deeper than it. A
  * split a micron or two from the corner was welded onto it (healCsgSeams), which bent the
@@ -2335,22 +2366,25 @@ <h2 id="drawersTitle">Your drawers</h2>
  * and none within 0.0039 but under a magnet on a shank under 1.2 mm (magnets of 3 to 13
  * mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every 0.001 mm round the sizes
  * that put a corner on a flat, and 6.7 million sizes drawn at random round them). The
- * nearest, 0.0032 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
+ * nearest, 0.0033 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
  * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. Half a facet, π/12,
  * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
  * mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell plates
  * with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times
  * them, every 0.001 mm round these sizes: 546 open before, and 1 now, a size the turn
  * leaves alone; none came out worse. On 1,800 random designs a counterbore's corner
- * turns, every kind of mount: 75 open or folded before, 15 now. It closed 72 and opened
- * 12: 11 with a 6 x 2 magnet from beneath under a 3 mm counterbore, all at 42 mm but one,
- * where about one size in ten leaks unturned too, by the same slivers at the magnet
- * pocket's corners in the underside; and 1 at 55 mm under an 8 x 3 magnet from above,
- * 1.723 under 1.89, among sizes that leak turned or not (of 26 turned round it, 6 leak
- * turned and 4 unturned). The magnet's corners change the turn of none of the 1,800. On
+ * turns, every kind of mount: 74 open or folded before, 14 now. It closed 71 and opened
+ * 11: 10 with a 6 x 2 magnet from beneath under a 3 mm counterbore, all at 42 mm but one,
+ * by slivers at the magnet pocket's corners in the underside, sizes main builds closed
+ * but one; and 1 at 55 mm under an 8 x 3 magnet from above, 1.723 under 1.89, among sizes
+ * that leak turned or not (of 26 turned round it, 6 leak turned and 4 unturned). That
+ * mount at 42 mm is the one where the turn does more harm than good: 5 closed against 9
+ * opened, and on 300 random sizes there 5 opened of the 27 it turns and none closed. The
+ * mount leaks by itself as well: of the 273 sizes it leaves unturned, 21 here, 17 on main.
+ * The magnet's corners change the turn of none of the 1,800. On
  * 1,500 random page designs that only a magnet's corner turns (34 to 56 mm; one cell,
  * 2 x 2, and two pieces joined by dovetails or jigsaws; magnets of 3 to 12.7 mm either
- * way up; 115 on corner bosses): 47 open or folded before, 5 now. It closed 43 and opened
+ * way up; 115 on corner bosses): 45 open or folded before, 5 now. It closed 41 and opened
  * 1, two pieces with a jigsaw at 44.46 mm and a 4 mm magnet from above: 3 open edges a
  * piece 2.8 mm up and 2.2 mm off the site, for every shank from 2.487 under a 2.895 head,
  * which builds closed unturned (the counterbore's corners turn it, and open it, from
@@ -2361,14 +2395,32 @@ <h2 id="drawersTitle">Your drawers</h2>
   head: { sides: 14, r: (d) => d/2 / Math.cos(Math.PI/14),
           fits: (room) => 2 * room * Math.cos(Math.PI / 14),
           over: (hole) => 2 * MOUNT_BORE.hole.r(hole) + 0.01,
-          cuts: (d, hole) => d >= MOUNT_BORE.head.over(hole) },
+          cuts: (d, hole) => d >= MOUNT_BORE.head.over(hole),
+          // how far out a counterbore headD across is cut at its corners, beside a magnet
+          // pocket magnetR out at its corners or none: within `snap` of the pocket's, at
+          // the pocket's (see above)
+          cut: (d, magnetR) => {
+            const r = MOUNT_BORE.head.r(d);
+            return magnetR && Math.abs(r - magnetR) < MOUNT_BORE.head.snap ? magnetR : r;
+          },
+          /* and back the other way, the largest size cut inside a room. `cut` never goes
+             down as the size goes up, so that is a size: below the band, `fits`; for a
+             room the pocket's corners fit but the band's top does not, the band's top,
+             since every size in the band is cut at the pocket's; for one the band's
+             bottom fits but the pocket does not, the band's bottom. */
+          fitsCut: (room, magnetR) => {
+            const { head } = MOUNT_BORE, s = head.snap;
+            if (!magnetR || room >= magnetR + s || room < magnetR - s) return head.fits(room);
+            return head.fits(room >= magnetR ? magnetR + s : magnetR - s) - 1e-6;
+          },
+          snap: 0.05 },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12),
-          // how far to turn the shank under a counterbore headD across, in a magnet pocket
-          // magnetR out at its corners or none (see above)
-          turn: (d, headD, magnetR) => {
+          // how far to turn the shank under a counterbore cut headR out at its corners
+          // (head.cut), in a magnet pocket magnetR out at its corners or none (see above)
+          turn: (d, headR, magnetR) => {
             // the magnet pocket's corners stand on the same rays as the counterbore's
-            const { head, hole } = MOUNT_BORE, rs = magnetR ? [head.r(headD), magnetR] : [head.r(headD)];
+            const { head, hole } = MOUNT_BORE, rs = magnetR ? [headR, magnetR] : [headR];
             const clear = (t) => {   // the nearest a corner comes to one of the flats' planes
               let g = Infinity;
               for (const R of rs) for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
@@ -2383,21 +2435,22 @@ <h2 id="drawersTitle">Your drawers</h2>
             }
             return most > clear(0) ? best : 0;
           } },
-  /* What fastenerCutter cuts for a design's screw, as { counterbore, turn }: whether the
-     counterbore is cut, and how far the shank is turned under it. Here so that mountLimits
-     measures the same shank the cutter cuts.
+  /* What fastenerCutter cuts for a design's screw, as { counterbore, headR, turn }:
+     whether the counterbore is cut, how far out its corners stand (head.cut), and how far
+     the shank is turned under it. Here so that mountLimits measures the same counterbore
+     and shank the cutter cuts.
      A counterbore the magnet pocket from beneath holds whole is that pocket already: both
-     14 sides, corners on the same rays, no deeper. Since the bores stand their flats on
-     the sizes, the default 6 mm head's walls stand 0.022 mm inside the 6 mm magnet's,
-     and unioned, the test tile at 42 mm with magnets and screws left 6 edges open in
-     its underside. Left out, the pocket is the same solid, and closed. */
+     14 sides, corners on the same rays, no deeper. Left out, the pocket is the same
+     solid. That is the default 6 mm head under the 6 mm magnet 2 deep, cut at the
+     pocket's corners (head.cut), and the test tile at 42 mm with magnets and screws. */
   screw: (cfg) => {
-    const { magnet, head, hole } = MOUNT_BORE, magnetR = magnet.r(cfg.magnetD);
+    const { magnet, head, hole } = MOUNT_BORE, magnetR = cfg.magnets ? magnet.r(cfg.magnetD) : 0;
+    const headR = head.cut(cfg.screwHeadD, magnetR);
     const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
-      head.r(cfg.screwHeadD) <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
+      headR <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
     const counterbore = head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet;
-    return { counterbore,
-             turn: counterbore ? hole.turn(cfg.screwHoleD, cfg.screwHeadD, cfg.magnets ? magnetR : 0) : 0 };
+    return { counterbore, headR,
+             turn: counterbore ? hole.turn(cfg.screwHoleD, headR, magnetR) : 0 };
   },
 };
 
@@ -2425,15 +2478,21 @@ <h2 id="drawersTitle">Your drawers</h2>
   // each bore as MOUNT_BORE shapes it
   const { magnet, head, hole } = MOUNT_BORE;
   const magnetR = magnet.r(cfg.magnetD);
+  const { counterbore, headR, turn: t } = cfg.screws ? MOUNT_BORE.screw(cfg) : { counterbore: false };
+  const above = cfg.magnetSide === 'top';
+  // a counterbore cut at the magnet pocket's corners (MOUNT_BORE.head.cut) that reaches the
+  // pocket is one prism with it, from the underside to the top of whichever ends higher:
+  // unioned, their shared walls came out split at the pocket's roof (see MOUNT_BORE)
+  const one = cfg.magnets && counterbore && headR === magnetR && (!above || cfg.screwHeadDepth >= magZ0);
   if (cfg.magnets)
-    add(cfg.magnetSide === 'top'
-      ? cylinder(0, 0, magnetR, magZ0, magZ1, magnet.sides)
+    add(one ? cylinder(0, 0, magnetR, -0.5, Math.max(above ? magZ1 : cfg.magnetH, cfg.screwHeadDepth), magnet.sides)
+      : above ? cylinder(0, 0, magnetR, magZ0, magZ1, magnet.sides)
       : cylinder(0, 0, magnetR, -0.5, cfg.magnetH, magnet.sides));
   if (cfg.screws) {
     // the counterbore, unless the magnet pocket from beneath is that already (MOUNT_BORE.screw)
-    const { counterbore, turn: t } = MOUNT_BORE.screw(cfg);
-    if (counterbore)
-      add(cylinder(0, 0, head.r(cfg.screwHeadD), -0.5, cfg.screwHeadDepth, head.sides));
+    // or it is cut as one with the pocket
+    if (counterbore && !one)
+      add(cylinder(0, 0, headR, -0.5, cfg.screwHeadDepth, head.sides));
     // the shank, turned where a corner of the counterbore or the magnet pocket would stand
     // on one of its flats (#74)
     const shank = cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides);
@@ -2455,20 +2514,6 @@ <h2 id="drawersTitle">Your drawers</h2>
   }));
 }
 
-// counterbore: hole cylinder full height + wider recess from chosen face, each bore as
-// MOUNT_BORE shapes it
-function screwCutter(cx, cy, holeD, headD, z0, z1, headDepth, fromTop) {
-  const { head, hole } = MOUNT_BORE;
-  let polys = cylinder(cx, cy, hole.r(holeD), z0 - 0.5, z1 + 0.5, hole.sides);
-  if (head.cuts(headD, holeD)) {
-    const rec = fromTop
-      ? cylinder(cx, cy, head.r(headD), z1 - headDepth, z1 + 0.5, head.sides)
-      : cylinder(cx, cy, head.r(headD), z0 - 0.5, z0 + headDepth, head.sides);
-    polys = csgUnion(polys, rec);
-  }
-  return polys;
-}
-
 // dovetail tab footprint (2D); edge: '+x'|'-x'|'+y'|'-y', e = edge coordinate, s = centre along edge
 function tabFootprint(edge, e, s, wr, wt, dp, back) {
   let pts;
@@ -4212,8 +4257,13 @@ <h2 id="drawersTitle">Your drawers</h2>
      corners stand out past it, and a magnet's 0.1 mm over its radius where that is
      further. The shank is turned where the cutter turns it, and measured so: its turn
      goes by the sizes asked, the head's and the magnet's as well as its own, so it is
-     the shank of this design that is measured. */
-  const BORE = { magnetD: MOUNT_BORE.magnet, screwHeadD: MOUNT_BORE.head, screwHoleD: MOUNT_BORE.hole };
+     the shank of this design that is measured. A counterbore within MOUNT_BORE.head.snap
+     of the magnet pocket's corners is cut at the pocket's, up to 0.05 mm further out or
+     in, so its sizes are read back through that (head.fitsCut), which goes by the room
+     alone: the cap does not move with the head typed. */
+  const magnetR = cfg.magnets ? MOUNT_BORE.magnet.r(cfg.magnetD) : 0;
+  const BORE = { magnetD: MOUNT_BORE.magnet, screwHoleD: MOUNT_BORE.hole,
+                 screwHeadD: { sides: MOUNT_BORE.head.sides, fits: (room) => MOUNT_BORE.head.fitsCut(room, magnetR) } };
   const shankTurn = cfg.screws ? MOUNT_BORE.screw(cfg).turn : 0;
   // the room the cell, the floor or a boss leaves, and the hole beside
   const own = { magnetD: fit(cfg.magnetSide === 'top' ? top : under), screwHoleD: fit(top), screwHeadD: fit(under) };
@@ -8047,7 +8097,8 @@ <h2 id="drawersTitle">Your drawers</h2>
    pocket stops is stopped whatever the pitch, so that is all it says. */
 const mountWhy = (opens, field) => {
   if (field === 'screwHoleD' && mount().throughMagnet)
-    return `— it runs through the ${state.magnetD} mm magnet's pocket, and has to be narrower than the pocket`;
+    return `— it runs through the ${state.magnetD} mm magnet's pocket, and has to stay inside the pocket's sides ` +
+      'to leave the magnet a ledge to sit on';
   const joint = mount().joint[field];
   const cuts = cutsNamed();
   return `${atPitch()} — mounting holes sit ` +
@@ -8349,13 +8400,21 @@ <h2 id="drawersTitle">Your drawers</h2>
   $('screwRow').style.display = state.screws ? '' : 'none';
   /* A head wider than the hole that does not clear its corners is cut as none (#73); the
      README said so, and nothing at the field did. Not while either size is refused: the
-     red line under the fields says what to do first. */
+     red line under the fields says what to do first. And the size one is cut from only
+     where the field takes it, past any sizes it refuses: a bowtie in the floor at 42 mm
+     holds the head to 7.6 mm, and over a 7.5 mm hole one is cut only from 7.78. */
   const noBore = state.screws && headCutAsNone() &&
     !['screwHoleD', 'screwHeadD'].some((id) => fieldErrors.has(id) || noRoom.has(id));
   $('screwHeadHint').hidden = !noBore;
-  if (noBore) $('screwHeadHint').textContent = `A ${state.screwHeadD} mm head does not clear ` +
-    `the corners of a ${state.screwHoleD} mm hole, so no counterbore is cut. One is from ` +
-    `${headClearsFrom(state.screwHoleD)} mm.`;
+  if (noBore) {
+    const from = headClearsFrom(state.screwHoleD), m = mount();
+    let at = from;
+    for (const [a, b] of m.gaps.screwHeadD) if (at >= a - 1e-9 && at <= b + 1e-9) at = Math.round(b * 100 + 1) / 100;
+    $('screwHeadHint').textContent = `A ${state.screwHeadD} mm head does not clear ` +
+      `the corners of a ${state.screwHoleD} mm hole, so no counterbore is cut. ` +
+      (at <= m.screwHeadD + 1e-9 ? `One is from ${at} mm.`
+        : `None fits here: one is from ${from} mm, and the head stops at ${m.screwHeadD} mm.`);
+  }
   $('connHintDove').style.display = state.connector === 'dovetail' ? '' : 'none';
   $('connHintPuzzle').style.display = state.connector === 'puzzle' ? '' : 'none';
   // Bowtie and puzzle key shared one hint, so picking between them meant reading the
diff --git a/sw.js b/sw.js
index 0f69737..8804728 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "2187bb259559";
+const VERSION = "b7c606e28a3f";
 const FILES = [
   "./",
   "bins/",

From a4bdbd22d4039a469e3db68b2e088d7e357295ac Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 23:56:35 +0000
Subject: [PATCH 31/58] Drop a re-ask timing from the comment on a turned
 shank's kept reach

The 3.6 ms it gave for asking again on a 30 x 30 puzzle plate does not
reproduce: measured again, asking again on the same cuts takes about
0.07 ms with the reach kept and about 1.2 ms without it. Say what the
cost was instead of a figure.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 src/core.js | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/core.js b/src/core.js
index 8822168..9b52509 100644
--- a/src/core.js
+++ b/src/core.js
@@ -2909,7 +2909,8 @@ function mountLimits(cfg, layout, known) {
     const { sides, fits } = BORE[f];
     /* the room a bore has, measured again for a shank turned under its counterbore, and
        kept on the site by its turn: the page asks again on the same cuts (`known`) once
-       the head and the magnet are read, and on a 30 x 30 puzzle plate that took 3.6 ms */
+       the head and the magnet are read, and measuring every site again was nearly all
+       that asking again cost */
     const turn = f === 'screwHoleD' ? shankTurn : 0;
     const reach = (c, s) => {
       if (!turn) return s.bore[sides];

From 05d0b9a38ed3ac623b334b30256a85f33dc7a2dc Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 23:56:46 +0000
Subject: [PATCH 32/58] Cut main's head apart from the magnet pocket in the
 audit, to keep reaching the seam guard

The 41.24 mm jigsaw with main's bores (7.504 cos(pi/14) over 3 cos(pi/12))
ran the seam repair out of passes, and was the audit's only row that reached
the guard which throws on a second run that settles open. Its head's corners
stand 0.002 mm outside the 7.3 mm magnet pocket's, inside the band where the
counterbore is now cut as the pocket, so it builds whole and the guard went
untested. Export MOUNT_BORE and add a row that sets its snap to 0 for that
build: it throws as on main, and with the guard removed it builds both
pieces with 55 bad edges, so the row fails.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 src/core.js         |  6 ++++--
 test/plate-audit.js | 17 +++++++++++++----
 2 files changed, 17 insertions(+), 6 deletions(-)

diff --git a/src/core.js b/src/core.js
index 9b52509..ef80736 100644
--- a/src/core.js
+++ b/src/core.js
@@ -404,7 +404,9 @@ function healCsgSeams(polys, again) {
      the fastener cut in buildPiece), and so does a jigsaw plate at 41.24 mm with magnets
      from above and a 3.126 mm counterbore, on the first cut of both its pieces, with
      main's 7.504 mm head over a 3 mm shank (the bores 7.504 cos(π/14) and 3 cos(π/12) here,
-     where a bore's flats stand on its size).
+     where a bore's flats stand on its size) cut apart from the magnet's pocket. Here that
+     head is cut as the pocket (MOUNT_BORE.head.snap) and the plate builds whole; the audit
+     cuts it apart again to reach this guard.
 
      The second run is kept only if it comes out closed, and that jigsaw plate is why.
      The merge lets its repair settle, but open, and returned that was 55 bad edges on
@@ -4894,7 +4896,7 @@ const DEFAULTS = {
 
 if (typeof module !== 'undefined') {
   module.exports = { computeLayout, gridCells, halfStrips, pieceConnectors, keysMeet, jointsThatFit, buildPiece, buildTestTile, buildFitSample, jointKind, keyOutline, buildKey, puzzleShape, keyHalf, hclipPrm, snapTopClip, snapTopParts, snapTopPrm, keySiteOps, topPocketCup, snapTopPocket, build3mfXML, packPlates, optimizeForPlates, transformPolys, stlBinary, checkManifold, DEFAULTS, csgSubtract, csgUnion, extrudePoly, socketCutter, polysToTriangles,
-    platePad, cornerBosses, mountLimits, pieceColumn, compositions, PLATE_RANGES, PLATE_MAX_CELLS, MOUNT_SKIN,
+    platePad, cornerBosses, mountLimits, MOUNT_BORE, pieceColumn, compositions, PLATE_RANGES, PLATE_MAX_CELLS, MOUNT_SKIN,
     connClrCeiling, fitClearances, PRINT_LAYER,
     // shared mesh primitives — also used by the bins tool
     makePoly, triangulateRing, earTriangulate, roundedSquareRing, roundedRectRing, clampZ, profilePrism,
diff --git a/test/plate-audit.js b/test/plate-audit.js
index 809adaa..0e866f8 100644
--- a/test/plate-audit.js
+++ b/test/plate-audit.js
@@ -1489,8 +1489,11 @@ function sectionArea(polys, z, dy) {
  * the third, a 7.4 mm head, which main builds whole as well. Of those heads only 7.31 mm
  * still leaks, its corners 0.001 mm inside the magnet's (#77). The fourth cuts main's
  * bores, the head and shank whose polygons are main's 7.504 and 3 mm ones, 7.504 cos(π/14)
- * and 3 cos(π/12): it runs out of passes here as on main and throws, so the second run's
- * guard is still tested. */
+ * and 3 cos(π/12). That head's corners stand 0.002 mm outside the magnet's, inside the band
+ * where the counterbore is cut as the magnet's pocket (MOUNT_BORE.head.snap), so it builds
+ * whole now. The fifth cuts the same head apart from the pocket, as before the band: it runs
+ * out of passes as on main and throws, so the second run's guard is still tested (without
+ * the guard it builds both pieces with 55 bad edges). */
 console.log('\na counterbore whose ceiling three cut lines cross at one point (#76):');
 {
   const PLATE = { pitch: 39.07, drawerW: 170, drawerD: 90, bedW: 100, bedD: 400, marginMode: 'auto',
@@ -1527,8 +1530,14 @@ console.log('\na counterbore whose ceiling three cut lines cross at one point (#
                                ['2.264 mm magnet: folded twice', { magnetH: 2.264 }],
                                ['7.4 mm head', { screwHeadD: 7.4 }],
                                ["main's bores", { screwHeadD: 7.504 * Math.cos(Math.PI / 14),
-                                                  screwHoleD: 3 * Math.cos(Math.PI / 12) }]]) {
-    const b = build({ ...JIGSAW, ...over });
+                                                  screwHoleD: 3 * Math.cos(Math.PI / 12) }],
+                               ["main's bores, cut apart", { screwHeadD: 7.504 * Math.cos(Math.PI / 14),
+                                                             screwHoleD: 3 * Math.cos(Math.PI / 12),
+                                                             apart: true }]]) {
+    const { apart, ...sizes } = over, snap = G.MOUNT_BORE.head.snap;
+    if (apart) G.MOUNT_BORE.head.snap = 0;
+    let b;
+    try { b = build({ ...JIGSAW, ...sizes }); } finally { G.MOUNT_BORE.head.snap = snap; }
     const held = b.whole || /^healCsgSeams/.test(b.err || '');
     console.log(`  ${label.padEnd(38)} ${b.text}${held ? '' : '  NEITHER THREW NOR BUILT WHOLE'}`);
     if (!held) bad++;

From 02a78f36dee17d439f781bea4ca9ff80a93d6317 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 9 Oct 2026 23:56:53 +0000
Subject: [PATCH 33/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html | 9 ++++++---
 index.html      | 9 ++++++---
 sw.js           | 2 +-
 3 files changed, 13 insertions(+), 7 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index ab5bbdb..e7f9804 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -2010,7 +2010,9 @@ <h2 id="drawersTitle">Your drawers</h2>
      the fastener cut in buildPiece), and so does a jigsaw plate at 41.24 mm with magnets
      from above and a 3.126 mm counterbore, on the first cut of both its pieces, with
      main's 7.504 mm head over a 3 mm shank (the bores 7.504 cos(π/14) and 3 cos(π/12) here,
-     where a bore's flats stand on its size).
+     where a bore's flats stand on its size) cut apart from the magnet's pocket. Here that
+     head is cut as the pocket (MOUNT_BORE.head.snap) and the plate builds whole; the audit
+     cuts it apart again to reach this guard.
 
      The second run is kept only if it comes out closed, and that jigsaw plate is why.
      The merge lets its repair settle, but open, and returned that was 55 bad edges on
@@ -4515,7 +4517,8 @@ <h2 id="drawersTitle">Your drawers</h2>
     const { sides, fits } = BORE[f];
     /* the room a bore has, measured again for a shank turned under its counterbore, and
        kept on the site by its turn: the page asks again on the same cuts (`known`) once
-       the head and the magnet are read, and on a 30 x 30 puzzle plate that took 3.6 ms */
+       the head and the magnet are read, and measuring every site again was nearly all
+       that asking again cost */
     const turn = f === 'screwHoleD' ? shankTurn : 0;
     const reach = (c, s) => {
       if (!turn) return s.bore[sides];
@@ -6499,7 +6502,7 @@ <h2 id="drawersTitle">Your drawers</h2>
 
 if (typeof module !== 'undefined') {
   module.exports = { computeLayout, gridCells, halfStrips, pieceConnectors, keysMeet, jointsThatFit, buildPiece, buildTestTile, buildFitSample, jointKind, keyOutline, buildKey, puzzleShape, keyHalf, hclipPrm, snapTopClip, snapTopParts, snapTopPrm, keySiteOps, topPocketCup, snapTopPocket, build3mfXML, packPlates, optimizeForPlates, transformPolys, stlBinary, checkManifold, DEFAULTS, csgSubtract, csgUnion, extrudePoly, socketCutter, polysToTriangles,
-    platePad, cornerBosses, mountLimits, pieceColumn, compositions, PLATE_RANGES, PLATE_MAX_CELLS, MOUNT_SKIN,
+    platePad, cornerBosses, mountLimits, MOUNT_BORE, pieceColumn, compositions, PLATE_RANGES, PLATE_MAX_CELLS, MOUNT_SKIN,
     connClrCeiling, fitClearances, PRINT_LAYER,
     // shared mesh primitives — also used by the bins tool
     makePoly, triangulateRing, earTriangulate, roundedSquareRing, roundedRectRing, clampZ, profilePrism,
diff --git a/index.html b/index.html
index 350796d..0275097 100644
--- a/index.html
+++ b/index.html
@@ -1798,7 +1798,9 @@ <h2 id="drawersTitle">Your drawers</h2>
      the fastener cut in buildPiece), and so does a jigsaw plate at 41.24 mm with magnets
      from above and a 3.126 mm counterbore, on the first cut of both its pieces, with
      main's 7.504 mm head over a 3 mm shank (the bores 7.504 cos(π/14) and 3 cos(π/12) here,
-     where a bore's flats stand on its size).
+     where a bore's flats stand on its size) cut apart from the magnet's pocket. Here that
+     head is cut as the pocket (MOUNT_BORE.head.snap) and the plate builds whole; the audit
+     cuts it apart again to reach this guard.
 
      The second run is kept only if it comes out closed, and that jigsaw plate is why.
      The merge lets its repair settle, but open, and returned that was 55 bad edges on
@@ -4303,7 +4305,8 @@ <h2 id="drawersTitle">Your drawers</h2>
     const { sides, fits } = BORE[f];
     /* the room a bore has, measured again for a shank turned under its counterbore, and
        kept on the site by its turn: the page asks again on the same cuts (`known`) once
-       the head and the magnet are read, and on a 30 x 30 puzzle plate that took 3.6 ms */
+       the head and the magnet are read, and measuring every site again was nearly all
+       that asking again cost */
     const turn = f === 'screwHoleD' ? shankTurn : 0;
     const reach = (c, s) => {
       if (!turn) return s.bore[sides];
@@ -6287,7 +6290,7 @@ <h2 id="drawersTitle">Your drawers</h2>
 
 if (typeof module !== 'undefined') {
   module.exports = { computeLayout, gridCells, halfStrips, pieceConnectors, keysMeet, jointsThatFit, buildPiece, buildTestTile, buildFitSample, jointKind, keyOutline, buildKey, puzzleShape, keyHalf, hclipPrm, snapTopClip, snapTopParts, snapTopPrm, keySiteOps, topPocketCup, snapTopPocket, build3mfXML, packPlates, optimizeForPlates, transformPolys, stlBinary, checkManifold, DEFAULTS, csgSubtract, csgUnion, extrudePoly, socketCutter, polysToTriangles,
-    platePad, cornerBosses, mountLimits, pieceColumn, compositions, PLATE_RANGES, PLATE_MAX_CELLS, MOUNT_SKIN,
+    platePad, cornerBosses, mountLimits, MOUNT_BORE, pieceColumn, compositions, PLATE_RANGES, PLATE_MAX_CELLS, MOUNT_SKIN,
     connClrCeiling, fitClearances, PRINT_LAYER,
     // shared mesh primitives — also used by the bins tool
     makePoly, triangulateRing, earTriangulate, roundedSquareRing, roundedRectRing, clampZ, profilePrism,
diff --git a/sw.js b/sw.js
index 8804728..de06780 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "b7c606e28a3f";
+const VERSION = "25e92542fc09";
 const FILES = [
   "./",
   "bins/",

From 2da85dbe098cfe51bfae5c8d08e662c9e66046f7 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 01:58:55 +0000
Subject: [PATCH 34/58] Turn the shank under a bare magnet pocket for the
 pocket's corners

The shank was turned only where a counterbore was cut. A counterbore within
0.05 mm of the magnet pocket is cut at the pocket's corners now, and from
beneath, no deeper than the magnet, the pocket holds it whole, so it is not
cut and the shank stopped turning: 4.18 mm under a 5 mm magnet and a 5.12
head, the pocket's corner 0.002 mm off a flat, left 12 open edges at 42 mm
(24 with a 5 x 3 magnet over two cells, 51 under a 5.08 head at 41.14 mm),
where main and the counterbore cut beside the pocket were closed. A bare
pocket from above, under a head too narrow to cut, leaked the same way and
was never turned: 30 for the same shank under a 5 x 2 magnet.

MOUNT_BORE.screw turns the shank for the pocket's corners alone where no
counterbore is cut, either way up, and mountLimits, which reads the turn
from it, measures the shank as cut. On 1,000 random designs from beneath
with no counterbore and a pocket corner within 0.0045 mm of a flat, 6 of
the 859 taken were bad and 2 are now (both 6 edges under a 4.16 x 2 magnet,
as before); on 800 from above, 11 of 566 with 351 open edges, and 3 now,
test tiles with a face turned over and none open. Of 700 random designs
with screws, the 7 that change bytes are the ones turned now, each with a
magnet and no counterbore cut. Eight audit rows build those sizes; each
fails on the head before this.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md      | 13 +++++++-----
 src/core.js         | 52 ++++++++++++++++++++++++++++++---------------
 test/plate-audit.js | 41 +++++++++++++++++++++++++++++++++++
 3 files changed, 84 insertions(+), 22 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index 8dec180..f7cd73a 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -766,11 +766,14 @@ currently installed):
   6 × 2 magnet from beneath it left 6 edges open a cell at 42 mm, the test tile among
   them; main's head, its corners on the size, stood 0.1 off and built closed. A head in
   the band is cut up to 0.1 mm wider or narrower across its flats than typed, and
-  `mountLimits` reads it back as cut (`head.fitsCut`). Where a counterbore is cut, and
-  only there, the shank is turned π/84 about its axis where one of the counterbore's
-  corners, or one of the magnet pocket's, would otherwise stand within 0.005 mm of a
-  flat's plane carried on past the shank (`MOUNT_BORE.hole.turn`, which goes by the
-  counterbore as cut): the BSP splits a magnet pocket's floor or roof
+  `mountLimits` reads it back as cut (`head.fitsCut`). The shank is turned π/84 about
+  its axis where one of the counterbore's corners, or one of the magnet pocket's, would
+  otherwise stand within 0.005 mm of a flat's plane carried on past the shank
+  (`MOUNT_BORE.hole.turn`, which goes by the counterbore as cut, and by the pocket's
+  corners alone where no counterbore is cut: a 5 mm magnet from beneath that holds a
+  5.12 mm head whole over 4.18 mm left 12 edges open at 42 mm unturned, and the same
+  shank under the magnet from above with no counterbore 30): the BSP splits a magnet
+  pocket's floor or roof
   along that whole plane, the weld pulled the corner onto the split, and the plate came
   out open by the dozen round every site (#74: 136 edges a piece for 1.0353 mm under
   1.0873 with a magnet from above at 42 mm, on main; and 26 a piece at 41.24 mm for a 3 mm
diff --git a/src/core.js b/src/core.js
index 066e0de..94d0df7 100644
--- a/src/core.js
+++ b/src/core.js
@@ -930,7 +930,8 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * roof, and a jigsaw at 41.76 mm folded there; as one prism it is the pocket made deeper.
  * A head in the band is cut up to 0.1 mm wider or narrower across its flats than typed,
  * mountLimits measures it as cut (head.fitsCut), and one the pocket from beneath then
- * holds whole is not cut, as before. The shank's turn goes by the counterbore as cut: one
+ * holds whole is not cut, as before, the shank turned for the pocket's corners alone
+ * (below). The shank's turn goes by the counterbore as cut: one
  * turned for a 6.02 mm head's corners while it was cut at the 6 mm magnet's left 3.66
  * under it open at 42 mm. Measured on 240 random designs whose counterbore's corners are
  * in the band and reach the pocket (two in three a 6 x 2 magnet, either way up; half at
@@ -938,14 +939,12 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * jigsaws): of the 223 taken, 12 were open, folded or turned before, with 380 open edges,
  * and 2 now: one tile at 36.43 mm with a face turned on main as well, and 5.376 under
  * 6.006 at 42 mm, 12 open edges, a shank that leaks as many under the bare pocket with
- * no counterbore at all. Main leaves 7 of its 225 bad. A design whose counterbore is not
- * in the band builds the same bytes as before.
+ * no counterbore at all. Main leaves 7 of its 225 bad. The band changes no design whose
+ * counterbore is not in it.
  *
- * Where a counterbore is cut, and only there, the shank is turned a little about its
- * axis (`turn`, #74) where a corner of the counterbore or of the magnet pocket would
- * stand on one of its flats carried on past the shank. With no counterbore a magnet
- * pocket's corners alone do not turn it: at 41.24 mm a 3 mm shank under a 7.3 mm magnet
- * from above, a corner on a flat, builds closed unturned with no counterbore over it.
+ * The shank is turned a little about its axis (`turn`, #74) where a corner of the
+ * counterbore or of the magnet pocket would stand on one of its flats carried on past
+ * the shank, and where no counterbore is cut, the pocket's corners alone turn it.
  * The BSP splits what it meets along a flat's whole plane, not
  * just the flat: the floor of a magnet pocket from above, which is a ring round the
  * counterbore, or the roof of one from beneath round a counterbore deeper than it. A
@@ -968,12 +967,29 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * a magnet's corner on a flat all the same: at 41.24 mm a 3 mm shank under a 7.3 mm
  * magnet from above, a corner 0.4 microns off a flat, left 26 edges a piece in the socket
  * floor whatever the head, and 4.9911 under 7.246 with a 6 mm one left 44 at 49.02 mm. A
+ * bare pocket, with no counterbore cut, leaks the same way: 4.18 mm under a 5 mm magnet,
+ * a corner 0.002 mm off a flat, left 12 edges a cell at 42 mm from beneath, where the
+ * pocket holds a 5.12 mm head whole, and 30 from above under a head too narrow to cut.
+ * From beneath, that came with the band above: a 5.12 head had been cut beside the pocket
+ * and turned the shank, and held whole it no longer did. On 1,000 random designs from
+ * beneath with no counterbore cut and a corner of the pocket within 0.0045 mm of a flat
+ * (34 to 56 mm; one cell, the test tile, 2 x 2, corner bosses, two pieces with dovetails
+ * or jigsaws; magnets of 3 to 13 mm), of the 859 taken 6 were open or had a face turned
+ * over before, with 83 open edges, and 2 now, under a 4.16 x 2 magnet at 42 mm, 6 edges
+ * each as before, where main leaves 12. On 800 from above, of the 566 taken, 11 before,
+ * with 351 open edges, and 3 now, none open: test tiles with a face turned over, one of
+ * them as before. Turned, 2.58 under a 4.34 head the 4.16 x 2 magnet holds whole at
+ * 42 mm leaves 9, where it built closed unturned and main leaves 10; its pocket's
+ * corners stand 0.06 mm off its flats, and it leaks in bands as the turn goes on through
+ * the 24 steps, a size that leaks with no corner near. A
  * shank the magnet pocket does not clear as it would a counterbore is refused
  * (mountLimits): the two walls weave, and no turn kept them closed. On every shank taken,
  * whichever called the turn, no corner of either then comes within 0.003 mm of a flat,
  * and none within 0.0039 but under a magnet on a shank under 1.2 mm (magnets of 3 to 13
  * mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every 0.001 mm round the sizes
- * that put a corner on a flat, and 6.7 million sizes drawn at random round them). The
+ * that put a corner on a flat, and 6.7 million sizes drawn at random round them); under
+ * a bare pocket none comes within 0.005 (the same magnets every 0.01 mm, shanks every
+ * 0.0005 mm within 0.012 of each size that puts a corner on a flat). The
  * nearest, 0.0033 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
  * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. Half a facet, π/12,
  * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
@@ -1025,10 +1041,12 @@ const MOUNT_BORE = {
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12),
           // how far to turn the shank under a counterbore cut headR out at its corners
-          // (head.cut), in a magnet pocket magnetR out at its corners or none (see above)
+          // (head.cut) or none (0), in a magnet pocket magnetR out at its corners or none
+          // (see above)
           turn: (d, headR, magnetR) => {
             // the magnet pocket's corners stand on the same rays as the counterbore's
-            const { head, hole } = MOUNT_BORE, rs = magnetR ? [headR, magnetR] : [headR];
+            const { head, hole } = MOUNT_BORE, rs = [headR, magnetR].filter((r) => r > 0);
+            if (!rs.length) return 0;
             const clear = (t) => {   // the nearest a corner comes to one of the flats' planes
               let g = Infinity;
               for (const R of rs) for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
@@ -1045,8 +1063,9 @@ const MOUNT_BORE = {
           } },
   /* What fastenerCutter cuts for a design's screw, as { counterbore, headR, turn }:
      whether the counterbore is cut, how far out its corners stand (head.cut), and how far
-     the shank is turned under it. Here so that mountLimits measures the same counterbore
-     and shank the cutter cuts.
+     the shank is turned, for the counterbore's corners and the magnet pocket's, or the
+     pocket's alone where no counterbore is cut. Here so that mountLimits measures the
+     same counterbore and shank the cutter cuts.
      A counterbore the magnet pocket from beneath holds whole is that pocket already: both
      14 sides, corners on the same rays, no deeper. Left out, the pocket is the same
      solid. That is the default 6 mm head under the 6 mm magnet 2 deep, cut at the
@@ -1057,8 +1076,7 @@ const MOUNT_BORE = {
     const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
       headR <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
     const counterbore = head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet;
-    return { counterbore, headR,
-             turn: counterbore ? hole.turn(cfg.screwHoleD, headR, magnetR) : 0 };
+    return { counterbore, headR, turn: hole.turn(cfg.screwHoleD, counterbore ? headR : 0, magnetR) };
   },
 };
 
@@ -2801,7 +2819,7 @@ function mountLimits(cfg, layout, known) {
      of it as how far a bore's corner circle (`room`) and the bores themselves (`bore`, by
      their sides) can grow before they meet the cut, and a magnet or screw (`body`) before
      it meets the part in it. Where the site stands from the cut's own origin (`x`, `y`)
-     is kept for a shank turned under its counterbore, measured for the sizes asked. */
+     is kept for a turned shank (MOUNT_BORE.screw), measured for the sizes asked. */
   const jointCuts = again ? known.list : [];
   /* Room past the most the cell or the floor leaves cannot stop a size, so nothing
      further off than that is measured, and nothing at all where neither leaves any. A
@@ -2938,7 +2956,7 @@ function mountLimits(cfg, layout, known) {
      into, but not stop just short of. */
   const jointFor = (f) => {
     const { sides, fits } = BORE[f];
-    /* the room a bore has, measured again for a shank turned under its counterbore, and
+    /* the room a bore has, measured again for a turned shank (MOUNT_BORE.screw), and
        kept on the site by its turn: the page asks again on the same cuts (`known`) once
        the head and the magnet are read, and measuring every site again was nearly all
        that asking again cost */
diff --git a/test/plate-audit.js b/test/plate-audit.js
index 1c45c31..5a065cf 100644
--- a/test/plate-audit.js
+++ b/test/plate-audit.js
@@ -2239,6 +2239,47 @@ console.log('\nthe other limits, built at their ends:');
     console.log(`  ${nm.padEnd(30)} ${taken ? '' : 'REFUSED, '}${leakText(r)}${folds ? `, ${folds} FOLDS` : ''}`);
     if (!taken || r.bad || folds) bad++;
   }
+  /* A bare magnet pocket, with no counterbore cut, whose corner stands on a flat of the
+     shank carried on past it. The BSP splits the pocket's roof or floor along that plane
+     as it does round a counterbore (#74), and the plate leaks. From beneath, where the
+     pocket holds the counterbore whole: a 4.18 mm shank under a 5 mm magnet and a 5.12 mm
+     head, a corner 0.002 mm off a flat, left 12 edges open at 42 mm, 24 with a 5 x 3
+     magnet over two cells, and 51 under a 5.08 head at 41.14 mm; 1.96 under 4.16 with a
+     4 x 1.5 magnet folded 12 times; and 6.689 under an 8.068 head in an 8.11 x 3 magnet's
+     pocket left 12 at 52.26 mm. From above, under heads too narrow to cut a counterbore:
+     4.18 under a 5 x 2 magnet left 30, 3.296 under a 6 x 3 one 16, and 7.268 under a
+     7.734 x 2.5 one 84 over a 2 x 2 piece. The first four came with the counterbore cut
+     at the pocket's corners, which the pocket from beneath then holds whole and which so
+     no longer turned the shank; the other four leaked before it as well. The shank is
+     turned for the pocket's corners alone now (MOUNT_BORE.screw), and main, whose bores
+     stand elsewhere, builds every one of them closed. Each is a size the page takes, and
+     has to build closed, with no folds. */
+  for (const [nm, o] of [
+    ['4.18 under 5.12, 5 x 2 below, 42', { bedW: 52, magnetD: 5, screwHoleD: 4.18, screwHeadD: 5.12 }],
+    ['4.18 under 5.12, 5 x 3 below, 84 x 42', { drawerW: 84, tolerance: 'tight', magnetD: 5, magnetH: 3,
+      screwHoleD: 4.18, screwHeadD: 5.12, screwHeadDepth: 3 }],
+    ['4.18 under 5.08, 5 x 2 below, 41.14', { pitch: 41.14, drawerW: 82.28, drawerD: 82.28, magnetD: 5,
+      screwHoleD: 4.18, screwHeadD: 5.08 }],
+    ['1.96 under 4.16, 4 x 1.5 below, 42', { drawerW: 84, drawerD: 84, magnetD: 4, magnetH: 1.5,
+      screwHoleD: 1.96, screwHeadD: 4.16, screwHeadDepth: 1 }],
+    ['6.689 under 8.068, 8.11 x 3 below', { pitch: 52.26, drawerW: 52.26, drawerD: 52.26, tolerance: 'loose',
+      magnetD: 8.11, magnetH: 3, screwHoleD: 6.689, screwHeadD: 8.068, screwHeadDepth: 2.747 }],
+    ['4.18 bare, 5 x 2 above, 42', { magnetD: 5, magnetSide: 'top', screwHoleD: 4.18, screwHeadD: 4.19,
+      screwHeadDepth: 1 }],
+    ['3.296 bare, 6 x 3 above, 42', { tolerance: 'tight', magnetD: 6, magnetH: 3, magnetSide: 'top',
+      screwHoleD: 3.296, screwHeadD: 3.335, screwHeadDepth: 2.026 }],
+    ['7.268 bare, 7.734 x 2.5 above, 2 x 2', { drawerW: 84, drawerD: 84, magnetD: 7.734, magnetH: 2.5,
+      magnetSide: 'top', screwHoleD: 7.268, screwHeadD: 7.365, screwHeadDepth: 2.66 }],
+  ]) {
+    const at = { pitch: 42, drawerW: 42, drawerD: 42, connector: 'none', magnets: true, screws: true, ...o };
+    const cfg = designCfg(at), lim = G.mountLimits(cfg, G.computeLayout(cfg));
+    const taken = ['magnetD', 'screwHoleD', 'screwHeadD'].every((f) => cfg[f] <= lim[f] + 1e-9 &&
+      !lim.gaps[f].some(([a, b]) => cfg[f] > a + 1e-9 && cfg[f] < b - 1e-9));
+    const r = buildAll(at);
+    const folds = r.pieces.reduce((s, pp) => s + checkOrientation(pp).folds, 0);
+    console.log(`  ${nm.padEnd(38)} ${taken ? '' : 'REFUSED, '}${leakText(r)}${folds ? `, ${folds} FOLDS` : ''}`);
+    if (!taken || r.bad || folds) bad++;
+  }
   /* A pocket against a joint's cut in the floor (#64). A bowtie housed in the floor at
      42 mm, with magnets from beneath, built 12 bad edges at 7.9 mm and 19 at 10 with
      Download on: the pocket reached the key's recess, and with both ceilings 2 mm up the

From ac491d538f80f2c0a82507a7c32d7834147421b0 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 01:59:10 +0000
Subject: [PATCH 35/58] Take a gap's ends as the field takes them in the
 counterbore line

The line under the screw fields stepped past a refused gap to the
hundredth after its end, but readNumber refuses only sizes inside a gap,
and mountLimits gives each gap's ends as sizes it takes. Step to the end.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 src/ui.js | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/ui.js b/src/ui.js
index a81669c..130f50e 100644
--- a/src/ui.js
+++ b/src/ui.js
@@ -428,7 +428,8 @@ function readControls() {
   if (noBore) {
     const from = headClearsFrom(state.screwHoleD), m = mount();
     let at = from;
-    for (const [a, b] of m.gaps.screwHeadD) if (at >= a - 1e-9 && at <= b + 1e-9) at = Math.round(b * 100 + 1) / 100;
+    // a gap's ends are taken, as readNumber takes them
+    for (const [a, b] of m.gaps.screwHeadD) if (at > a + 1e-9 && at < b - 1e-9) at = b;
     $('screwHeadHint').textContent = `A ${state.screwHeadD} mm head does not clear ` +
       `the corners of a ${state.screwHoleD} mm hole, so no counterbore is cut. ` +
       (at <= m.screwHeadD + 1e-9 ? `One is from ${at} mm.`

From a1ceb948a596ed3eb4467a2034e48ad6de81528c Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 01:59:10 +0000
Subject: [PATCH 36/58] Say the screw hole leaves a ledge that holds the
 magnet, either way up

"A ledge to sit on" read oddly for a magnet pressed in from beneath, which
the ledge stops rather than carries.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 src/ui.js                         | 2 +-
 test/ui/plates-robustness.spec.js | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/ui.js b/src/ui.js
index 130f50e..07f68e6 100644
--- a/src/ui.js
+++ b/src/ui.js
@@ -112,7 +112,7 @@ const cutsNamed = () => `${['dovetail', 'puzzle'].includes(state.connector) ? 'n
 const mountWhy = (opens, field) => {
   if (field === 'screwHoleD' && mount().throughMagnet)
     return `— it runs through the ${state.magnetD} mm magnet's pocket, and has to stay inside the pocket's sides ` +
-      'to leave the magnet a ledge to sit on';
+      'to leave a ledge round it that holds the magnet';
   const joint = mount().joint[field];
   const cuts = cutsNamed();
   return `${atPitch()} — mounting holes sit ` +
diff --git a/test/ui/plates-robustness.spec.js b/test/ui/plates-robustness.spec.js
index 9d98c2f..2a5c088 100644
--- a/test/ui/plates-robustness.spec.js
+++ b/test/ui/plates-robustness.spec.js
@@ -147,7 +147,7 @@ test.describe('ranges on the geometry fields', () => {
        counterbore. 5 mm under a 5.1 mm magnet and a 5.4 mm head built 47 open edges at
        42 mm. */
     ['#cn=none&mg=1&md=5.1&ms=top&sc=1&sh=5&sd=5.4', 'errScrew',
-      /Screw hole Ø must be 4\.9 mm or less — it runs through the 5\.1 mm magnet's pocket, and has to stay inside the pocket's sides to leave the magnet a ledge to sit on\./],
+      /Screw hole Ø must be 4\.9 mm or less — it runs through the 5\.1 mm magnet's pocket, and has to stay inside the pocket's sides to leave a ledge round it that holds the magnet\./],
   ];
   for (const [hash, errId, msg] of CASES) {
     test(`${hash} is refused at the field`, async ({ page }) => {

From b7ffea361a48512a8f701f10aa48a3702fb48585 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 01:59:11 +0000
Subject: [PATCH 37/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html | 52 +++++++++++++++++++++++++++++---------------
 index.html      | 57 ++++++++++++++++++++++++++++++++-----------------
 sw.js           |  2 +-
 3 files changed, 74 insertions(+), 37 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index 6dd241a..365786d 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -2536,7 +2536,8 @@ <h2 id="drawersTitle">Your drawers</h2>
  * roof, and a jigsaw at 41.76 mm folded there; as one prism it is the pocket made deeper.
  * A head in the band is cut up to 0.1 mm wider or narrower across its flats than typed,
  * mountLimits measures it as cut (head.fitsCut), and one the pocket from beneath then
- * holds whole is not cut, as before. The shank's turn goes by the counterbore as cut: one
+ * holds whole is not cut, as before, the shank turned for the pocket's corners alone
+ * (below). The shank's turn goes by the counterbore as cut: one
  * turned for a 6.02 mm head's corners while it was cut at the 6 mm magnet's left 3.66
  * under it open at 42 mm. Measured on 240 random designs whose counterbore's corners are
  * in the band and reach the pocket (two in three a 6 x 2 magnet, either way up; half at
@@ -2544,14 +2545,12 @@ <h2 id="drawersTitle">Your drawers</h2>
  * jigsaws): of the 223 taken, 12 were open, folded or turned before, with 380 open edges,
  * and 2 now: one tile at 36.43 mm with a face turned on main as well, and 5.376 under
  * 6.006 at 42 mm, 12 open edges, a shank that leaks as many under the bare pocket with
- * no counterbore at all. Main leaves 7 of its 225 bad. A design whose counterbore is not
- * in the band builds the same bytes as before.
+ * no counterbore at all. Main leaves 7 of its 225 bad. The band changes no design whose
+ * counterbore is not in it.
  *
- * Where a counterbore is cut, and only there, the shank is turned a little about its
- * axis (`turn`, #74) where a corner of the counterbore or of the magnet pocket would
- * stand on one of its flats carried on past the shank. With no counterbore a magnet
- * pocket's corners alone do not turn it: at 41.24 mm a 3 mm shank under a 7.3 mm magnet
- * from above, a corner on a flat, builds closed unturned with no counterbore over it.
+ * The shank is turned a little about its axis (`turn`, #74) where a corner of the
+ * counterbore or of the magnet pocket would stand on one of its flats carried on past
+ * the shank, and where no counterbore is cut, the pocket's corners alone turn it.
  * The BSP splits what it meets along a flat's whole plane, not
  * just the flat: the floor of a magnet pocket from above, which is a ring round the
  * counterbore, or the roof of one from beneath round a counterbore deeper than it. A
@@ -2574,12 +2573,29 @@ <h2 id="drawersTitle">Your drawers</h2>
  * a magnet's corner on a flat all the same: at 41.24 mm a 3 mm shank under a 7.3 mm
  * magnet from above, a corner 0.4 microns off a flat, left 26 edges a piece in the socket
  * floor whatever the head, and 4.9911 under 7.246 with a 6 mm one left 44 at 49.02 mm. A
+ * bare pocket, with no counterbore cut, leaks the same way: 4.18 mm under a 5 mm magnet,
+ * a corner 0.002 mm off a flat, left 12 edges a cell at 42 mm from beneath, where the
+ * pocket holds a 5.12 mm head whole, and 30 from above under a head too narrow to cut.
+ * From beneath, that came with the band above: a 5.12 head had been cut beside the pocket
+ * and turned the shank, and held whole it no longer did. On 1,000 random designs from
+ * beneath with no counterbore cut and a corner of the pocket within 0.0045 mm of a flat
+ * (34 to 56 mm; one cell, the test tile, 2 x 2, corner bosses, two pieces with dovetails
+ * or jigsaws; magnets of 3 to 13 mm), of the 859 taken 6 were open or had a face turned
+ * over before, with 83 open edges, and 2 now, under a 4.16 x 2 magnet at 42 mm, 6 edges
+ * each as before, where main leaves 12. On 800 from above, of the 566 taken, 11 before,
+ * with 351 open edges, and 3 now, none open: test tiles with a face turned over, one of
+ * them as before. Turned, 2.58 under a 4.34 head the 4.16 x 2 magnet holds whole at
+ * 42 mm leaves 9, where it built closed unturned and main leaves 10; its pocket's
+ * corners stand 0.06 mm off its flats, and it leaks in bands as the turn goes on through
+ * the 24 steps, a size that leaks with no corner near. A
  * shank the magnet pocket does not clear as it would a counterbore is refused
  * (mountLimits): the two walls weave, and no turn kept them closed. On every shank taken,
  * whichever called the turn, no corner of either then comes within 0.003 mm of a flat,
  * and none within 0.0039 but under a magnet on a shank under 1.2 mm (magnets of 3 to 13
  * mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every 0.001 mm round the sizes
- * that put a corner on a flat, and 6.7 million sizes drawn at random round them). The
+ * that put a corner on a flat, and 6.7 million sizes drawn at random round them); under
+ * a bare pocket none comes within 0.005 (the same magnets every 0.01 mm, shanks every
+ * 0.0005 mm within 0.012 of each size that puts a corner on a flat). The
  * nearest, 0.0033 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
  * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. Half a facet, π/12,
  * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
@@ -2631,10 +2647,12 @@ <h2 id="drawersTitle">Your drawers</h2>
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12),
           // how far to turn the shank under a counterbore cut headR out at its corners
-          // (head.cut), in a magnet pocket magnetR out at its corners or none (see above)
+          // (head.cut) or none (0), in a magnet pocket magnetR out at its corners or none
+          // (see above)
           turn: (d, headR, magnetR) => {
             // the magnet pocket's corners stand on the same rays as the counterbore's
-            const { head, hole } = MOUNT_BORE, rs = magnetR ? [headR, magnetR] : [headR];
+            const { head, hole } = MOUNT_BORE, rs = [headR, magnetR].filter((r) => r > 0);
+            if (!rs.length) return 0;
             const clear = (t) => {   // the nearest a corner comes to one of the flats' planes
               let g = Infinity;
               for (const R of rs) for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
@@ -2651,8 +2669,9 @@ <h2 id="drawersTitle">Your drawers</h2>
           } },
   /* What fastenerCutter cuts for a design's screw, as { counterbore, headR, turn }:
      whether the counterbore is cut, how far out its corners stand (head.cut), and how far
-     the shank is turned under it. Here so that mountLimits measures the same counterbore
-     and shank the cutter cuts.
+     the shank is turned, for the counterbore's corners and the magnet pocket's, or the
+     pocket's alone where no counterbore is cut. Here so that mountLimits measures the
+     same counterbore and shank the cutter cuts.
      A counterbore the magnet pocket from beneath holds whole is that pocket already: both
      14 sides, corners on the same rays, no deeper. Left out, the pocket is the same
      solid. That is the default 6 mm head under the 6 mm magnet 2 deep, cut at the
@@ -2663,8 +2682,7 @@ <h2 id="drawersTitle">Your drawers</h2>
     const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
       headR <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
     const counterbore = head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet;
-    return { counterbore, headR,
-             turn: counterbore ? hole.turn(cfg.screwHoleD, headR, magnetR) : 0 };
+    return { counterbore, headR, turn: hole.turn(cfg.screwHoleD, counterbore ? headR : 0, magnetR) };
   },
 };
 
@@ -4407,7 +4425,7 @@ <h2 id="drawersTitle">Your drawers</h2>
      of it as how far a bore's corner circle (`room`) and the bores themselves (`bore`, by
      their sides) can grow before they meet the cut, and a magnet or screw (`body`) before
      it meets the part in it. Where the site stands from the cut's own origin (`x`, `y`)
-     is kept for a shank turned under its counterbore, measured for the sizes asked. */
+     is kept for a turned shank (MOUNT_BORE.screw), measured for the sizes asked. */
   const jointCuts = again ? known.list : [];
   /* Room past the most the cell or the floor leaves cannot stop a size, so nothing
      further off than that is measured, and nothing at all where neither leaves any. A
@@ -4544,7 +4562,7 @@ <h2 id="drawersTitle">Your drawers</h2>
      into, but not stop just short of. */
   const jointFor = (f) => {
     const { sides, fits } = BORE[f];
-    /* the room a bore has, measured again for a shank turned under its counterbore, and
+    /* the room a bore has, measured again for a turned shank (MOUNT_BORE.screw), and
        kept on the site by its turn: the page asks again on the same cuts (`known`) once
        the head and the magnet are read, and measuring every site again was nearly all
        that asking again cost */
diff --git a/index.html b/index.html
index 2d3301c..7936b6f 100644
--- a/index.html
+++ b/index.html
@@ -2324,7 +2324,8 @@ <h2 id="drawersTitle">Your drawers</h2>
  * roof, and a jigsaw at 41.76 mm folded there; as one prism it is the pocket made deeper.
  * A head in the band is cut up to 0.1 mm wider or narrower across its flats than typed,
  * mountLimits measures it as cut (head.fitsCut), and one the pocket from beneath then
- * holds whole is not cut, as before. The shank's turn goes by the counterbore as cut: one
+ * holds whole is not cut, as before, the shank turned for the pocket's corners alone
+ * (below). The shank's turn goes by the counterbore as cut: one
  * turned for a 6.02 mm head's corners while it was cut at the 6 mm magnet's left 3.66
  * under it open at 42 mm. Measured on 240 random designs whose counterbore's corners are
  * in the band and reach the pocket (two in three a 6 x 2 magnet, either way up; half at
@@ -2332,14 +2333,12 @@ <h2 id="drawersTitle">Your drawers</h2>
  * jigsaws): of the 223 taken, 12 were open, folded or turned before, with 380 open edges,
  * and 2 now: one tile at 36.43 mm with a face turned on main as well, and 5.376 under
  * 6.006 at 42 mm, 12 open edges, a shank that leaks as many under the bare pocket with
- * no counterbore at all. Main leaves 7 of its 225 bad. A design whose counterbore is not
- * in the band builds the same bytes as before.
+ * no counterbore at all. Main leaves 7 of its 225 bad. The band changes no design whose
+ * counterbore is not in it.
  *
- * Where a counterbore is cut, and only there, the shank is turned a little about its
- * axis (`turn`, #74) where a corner of the counterbore or of the magnet pocket would
- * stand on one of its flats carried on past the shank. With no counterbore a magnet
- * pocket's corners alone do not turn it: at 41.24 mm a 3 mm shank under a 7.3 mm magnet
- * from above, a corner on a flat, builds closed unturned with no counterbore over it.
+ * The shank is turned a little about its axis (`turn`, #74) where a corner of the
+ * counterbore or of the magnet pocket would stand on one of its flats carried on past
+ * the shank, and where no counterbore is cut, the pocket's corners alone turn it.
  * The BSP splits what it meets along a flat's whole plane, not
  * just the flat: the floor of a magnet pocket from above, which is a ring round the
  * counterbore, or the roof of one from beneath round a counterbore deeper than it. A
@@ -2362,12 +2361,29 @@ <h2 id="drawersTitle">Your drawers</h2>
  * a magnet's corner on a flat all the same: at 41.24 mm a 3 mm shank under a 7.3 mm
  * magnet from above, a corner 0.4 microns off a flat, left 26 edges a piece in the socket
  * floor whatever the head, and 4.9911 under 7.246 with a 6 mm one left 44 at 49.02 mm. A
+ * bare pocket, with no counterbore cut, leaks the same way: 4.18 mm under a 5 mm magnet,
+ * a corner 0.002 mm off a flat, left 12 edges a cell at 42 mm from beneath, where the
+ * pocket holds a 5.12 mm head whole, and 30 from above under a head too narrow to cut.
+ * From beneath, that came with the band above: a 5.12 head had been cut beside the pocket
+ * and turned the shank, and held whole it no longer did. On 1,000 random designs from
+ * beneath with no counterbore cut and a corner of the pocket within 0.0045 mm of a flat
+ * (34 to 56 mm; one cell, the test tile, 2 x 2, corner bosses, two pieces with dovetails
+ * or jigsaws; magnets of 3 to 13 mm), of the 859 taken 6 were open or had a face turned
+ * over before, with 83 open edges, and 2 now, under a 4.16 x 2 magnet at 42 mm, 6 edges
+ * each as before, where main leaves 12. On 800 from above, of the 566 taken, 11 before,
+ * with 351 open edges, and 3 now, none open: test tiles with a face turned over, one of
+ * them as before. Turned, 2.58 under a 4.34 head the 4.16 x 2 magnet holds whole at
+ * 42 mm leaves 9, where it built closed unturned and main leaves 10; its pocket's
+ * corners stand 0.06 mm off its flats, and it leaks in bands as the turn goes on through
+ * the 24 steps, a size that leaks with no corner near. A
  * shank the magnet pocket does not clear as it would a counterbore is refused
  * (mountLimits): the two walls weave, and no turn kept them closed. On every shank taken,
  * whichever called the turn, no corner of either then comes within 0.003 mm of a flat,
  * and none within 0.0039 but under a magnet on a shank under 1.2 mm (magnets of 3 to 13
  * mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every 0.001 mm round the sizes
- * that put a corner on a flat, and 6.7 million sizes drawn at random round them). The
+ * that put a corner on a flat, and 6.7 million sizes drawn at random round them); under
+ * a bare pocket none comes within 0.005 (the same magnets every 0.01 mm, shanks every
+ * 0.0005 mm within 0.012 of each size that puts a corner on a flat). The
  * nearest, 0.0033 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
  * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. Half a facet, π/12,
  * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
@@ -2419,10 +2435,12 @@ <h2 id="drawersTitle">Your drawers</h2>
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12),
           // how far to turn the shank under a counterbore cut headR out at its corners
-          // (head.cut), in a magnet pocket magnetR out at its corners or none (see above)
+          // (head.cut) or none (0), in a magnet pocket magnetR out at its corners or none
+          // (see above)
           turn: (d, headR, magnetR) => {
             // the magnet pocket's corners stand on the same rays as the counterbore's
-            const { head, hole } = MOUNT_BORE, rs = magnetR ? [headR, magnetR] : [headR];
+            const { head, hole } = MOUNT_BORE, rs = [headR, magnetR].filter((r) => r > 0);
+            if (!rs.length) return 0;
             const clear = (t) => {   // the nearest a corner comes to one of the flats' planes
               let g = Infinity;
               for (const R of rs) for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
@@ -2439,8 +2457,9 @@ <h2 id="drawersTitle">Your drawers</h2>
           } },
   /* What fastenerCutter cuts for a design's screw, as { counterbore, headR, turn }:
      whether the counterbore is cut, how far out its corners stand (head.cut), and how far
-     the shank is turned under it. Here so that mountLimits measures the same counterbore
-     and shank the cutter cuts.
+     the shank is turned, for the counterbore's corners and the magnet pocket's, or the
+     pocket's alone where no counterbore is cut. Here so that mountLimits measures the
+     same counterbore and shank the cutter cuts.
      A counterbore the magnet pocket from beneath holds whole is that pocket already: both
      14 sides, corners on the same rays, no deeper. Left out, the pocket is the same
      solid. That is the default 6 mm head under the 6 mm magnet 2 deep, cut at the
@@ -2451,8 +2470,7 @@ <h2 id="drawersTitle">Your drawers</h2>
     const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
       headR <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
     const counterbore = head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet;
-    return { counterbore, headR,
-             turn: counterbore ? hole.turn(cfg.screwHoleD, headR, magnetR) : 0 };
+    return { counterbore, headR, turn: hole.turn(cfg.screwHoleD, counterbore ? headR : 0, magnetR) };
   },
 };
 
@@ -4195,7 +4213,7 @@ <h2 id="drawersTitle">Your drawers</h2>
      of it as how far a bore's corner circle (`room`) and the bores themselves (`bore`, by
      their sides) can grow before they meet the cut, and a magnet or screw (`body`) before
      it meets the part in it. Where the site stands from the cut's own origin (`x`, `y`)
-     is kept for a shank turned under its counterbore, measured for the sizes asked. */
+     is kept for a turned shank (MOUNT_BORE.screw), measured for the sizes asked. */
   const jointCuts = again ? known.list : [];
   /* Room past the most the cell or the floor leaves cannot stop a size, so nothing
      further off than that is measured, and nothing at all where neither leaves any. A
@@ -4332,7 +4350,7 @@ <h2 id="drawersTitle">Your drawers</h2>
      into, but not stop just short of. */
   const jointFor = (f) => {
     const { sides, fits } = BORE[f];
-    /* the room a bore has, measured again for a shank turned under its counterbore, and
+    /* the room a bore has, measured again for a turned shank (MOUNT_BORE.screw), and
        kept on the site by its turn: the page asks again on the same cuts (`known`) once
        the head and the magnet are read, and measuring every site again was nearly all
        that asking again cost */
@@ -8165,7 +8183,7 @@ <h2 id="drawersTitle">Your drawers</h2>
 const mountWhy = (opens, field) => {
   if (field === 'screwHoleD' && mount().throughMagnet)
     return `— it runs through the ${state.magnetD} mm magnet's pocket, and has to stay inside the pocket's sides ` +
-      'to leave the magnet a ledge to sit on';
+      'to leave a ledge round it that holds the magnet';
   const joint = mount().joint[field];
   const cuts = cutsNamed();
   return `${atPitch()} — mounting holes sit ` +
@@ -8481,7 +8499,8 @@ <h2 id="drawersTitle">Your drawers</h2>
   if (noBore) {
     const from = headClearsFrom(state.screwHoleD), m = mount();
     let at = from;
-    for (const [a, b] of m.gaps.screwHeadD) if (at >= a - 1e-9 && at <= b + 1e-9) at = Math.round(b * 100 + 1) / 100;
+    // a gap's ends are taken, as readNumber takes them
+    for (const [a, b] of m.gaps.screwHeadD) if (at > a + 1e-9 && at < b - 1e-9) at = b;
     $('screwHeadHint').textContent = `A ${state.screwHeadD} mm head does not clear ` +
       `the corners of a ${state.screwHoleD} mm hole, so no counterbore is cut. ` +
       (at <= m.screwHeadD + 1e-9 ? `One is from ${at} mm.`
diff --git a/sw.js b/sw.js
index f0271f8..fe96f9e 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "7bb87d8a2a29";
+const VERSION = "83123bc4fa3b";
 const FILES = [
   "./",
   "bins/",

From 70dcc8173b74768514ab398f484325a61b58a699 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 04:19:21 +0000
Subject: [PATCH 38/58] Turn a counterbore off the magnet pocket's flats where
 a corner of either stands on the other's

The counterbore and the magnet pocket are 14-gons on the same rays, so at some
sizes a corner of one stands on the plane of one of the other's flats. The head
at its 13.6 mm cap at 42 mm, under the default 6 x 2 magnet from above, has a
corner 0.004 mm off such a plane, and the default plate came out with 160, 120,
128 and 96 coplanar folds a piece; the head at its cap folded the same way at 40,
43, 44 and 46 mm.

Where a corner of either comes within 0.005 mm of a plane of the other, the
counterbore is now turned pi/252 about its axis (MOUNT_BORE.head.turn), which
leaves every corner 0.007 mm or more off. Its flats stay where they were, so the
head fits as typed and the caps do not move. The shank's turn and mountLimits go
by the counterbore turned. pi/84 and pi/126 each opened designs that pi/252
builds closed; the audit holds two of them, with the review's rows.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md      |  16 ++++--
 src/core.js         | 129 ++++++++++++++++++++++++++++++++------------
 test/plate-audit.js |  43 +++++++++++++++
 3 files changed, 152 insertions(+), 36 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index f7cd73a..a9bebc0 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -766,7 +766,17 @@ currently installed):
   6 × 2 magnet from beneath it left 6 edges open a cell at 42 mm, the test tile among
   them; main's head, its corners on the size, stood 0.1 off and built closed. A head in
   the band is cut up to 0.1 mm wider or narrower across its flats than typed, and
-  `mountLimits` reads it back as cut (`head.fitsCut`). The shank is turned π/84 about
+  `mountLimits` reads it back as cut (`head.fitsCut`). Out of the band a corner of the
+  counterbore can still stand on the plane of one of the pocket's flats, or a corner of
+  the pocket on one of the counterbore's, and the strip the BSP splits off along it came
+  out folded: the head at its 13.6 mm cap at 42 mm, 1.5 deep under the default 6 × 2
+  magnet from above, folded the default plate 160, 120, 128 and 96 times a piece. Where
+  a corner of either comes within 0.005 mm of a plane of the other, the counterbore is
+  turned π/252 about its axis (`MOUNT_BORE.head.turn`), which leaves every corner of
+  each 0.007 mm or more off the other's flats; its flats stand where they did, so the
+  head fits as typed, and the shank's turn and `mountLimits` go by it turned. Turned
+  further, the counterbore's planes met other things: π/84 and π/126 each opened
+  designs that π/252 builds closed. The shank is turned π/84 about
   its axis where one of the counterbore's corners, or one of the magnet pocket's, would
   otherwise stand within 0.005 mm of a flat's plane carried on past the shank
   (`MOUNT_BORE.hole.turn`, which goes by the counterbore as cut, and by the pocket's
@@ -789,8 +799,8 @@ currently installed):
   shank under 1.2 mm; a shank no corner came near is cut as before. The page reads
   the shank again after the head and the magnet, since its turn and that cap go by both.
   `MOUNT_BORE.screw` says whether a design's counterbore is cut, how far out its corners
-  stand and how far its shank is turned, for the cutter and for `mountLimits`, which
-  measures that counterbore and that shank turned.
+  stand, and how far it and its shank are turned, for the cutter and for `mountLimits`,
+  which measures that counterbore and that shank turned.
 - **The socket's corner clearance is not uniform.** Known, documented, deliberately not
   fixed — see [socket-clearance.md](socket-clearance.md).
 - **The plate's outer corner radius has a ceiling, and it is the socket's.** Both the
diff --git a/src/core.js b/src/core.js
index 94d0df7..d87fcea 100644
--- a/src/core.js
+++ b/src/core.js
@@ -942,6 +942,37 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * no counterbore at all. Main leaves 7 of its 225 bad. The band changes no design whose
  * counterbore is not in it.
  *
+ * Out of the band a corner of the counterbore can still stand on the plane of one of the
+ * magnet pocket's flats, or a corner of the pocket on one of the counterbore's: on the
+ * same rays, a corner of one stands an odd multiple of π/14 off the normal of a flat of
+ * the other, and at some sizes that puts it on the flat's plane. The BSP carries the
+ * plane across the other bore and splits a strip a few thousandths wide off it, which
+ * came out folded back on itself, or open. The head at its cap at 42 mm, 13.6 mm, under
+ * the default 6 x 2 magnet from above, a corner 0.004 mm off a flat's plane at 5π/14,
+ * folded the default plate 160, 120, 128 and 96 times a piece 1.5 deep and a cell 14
+ * times 1 deep, and 2 times from beneath 3 deep; the head at its cap folded the same way
+ * at 40, 43, 44 and 46 mm, each with the one magnet that puts its corner there. Main, its
+ * corners on the size, has the same at 13.95 mm. So where a corner of either comes
+ * within 0.005 mm of a plane of the other, the counterbore is turned π/252 about its axis
+ * (head.turn), which leaves every corner of each 0.007 mm or more off the other's flats,
+ * and the shank's turn and mountLimits go by it turned. Its flats stand as far from the
+ * axis as before, so the head fits as typed and the caps stay where they were. Turned
+ * further the corners stand further off, but the turned counterbore's planes meet other
+ * things: π/84 opened two, a 3 x 1 magnet from above over a 2.5 mm head at 42 mm, and
+ * π/126 folded a 6.47 x 2 magnet from above under the 14.6 mm head at its cap at 43 mm
+ * and doubled the 6 open edges of a 4.844 mm head in a 6 x 3 pocket from beneath at
+ * 42 mm, all of which π/252 builds closed. π/252 opens one that π/126 closes: a 13.582
+ * head 0.251 deep under a 6 x 3 magnet from above at 42 mm, 12 open edges a cell. On 900
+ * designs drawn at random with a head within 0.012 mm of a size that puts a corner of
+ * either on a plane of the other (34 to 56 mm; one cell, the test tile, 2 x 2, corner
+ * bosses, two pieces with dovetails or jigsaws; magnets of 3 to 13 mm, either way up),
+ * of the 498 taken 56 were open, folded or had a face turned over before, 16 open with
+ * 384 edges, and 2 now: that one, and a cell at 39.72 mm with a face turned over as
+ * before; main leaves 2. With the head at its cap, every 0.5 mm of pitch from 34 to 56,
+ * 1, 1.5 and 2.5 deep, under each magnet to the hundredth that puts a corner of the
+ * counterbore on a flat's plane, of the 216 taken from above 5 were open or folded
+ * before and none now (main leaves 1), and of the 432 from beneath 4 before and none now.
+ *
  * The shank is turned a little about its axis (`turn`, #74) where a corner of the
  * counterbore or of the magnet pocket would stand on one of its flats carried on past
  * the shank, and where no counterbore is cut, the pocket's corners alone turn it.
@@ -958,7 +989,8 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * corner on a flat puts it midway between two. The turn is taken where a corner comes
  * nearer than 0.005 mm unturned and the turn leaves it further off, and a shank no corner
  * came near is cut as it was. The magnet pocket's corners stand on the same rays as the
- * counterbore's, and π/84 could bring one of those onto a flat instead: 4.85 mm under
+ * counterbore's (or π/252 off them, where it is turned), and π/84 could bring one of
+ * those onto a flat instead: 4.85 mm under
  * 7.246 with a 6 mm magnet from above left 35 edges in the socket floor at 49.02 mm, and
  * 5.773 under 12.053 25 at 55 mm, where the flats unturned miss them by 0.07 and 0.04. So
  * where π/84 leaves a corner of either nearer than 0.005 mm, the turn is the one of 24
@@ -989,7 +1021,9 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every 0.001 mm round the sizes
  * that put a corner on a flat, and 6.7 million sizes drawn at random round them); under
  * a bare pocket none comes within 0.005 (the same magnets every 0.01 mm, shanks every
- * 0.0005 mm within 0.012 of each size that puts a corner on a flat). The
+ * 0.0005 mm within 0.012 of each size that puts a corner on a flat), and under a
+ * counterbore turned off the pocket none within 0.003 (360,535 shanks drawn at random
+ * near a corner of either, under counterbores near the pocket's flats). The
  * nearest, 0.0033 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
  * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. Half a facet, π/12,
  * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
@@ -1037,20 +1071,41 @@ const MOUNT_BORE = {
             if (!magnetR || room >= magnetR + s || room < magnetR - s) return head.fits(room);
             return head.fits(room >= magnetR ? magnetR + s : magnetR - s) - 1e-6;
           },
-          snap: 0.05 },
+          snap: 0.05,
+          /* how far to turn a counterbore cut headR out at its corners about its axis,
+             beside a magnet pocket magnetR out at its corners: π/252 where a corner of either
+             would stand within 0.005 mm of the plane of one of the other's flats, and not at
+             all where they are cut as one prism (see above) */
+          turn: (headR, magnetR) => {
+            if (!headR || !magnetR || headR === magnetR) return 0;
+            const n = MOUNT_BORE.head.sides, h = Math.cos(Math.PI / n);
+            const clear = (t) => {   // the nearest a corner of either comes to one of the other's flats' planes
+              let g = Infinity;
+              for (let k = 0; k < n; k++) for (let j = 0; j < n; j++) {
+                const head = 2*Math.PI*k/n + t, magnet = 2*Math.PI*j/n;   // a corner of each
+                g = Math.min(g, Math.abs(headR * Math.cos(head - magnet - Math.PI/n) - magnetR * h),
+                             Math.abs(magnetR * Math.cos(magnet - head - Math.PI/n) - headR * h));
+              }
+              return g;
+            };
+            const c0 = clear(0);
+            return c0 < 0.005 && clear(Math.PI / 252) > c0 ? Math.PI / 252 : 0;
+          } },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12),
           // how far to turn the shank under a counterbore cut headR out at its corners
-          // (head.cut) or none (0), in a magnet pocket magnetR out at its corners or none
-          // (see above)
-          turn: (d, headR, magnetR) => {
-            // the magnet pocket's corners stand on the same rays as the counterbore's
-            const { head, hole } = MOUNT_BORE, rs = [headR, magnetR].filter((r) => r > 0);
+          // (head.cut) and turned headTurn (head.turn), or none (0), in a magnet pocket
+          // magnetR out at its corners or none (see above)
+          turn: (d, headR, magnetR, headTurn = 0) => {
+            // the magnet pocket's corners stand on the same rays as the counterbore's, but
+            // for a counterbore turned off them
+            const { head, hole } = MOUNT_BORE;
+            const rs = [[headR, headTurn], [magnetR, 0]].filter(([r]) => r > 0);
             if (!rs.length) return 0;
             const clear = (t) => {   // the nearest a corner comes to one of the flats' planes
               let g = Infinity;
-              for (const R of rs) for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
-                g = Math.min(g, Math.abs(R * Math.cos(2*Math.PI*k/head.sides - (2*m + 1)*Math.PI/hole.sides - t) - d/2));
+              for (const [R, p] of rs) for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
+                g = Math.min(g, Math.abs(R * Math.cos(2*Math.PI*k/head.sides + p - (2*m + 1)*Math.PI/hole.sides - t) - d/2));
               return g;
             };
             if (clear(0) >= 0.005) return 0;
@@ -1061,9 +1116,10 @@ const MOUNT_BORE = {
             }
             return most > clear(0) ? best : 0;
           } },
-  /* What fastenerCutter cuts for a design's screw, as { counterbore, headR, turn }:
-     whether the counterbore is cut, how far out its corners stand (head.cut), and how far
-     the shank is turned, for the counterbore's corners and the magnet pocket's, or the
+  /* What fastenerCutter cuts for a design's screw, as { counterbore, headR, headTurn,
+     turn }: whether the counterbore is cut, how far out its corners stand (head.cut) and
+     how far it is turned off the magnet pocket's flats (head.turn), and how far the
+     shank is turned, for the counterbore's corners and the magnet pocket's, or the
      pocket's alone where no counterbore is cut. Here so that mountLimits measures the
      same counterbore and shank the cutter cuts.
      A counterbore the magnet pocket from beneath holds whole is that pocket already: both
@@ -1076,7 +1132,9 @@ const MOUNT_BORE = {
     const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
       headR <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
     const counterbore = head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet;
-    return { counterbore, headR, turn: hole.turn(cfg.screwHoleD, counterbore ? headR : 0, magnetR) };
+    const headTurn = counterbore ? head.turn(headR, magnetR) : 0;
+    return { counterbore, headR, headTurn,
+             turn: hole.turn(cfg.screwHoleD, counterbore ? headR : 0, magnetR, headTurn) };
   },
 };
 
@@ -1104,7 +1162,13 @@ function fastenerCutter(cfg, magZ0, magZ1, shankTop) {
   // each bore as MOUNT_BORE shapes it
   const { magnet, head, hole } = MOUNT_BORE;
   const magnetR = magnet.r(cfg.magnetD);
-  const { counterbore, headR, turn: t } = cfg.screws ? MOUNT_BORE.screw(cfg) : { counterbore: false };
+  const { counterbore, headR, headTurn, turn: t } = cfg.screws ? MOUNT_BORE.screw(cfg) : { counterbore: false };
+  // a bore turned t about its axis
+  const turned = (polys, t) => {
+    if (!t) return polys;
+    const c = Math.cos(t), s = Math.sin(t), turn = (v) => [v[0]*c - v[1]*s, v[0]*s + v[1]*c, v[2]];
+    return polys.map((p) => ({ verts: p.verts.map(turn), plane: { n: turn(p.plane.n), w: p.plane.w } }));
+  };
   const above = cfg.magnetSide === 'top';
   // a counterbore cut at the magnet pocket's corners (MOUNT_BORE.head.cut) that reaches the
   // pocket is one prism with it, from the underside to the top of whichever ends higher:
@@ -1116,15 +1180,13 @@ function fastenerCutter(cfg, magZ0, magZ1, shankTop) {
       : cylinder(0, 0, magnetR, -0.5, cfg.magnetH, magnet.sides));
   if (cfg.screws) {
     // the counterbore, unless the magnet pocket from beneath is that already (MOUNT_BORE.screw)
-    // or it is cut as one with the pocket
+    // or it is cut as one with the pocket; turned where a corner of it or of the pocket
+    // would stand on one of the other's flats (MOUNT_BORE.head.turn)
     if (counterbore && !one)
-      add(cylinder(0, 0, headR, -0.5, cfg.screwHeadDepth, head.sides));
+      add(turned(cylinder(0, 0, headR, -0.5, cfg.screwHeadDepth, head.sides), headTurn));
     // the shank, turned where a corner of the counterbore or the magnet pocket would stand
     // on one of its flats (#74)
-    const shank = cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides);
-    const c = Math.cos(t), s = Math.sin(t), turn = (v) => [v[0]*c - v[1]*s, v[0]*s + v[1]*c, v[2]];
-    add(t ? shank.map((p) => ({ verts: p.verts.map(turn), plane: { n: turn(p.plane.n), w: p.plane.w } }))
-          : shank);
+    add(turned(cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides), t));
   }
   return cut;
 }
@@ -2910,16 +2972,17 @@ function mountLimits(cfg, layout, known) {
   /* The bores as fastenerCutter cuts them (MOUNT_BORE): how many sides, and the largest
      size whose corners stay inside a radius. Each stands its flats on its size, so its
      corners stand out past it, and a magnet's 0.1 mm over its radius where that is
-     further. The shank is turned where the cutter turns it, and measured so: its turn
-     goes by the sizes asked, the head's and the magnet's as well as its own, so it is
-     the shank of this design that is measured. A counterbore within MOUNT_BORE.head.snap
+     further. The shank and the counterbore are turned where the cutter turns them, and
+     measured so: their turns go by the sizes asked, the head's and the magnet's as well
+     as the shank's, so it is the bores of this design that are measured. A counterbore
+     within MOUNT_BORE.head.snap
      of the magnet pocket's corners is cut at the pocket's, up to 0.05 mm further out or
      in, so its sizes are read back through that (head.fitsCut), which goes by the room
      alone: the cap does not move with the head typed. */
   const magnetR = cfg.magnets ? MOUNT_BORE.magnet.r(cfg.magnetD) : 0;
   const BORE = { magnetD: MOUNT_BORE.magnet, screwHoleD: MOUNT_BORE.hole,
                  screwHeadD: { sides: MOUNT_BORE.head.sides, fits: (room) => MOUNT_BORE.head.fitsCut(room, magnetR) } };
-  const shankTurn = cfg.screws ? MOUNT_BORE.screw(cfg).turn : 0;
+  const { turn: shankTurn, headTurn } = cfg.screws ? MOUNT_BORE.screw(cfg) : { turn: 0, headTurn: 0 };
   // the room the cell, the floor or a boss leaves, and the hole beside
   const own = { magnetD: fit(cfg.magnetSide === 'top' ? top : under), screwHoleD: fit(top), screwHeadD: fit(under) };
   /* A shank runs up the magnet pocket's axis, and has to clear it as it would a
@@ -2956,17 +3019,17 @@ function mountLimits(cfg, layout, known) {
      into, but not stop just short of. */
   const jointFor = (f) => {
     const { sides, fits } = BORE[f];
-    /* the room a bore has, measured again for a turned shank (MOUNT_BORE.screw), and
-       kept on the site by its turn: the page asks again on the same cuts (`known`) once
-       the head and the magnet are read, and measuring every site again was nearly all
-       that asking again cost */
-    const turn = f === 'screwHoleD' ? shankTurn : 0;
+    /* the room a bore has, measured again for a turned shank or counterbore
+       (MOUNT_BORE.screw), and kept on the site by its sides and turn: the page asks again
+       on the same cuts (`known`) once the head and the magnet are read, and measuring
+       every site again was nearly all that asking again cost */
+    const turn = f === 'screwHoleD' ? shankTurn : f === 'screwHeadD' ? headTurn : 0;
     const reach = (c, s) => {
       if (!turn) return s.bore[sides];
       if (!(s.room > 0)) return s.room;
-      const kept = s.turned || (s.turned = new Map());
-      if (!kept.has(turn)) kept.set(turn, boreReach(sides, c.segs, s.x, s.y, turn));
-      return kept.get(turn);
+      const kept = s.turned || (s.turned = new Map()), key = `${sides} ${turn}`;
+      if (!kept.has(key)) kept.set(key, boreReach(sides, c.segs, s.x, s.y, turn));
+      return kept.get(key);
     };
     const above = f === 'magnetD' && cfg.magnetSide === 'top';
     // how high a pocket from beneath goes; a shank goes through
diff --git a/test/plate-audit.js b/test/plate-audit.js
index 5a065cf..d24b5ca 100644
--- a/test/plate-audit.js
+++ b/test/plate-audit.js
@@ -2280,6 +2280,49 @@ console.log('\nthe other limits, built at their ends:');
     console.log(`  ${nm.padEnd(38)} ${taken ? '' : 'REFUSED, '}${leakText(r)}${folds ? `, ${folds} FOLDS` : ''}`);
     if (!taken || r.bad || folds) bad++;
   }
+  /* A counterbore's corner on the plane of one of the magnet pocket's flats. The two are
+     14-gons on the same rays, so a corner of one stands an odd multiple of π/14 off a
+     normal of the other's flats, and at some sizes that puts it on the flat's plane
+     carried on past the pocket. The BSP splits the counterbore along that plane a few
+     thousandths from the corner, and the strip came out folded back on itself: the head
+     at its cap, 13.6 mm at 42 mm, under the default 6 x 2 magnet from above, its corner
+     0.004 mm off the pocket's flat at 5π/14, folded 8 times a cell 1.5 deep and 14 at 1,
+     160, 120, 128 and 96 over the default plate's four pieces; from beneath, 3 deep, 2.
+     The head at its cap folded the same way at 40, 43, 44 and 46 mm, each with the one
+     magnet that puts its corner there. Main, its corners on the size, builds these closed
+     (it has the same at 13.95 mm). The counterbore is turned π/252 off the pocket's flats
+     now (MOUNT_BORE.head.turn). The last two hold it to that: turned π/126, the 6.47 x 2
+     magnet under the head at its cap at 43 mm came out with 2 bad edges and a face turned
+     over, and a 4.844 head held whole in a 6 x 3 pocket from beneath, a corner of the
+     pocket 0.002 mm off the plane of one of the counterbore's flats, left 12 edges open a
+     cell, where unturned it left 6 and main none. Each is a size the page takes, and has to build
+     closed, with no folds. */
+  for (const [nm, o] of [
+    ['13.6 head, 6 x 2 above, 42, 1.5 deep', { magnetSide: 'top', screwHeadD: 13.6, screwHeadDepth: 1.5 }],
+    ['13.6 head, 6 x 2 above, 42, 1 deep', { magnetSide: 'top', screwHeadD: 13.6, screwHeadDepth: 1 }],
+    ['13.6 head, 6 x 2 below, 42, 3 deep', { screwHeadD: 13.6, screwHeadDepth: 3 }],
+    ['11.6 head, 5.09 x 2 above, 40', { pitch: 40, drawerW: 40, drawerD: 40, magnetD: 5.09, magnetSide: 'top',
+      screwHeadD: 11.6, screwHeadDepth: 1.5 }],
+    ['14.6 head, 6.46 x 2 above, 43', { pitch: 43, drawerW: 43, drawerD: 43, magnetD: 6.46, magnetSide: 'top',
+      screwHeadD: 14.6, screwHeadDepth: 1.5 }],
+    ['15.5 head, 6.87 x 2 above, 44', { pitch: 44, drawerW: 44, drawerD: 44, magnetD: 6.87, magnetSide: 'top',
+      screwHeadD: 15.5, screwHeadDepth: 1.5 }],
+    ['17.5 head, 7.78 x 2 above, 46', { pitch: 46, drawerW: 46, drawerD: 46, magnetD: 7.78, magnetSide: 'top',
+      screwHeadD: 17.5, screwHeadDepth: 1 }],
+    ['14.6 head, 6.47 x 2 above, 43, 1 deep', { pitch: 43, drawerW: 43, drawerD: 43, magnetD: 6.47,
+      magnetSide: 'top', screwHeadD: 14.6, screwHeadDepth: 1 }],
+    ['4.844 head in a 6 x 3 pocket below, 42', { magnetD: 6, magnetH: 3, screwHoleD: 3.48, screwHeadD: 4.844,
+      screwHeadDepth: 3.408 }],
+  ]) {
+    const at = { pitch: 42, drawerW: 42, drawerD: 42, connector: 'none', magnets: true, screws: true, ...o };
+    const cfg = designCfg(at), lim = G.mountLimits(cfg, G.computeLayout(cfg));
+    const taken = ['magnetD', 'screwHoleD', 'screwHeadD'].every((f) => cfg[f] <= lim[f] + 1e-9 &&
+      !lim.gaps[f].some(([a, b]) => cfg[f] > a + 1e-9 && cfg[f] < b - 1e-9));
+    const r = buildAll(at);
+    const folds = r.pieces.reduce((s, pp) => s + checkOrientation(pp).folds, 0);
+    console.log(`  ${nm.padEnd(38)} ${taken ? '' : 'REFUSED, '}${leakText(r)}${folds ? `, ${folds} FOLDS` : ''}`);
+    if (!taken || r.bad || folds) bad++;
+  }
   /* A pocket against a joint's cut in the floor (#64). A bowtie housed in the floor at
      42 mm, with magnets from beneath, built 12 bad edges at 7.9 mm and 19 at 10 with
      Download on: the pocket reached the key's recess, and with both ceilings 2 mm up the

From d59953115c390357a1543e24343ffc6ba43a8b25 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 04:19:28 +0000
Subject: [PATCH 39/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html | 129 +++++++++++++++++++++++++++++++++++-------------
 index.html      | 129 +++++++++++++++++++++++++++++++++++-------------
 sw.js           |   2 +-
 3 files changed, 193 insertions(+), 67 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index 365786d..ca7b5cb 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -2548,6 +2548,37 @@ <h2 id="drawersTitle">Your drawers</h2>
  * no counterbore at all. Main leaves 7 of its 225 bad. The band changes no design whose
  * counterbore is not in it.
  *
+ * Out of the band a corner of the counterbore can still stand on the plane of one of the
+ * magnet pocket's flats, or a corner of the pocket on one of the counterbore's: on the
+ * same rays, a corner of one stands an odd multiple of π/14 off the normal of a flat of
+ * the other, and at some sizes that puts it on the flat's plane. The BSP carries the
+ * plane across the other bore and splits a strip a few thousandths wide off it, which
+ * came out folded back on itself, or open. The head at its cap at 42 mm, 13.6 mm, under
+ * the default 6 x 2 magnet from above, a corner 0.004 mm off a flat's plane at 5π/14,
+ * folded the default plate 160, 120, 128 and 96 times a piece 1.5 deep and a cell 14
+ * times 1 deep, and 2 times from beneath 3 deep; the head at its cap folded the same way
+ * at 40, 43, 44 and 46 mm, each with the one magnet that puts its corner there. Main, its
+ * corners on the size, has the same at 13.95 mm. So where a corner of either comes
+ * within 0.005 mm of a plane of the other, the counterbore is turned π/252 about its axis
+ * (head.turn), which leaves every corner of each 0.007 mm or more off the other's flats,
+ * and the shank's turn and mountLimits go by it turned. Its flats stand as far from the
+ * axis as before, so the head fits as typed and the caps stay where they were. Turned
+ * further the corners stand further off, but the turned counterbore's planes meet other
+ * things: π/84 opened two, a 3 x 1 magnet from above over a 2.5 mm head at 42 mm, and
+ * π/126 folded a 6.47 x 2 magnet from above under the 14.6 mm head at its cap at 43 mm
+ * and doubled the 6 open edges of a 4.844 mm head in a 6 x 3 pocket from beneath at
+ * 42 mm, all of which π/252 builds closed. π/252 opens one that π/126 closes: a 13.582
+ * head 0.251 deep under a 6 x 3 magnet from above at 42 mm, 12 open edges a cell. On 900
+ * designs drawn at random with a head within 0.012 mm of a size that puts a corner of
+ * either on a plane of the other (34 to 56 mm; one cell, the test tile, 2 x 2, corner
+ * bosses, two pieces with dovetails or jigsaws; magnets of 3 to 13 mm, either way up),
+ * of the 498 taken 56 were open, folded or had a face turned over before, 16 open with
+ * 384 edges, and 2 now: that one, and a cell at 39.72 mm with a face turned over as
+ * before; main leaves 2. With the head at its cap, every 0.5 mm of pitch from 34 to 56,
+ * 1, 1.5 and 2.5 deep, under each magnet to the hundredth that puts a corner of the
+ * counterbore on a flat's plane, of the 216 taken from above 5 were open or folded
+ * before and none now (main leaves 1), and of the 432 from beneath 4 before and none now.
+ *
  * The shank is turned a little about its axis (`turn`, #74) where a corner of the
  * counterbore or of the magnet pocket would stand on one of its flats carried on past
  * the shank, and where no counterbore is cut, the pocket's corners alone turn it.
@@ -2564,7 +2595,8 @@ <h2 id="drawersTitle">Your drawers</h2>
  * corner on a flat puts it midway between two. The turn is taken where a corner comes
  * nearer than 0.005 mm unturned and the turn leaves it further off, and a shank no corner
  * came near is cut as it was. The magnet pocket's corners stand on the same rays as the
- * counterbore's, and π/84 could bring one of those onto a flat instead: 4.85 mm under
+ * counterbore's (or π/252 off them, where it is turned), and π/84 could bring one of
+ * those onto a flat instead: 4.85 mm under
  * 7.246 with a 6 mm magnet from above left 35 edges in the socket floor at 49.02 mm, and
  * 5.773 under 12.053 25 at 55 mm, where the flats unturned miss them by 0.07 and 0.04. So
  * where π/84 leaves a corner of either nearer than 0.005 mm, the turn is the one of 24
@@ -2595,7 +2627,9 @@ <h2 id="drawersTitle">Your drawers</h2>
  * mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every 0.001 mm round the sizes
  * that put a corner on a flat, and 6.7 million sizes drawn at random round them); under
  * a bare pocket none comes within 0.005 (the same magnets every 0.01 mm, shanks every
- * 0.0005 mm within 0.012 of each size that puts a corner on a flat). The
+ * 0.0005 mm within 0.012 of each size that puts a corner on a flat), and under a
+ * counterbore turned off the pocket none within 0.003 (360,535 shanks drawn at random
+ * near a corner of either, under counterbores near the pocket's flats). The
  * nearest, 0.0033 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
  * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. Half a facet, π/12,
  * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
@@ -2643,20 +2677,41 @@ <h2 id="drawersTitle">Your drawers</h2>
             if (!magnetR || room >= magnetR + s || room < magnetR - s) return head.fits(room);
             return head.fits(room >= magnetR ? magnetR + s : magnetR - s) - 1e-6;
           },
-          snap: 0.05 },
+          snap: 0.05,
+          /* how far to turn a counterbore cut headR out at its corners about its axis,
+             beside a magnet pocket magnetR out at its corners: π/252 where a corner of either
+             would stand within 0.005 mm of the plane of one of the other's flats, and not at
+             all where they are cut as one prism (see above) */
+          turn: (headR, magnetR) => {
+            if (!headR || !magnetR || headR === magnetR) return 0;
+            const n = MOUNT_BORE.head.sides, h = Math.cos(Math.PI / n);
+            const clear = (t) => {   // the nearest a corner of either comes to one of the other's flats' planes
+              let g = Infinity;
+              for (let k = 0; k < n; k++) for (let j = 0; j < n; j++) {
+                const head = 2*Math.PI*k/n + t, magnet = 2*Math.PI*j/n;   // a corner of each
+                g = Math.min(g, Math.abs(headR * Math.cos(head - magnet - Math.PI/n) - magnetR * h),
+                             Math.abs(magnetR * Math.cos(magnet - head - Math.PI/n) - headR * h));
+              }
+              return g;
+            };
+            const c0 = clear(0);
+            return c0 < 0.005 && clear(Math.PI / 252) > c0 ? Math.PI / 252 : 0;
+          } },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12),
           // how far to turn the shank under a counterbore cut headR out at its corners
-          // (head.cut) or none (0), in a magnet pocket magnetR out at its corners or none
-          // (see above)
-          turn: (d, headR, magnetR) => {
-            // the magnet pocket's corners stand on the same rays as the counterbore's
-            const { head, hole } = MOUNT_BORE, rs = [headR, magnetR].filter((r) => r > 0);
+          // (head.cut) and turned headTurn (head.turn), or none (0), in a magnet pocket
+          // magnetR out at its corners or none (see above)
+          turn: (d, headR, magnetR, headTurn = 0) => {
+            // the magnet pocket's corners stand on the same rays as the counterbore's, but
+            // for a counterbore turned off them
+            const { head, hole } = MOUNT_BORE;
+            const rs = [[headR, headTurn], [magnetR, 0]].filter(([r]) => r > 0);
             if (!rs.length) return 0;
             const clear = (t) => {   // the nearest a corner comes to one of the flats' planes
               let g = Infinity;
-              for (const R of rs) for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
-                g = Math.min(g, Math.abs(R * Math.cos(2*Math.PI*k/head.sides - (2*m + 1)*Math.PI/hole.sides - t) - d/2));
+              for (const [R, p] of rs) for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
+                g = Math.min(g, Math.abs(R * Math.cos(2*Math.PI*k/head.sides + p - (2*m + 1)*Math.PI/hole.sides - t) - d/2));
               return g;
             };
             if (clear(0) >= 0.005) return 0;
@@ -2667,9 +2722,10 @@ <h2 id="drawersTitle">Your drawers</h2>
             }
             return most > clear(0) ? best : 0;
           } },
-  /* What fastenerCutter cuts for a design's screw, as { counterbore, headR, turn }:
-     whether the counterbore is cut, how far out its corners stand (head.cut), and how far
-     the shank is turned, for the counterbore's corners and the magnet pocket's, or the
+  /* What fastenerCutter cuts for a design's screw, as { counterbore, headR, headTurn,
+     turn }: whether the counterbore is cut, how far out its corners stand (head.cut) and
+     how far it is turned off the magnet pocket's flats (head.turn), and how far the
+     shank is turned, for the counterbore's corners and the magnet pocket's, or the
      pocket's alone where no counterbore is cut. Here so that mountLimits measures the
      same counterbore and shank the cutter cuts.
      A counterbore the magnet pocket from beneath holds whole is that pocket already: both
@@ -2682,7 +2738,9 @@ <h2 id="drawersTitle">Your drawers</h2>
     const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
       headR <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
     const counterbore = head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet;
-    return { counterbore, headR, turn: hole.turn(cfg.screwHoleD, counterbore ? headR : 0, magnetR) };
+    const headTurn = counterbore ? head.turn(headR, magnetR) : 0;
+    return { counterbore, headR, headTurn,
+             turn: hole.turn(cfg.screwHoleD, counterbore ? headR : 0, magnetR, headTurn) };
   },
 };
 
@@ -2710,7 +2768,13 @@ <h2 id="drawersTitle">Your drawers</h2>
   // each bore as MOUNT_BORE shapes it
   const { magnet, head, hole } = MOUNT_BORE;
   const magnetR = magnet.r(cfg.magnetD);
-  const { counterbore, headR, turn: t } = cfg.screws ? MOUNT_BORE.screw(cfg) : { counterbore: false };
+  const { counterbore, headR, headTurn, turn: t } = cfg.screws ? MOUNT_BORE.screw(cfg) : { counterbore: false };
+  // a bore turned t about its axis
+  const turned = (polys, t) => {
+    if (!t) return polys;
+    const c = Math.cos(t), s = Math.sin(t), turn = (v) => [v[0]*c - v[1]*s, v[0]*s + v[1]*c, v[2]];
+    return polys.map((p) => ({ verts: p.verts.map(turn), plane: { n: turn(p.plane.n), w: p.plane.w } }));
+  };
   const above = cfg.magnetSide === 'top';
   // a counterbore cut at the magnet pocket's corners (MOUNT_BORE.head.cut) that reaches the
   // pocket is one prism with it, from the underside to the top of whichever ends higher:
@@ -2722,15 +2786,13 @@ <h2 id="drawersTitle">Your drawers</h2>
       : cylinder(0, 0, magnetR, -0.5, cfg.magnetH, magnet.sides));
   if (cfg.screws) {
     // the counterbore, unless the magnet pocket from beneath is that already (MOUNT_BORE.screw)
-    // or it is cut as one with the pocket
+    // or it is cut as one with the pocket; turned where a corner of it or of the pocket
+    // would stand on one of the other's flats (MOUNT_BORE.head.turn)
     if (counterbore && !one)
-      add(cylinder(0, 0, headR, -0.5, cfg.screwHeadDepth, head.sides));
+      add(turned(cylinder(0, 0, headR, -0.5, cfg.screwHeadDepth, head.sides), headTurn));
     // the shank, turned where a corner of the counterbore or the magnet pocket would stand
     // on one of its flats (#74)
-    const shank = cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides);
-    const c = Math.cos(t), s = Math.sin(t), turn = (v) => [v[0]*c - v[1]*s, v[0]*s + v[1]*c, v[2]];
-    add(t ? shank.map((p) => ({ verts: p.verts.map(turn), plane: { n: turn(p.plane.n), w: p.plane.w } }))
-          : shank);
+    add(turned(cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides), t));
   }
   return cut;
 }
@@ -4516,16 +4578,17 @@ <h2 id="drawersTitle">Your drawers</h2>
   /* The bores as fastenerCutter cuts them (MOUNT_BORE): how many sides, and the largest
      size whose corners stay inside a radius. Each stands its flats on its size, so its
      corners stand out past it, and a magnet's 0.1 mm over its radius where that is
-     further. The shank is turned where the cutter turns it, and measured so: its turn
-     goes by the sizes asked, the head's and the magnet's as well as its own, so it is
-     the shank of this design that is measured. A counterbore within MOUNT_BORE.head.snap
+     further. The shank and the counterbore are turned where the cutter turns them, and
+     measured so: their turns go by the sizes asked, the head's and the magnet's as well
+     as the shank's, so it is the bores of this design that are measured. A counterbore
+     within MOUNT_BORE.head.snap
      of the magnet pocket's corners is cut at the pocket's, up to 0.05 mm further out or
      in, so its sizes are read back through that (head.fitsCut), which goes by the room
      alone: the cap does not move with the head typed. */
   const magnetR = cfg.magnets ? MOUNT_BORE.magnet.r(cfg.magnetD) : 0;
   const BORE = { magnetD: MOUNT_BORE.magnet, screwHoleD: MOUNT_BORE.hole,
                  screwHeadD: { sides: MOUNT_BORE.head.sides, fits: (room) => MOUNT_BORE.head.fitsCut(room, magnetR) } };
-  const shankTurn = cfg.screws ? MOUNT_BORE.screw(cfg).turn : 0;
+  const { turn: shankTurn, headTurn } = cfg.screws ? MOUNT_BORE.screw(cfg) : { turn: 0, headTurn: 0 };
   // the room the cell, the floor or a boss leaves, and the hole beside
   const own = { magnetD: fit(cfg.magnetSide === 'top' ? top : under), screwHoleD: fit(top), screwHeadD: fit(under) };
   /* A shank runs up the magnet pocket's axis, and has to clear it as it would a
@@ -4562,17 +4625,17 @@ <h2 id="drawersTitle">Your drawers</h2>
      into, but not stop just short of. */
   const jointFor = (f) => {
     const { sides, fits } = BORE[f];
-    /* the room a bore has, measured again for a turned shank (MOUNT_BORE.screw), and
-       kept on the site by its turn: the page asks again on the same cuts (`known`) once
-       the head and the magnet are read, and measuring every site again was nearly all
-       that asking again cost */
-    const turn = f === 'screwHoleD' ? shankTurn : 0;
+    /* the room a bore has, measured again for a turned shank or counterbore
+       (MOUNT_BORE.screw), and kept on the site by its sides and turn: the page asks again
+       on the same cuts (`known`) once the head and the magnet are read, and measuring
+       every site again was nearly all that asking again cost */
+    const turn = f === 'screwHoleD' ? shankTurn : f === 'screwHeadD' ? headTurn : 0;
     const reach = (c, s) => {
       if (!turn) return s.bore[sides];
       if (!(s.room > 0)) return s.room;
-      const kept = s.turned || (s.turned = new Map());
-      if (!kept.has(turn)) kept.set(turn, boreReach(sides, c.segs, s.x, s.y, turn));
-      return kept.get(turn);
+      const kept = s.turned || (s.turned = new Map()), key = `${sides} ${turn}`;
+      if (!kept.has(key)) kept.set(key, boreReach(sides, c.segs, s.x, s.y, turn));
+      return kept.get(key);
     };
     const above = f === 'magnetD' && cfg.magnetSide === 'top';
     // how high a pocket from beneath goes; a shank goes through
diff --git a/index.html b/index.html
index 7936b6f..d0c4bbe 100644
--- a/index.html
+++ b/index.html
@@ -2336,6 +2336,37 @@ <h2 id="drawersTitle">Your drawers</h2>
  * no counterbore at all. Main leaves 7 of its 225 bad. The band changes no design whose
  * counterbore is not in it.
  *
+ * Out of the band a corner of the counterbore can still stand on the plane of one of the
+ * magnet pocket's flats, or a corner of the pocket on one of the counterbore's: on the
+ * same rays, a corner of one stands an odd multiple of π/14 off the normal of a flat of
+ * the other, and at some sizes that puts it on the flat's plane. The BSP carries the
+ * plane across the other bore and splits a strip a few thousandths wide off it, which
+ * came out folded back on itself, or open. The head at its cap at 42 mm, 13.6 mm, under
+ * the default 6 x 2 magnet from above, a corner 0.004 mm off a flat's plane at 5π/14,
+ * folded the default plate 160, 120, 128 and 96 times a piece 1.5 deep and a cell 14
+ * times 1 deep, and 2 times from beneath 3 deep; the head at its cap folded the same way
+ * at 40, 43, 44 and 46 mm, each with the one magnet that puts its corner there. Main, its
+ * corners on the size, has the same at 13.95 mm. So where a corner of either comes
+ * within 0.005 mm of a plane of the other, the counterbore is turned π/252 about its axis
+ * (head.turn), which leaves every corner of each 0.007 mm or more off the other's flats,
+ * and the shank's turn and mountLimits go by it turned. Its flats stand as far from the
+ * axis as before, so the head fits as typed and the caps stay where they were. Turned
+ * further the corners stand further off, but the turned counterbore's planes meet other
+ * things: π/84 opened two, a 3 x 1 magnet from above over a 2.5 mm head at 42 mm, and
+ * π/126 folded a 6.47 x 2 magnet from above under the 14.6 mm head at its cap at 43 mm
+ * and doubled the 6 open edges of a 4.844 mm head in a 6 x 3 pocket from beneath at
+ * 42 mm, all of which π/252 builds closed. π/252 opens one that π/126 closes: a 13.582
+ * head 0.251 deep under a 6 x 3 magnet from above at 42 mm, 12 open edges a cell. On 900
+ * designs drawn at random with a head within 0.012 mm of a size that puts a corner of
+ * either on a plane of the other (34 to 56 mm; one cell, the test tile, 2 x 2, corner
+ * bosses, two pieces with dovetails or jigsaws; magnets of 3 to 13 mm, either way up),
+ * of the 498 taken 56 were open, folded or had a face turned over before, 16 open with
+ * 384 edges, and 2 now: that one, and a cell at 39.72 mm with a face turned over as
+ * before; main leaves 2. With the head at its cap, every 0.5 mm of pitch from 34 to 56,
+ * 1, 1.5 and 2.5 deep, under each magnet to the hundredth that puts a corner of the
+ * counterbore on a flat's plane, of the 216 taken from above 5 were open or folded
+ * before and none now (main leaves 1), and of the 432 from beneath 4 before and none now.
+ *
  * The shank is turned a little about its axis (`turn`, #74) where a corner of the
  * counterbore or of the magnet pocket would stand on one of its flats carried on past
  * the shank, and where no counterbore is cut, the pocket's corners alone turn it.
@@ -2352,7 +2383,8 @@ <h2 id="drawersTitle">Your drawers</h2>
  * corner on a flat puts it midway between two. The turn is taken where a corner comes
  * nearer than 0.005 mm unturned and the turn leaves it further off, and a shank no corner
  * came near is cut as it was. The magnet pocket's corners stand on the same rays as the
- * counterbore's, and π/84 could bring one of those onto a flat instead: 4.85 mm under
+ * counterbore's (or π/252 off them, where it is turned), and π/84 could bring one of
+ * those onto a flat instead: 4.85 mm under
  * 7.246 with a 6 mm magnet from above left 35 edges in the socket floor at 49.02 mm, and
  * 5.773 under 12.053 25 at 55 mm, where the flats unturned miss them by 0.07 and 0.04. So
  * where π/84 leaves a corner of either nearer than 0.005 mm, the turn is the one of 24
@@ -2383,7 +2415,9 @@ <h2 id="drawersTitle">Your drawers</h2>
  * mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every 0.001 mm round the sizes
  * that put a corner on a flat, and 6.7 million sizes drawn at random round them); under
  * a bare pocket none comes within 0.005 (the same magnets every 0.01 mm, shanks every
- * 0.0005 mm within 0.012 of each size that puts a corner on a flat). The
+ * 0.0005 mm within 0.012 of each size that puts a corner on a flat), and under a
+ * counterbore turned off the pocket none within 0.003 (360,535 shanks drawn at random
+ * near a corner of either, under counterbores near the pocket's flats). The
  * nearest, 0.0033 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
  * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. Half a facet, π/12,
  * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
@@ -2431,20 +2465,41 @@ <h2 id="drawersTitle">Your drawers</h2>
             if (!magnetR || room >= magnetR + s || room < magnetR - s) return head.fits(room);
             return head.fits(room >= magnetR ? magnetR + s : magnetR - s) - 1e-6;
           },
-          snap: 0.05 },
+          snap: 0.05,
+          /* how far to turn a counterbore cut headR out at its corners about its axis,
+             beside a magnet pocket magnetR out at its corners: π/252 where a corner of either
+             would stand within 0.005 mm of the plane of one of the other's flats, and not at
+             all where they are cut as one prism (see above) */
+          turn: (headR, magnetR) => {
+            if (!headR || !magnetR || headR === magnetR) return 0;
+            const n = MOUNT_BORE.head.sides, h = Math.cos(Math.PI / n);
+            const clear = (t) => {   // the nearest a corner of either comes to one of the other's flats' planes
+              let g = Infinity;
+              for (let k = 0; k < n; k++) for (let j = 0; j < n; j++) {
+                const head = 2*Math.PI*k/n + t, magnet = 2*Math.PI*j/n;   // a corner of each
+                g = Math.min(g, Math.abs(headR * Math.cos(head - magnet - Math.PI/n) - magnetR * h),
+                             Math.abs(magnetR * Math.cos(magnet - head - Math.PI/n) - headR * h));
+              }
+              return g;
+            };
+            const c0 = clear(0);
+            return c0 < 0.005 && clear(Math.PI / 252) > c0 ? Math.PI / 252 : 0;
+          } },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12),
           // how far to turn the shank under a counterbore cut headR out at its corners
-          // (head.cut) or none (0), in a magnet pocket magnetR out at its corners or none
-          // (see above)
-          turn: (d, headR, magnetR) => {
-            // the magnet pocket's corners stand on the same rays as the counterbore's
-            const { head, hole } = MOUNT_BORE, rs = [headR, magnetR].filter((r) => r > 0);
+          // (head.cut) and turned headTurn (head.turn), or none (0), in a magnet pocket
+          // magnetR out at its corners or none (see above)
+          turn: (d, headR, magnetR, headTurn = 0) => {
+            // the magnet pocket's corners stand on the same rays as the counterbore's, but
+            // for a counterbore turned off them
+            const { head, hole } = MOUNT_BORE;
+            const rs = [[headR, headTurn], [magnetR, 0]].filter(([r]) => r > 0);
             if (!rs.length) return 0;
             const clear = (t) => {   // the nearest a corner comes to one of the flats' planes
               let g = Infinity;
-              for (const R of rs) for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
-                g = Math.min(g, Math.abs(R * Math.cos(2*Math.PI*k/head.sides - (2*m + 1)*Math.PI/hole.sides - t) - d/2));
+              for (const [R, p] of rs) for (let k = 0; k < head.sides; k++) for (let m = 0; m < hole.sides; m++)
+                g = Math.min(g, Math.abs(R * Math.cos(2*Math.PI*k/head.sides + p - (2*m + 1)*Math.PI/hole.sides - t) - d/2));
               return g;
             };
             if (clear(0) >= 0.005) return 0;
@@ -2455,9 +2510,10 @@ <h2 id="drawersTitle">Your drawers</h2>
             }
             return most > clear(0) ? best : 0;
           } },
-  /* What fastenerCutter cuts for a design's screw, as { counterbore, headR, turn }:
-     whether the counterbore is cut, how far out its corners stand (head.cut), and how far
-     the shank is turned, for the counterbore's corners and the magnet pocket's, or the
+  /* What fastenerCutter cuts for a design's screw, as { counterbore, headR, headTurn,
+     turn }: whether the counterbore is cut, how far out its corners stand (head.cut) and
+     how far it is turned off the magnet pocket's flats (head.turn), and how far the
+     shank is turned, for the counterbore's corners and the magnet pocket's, or the
      pocket's alone where no counterbore is cut. Here so that mountLimits measures the
      same counterbore and shank the cutter cuts.
      A counterbore the magnet pocket from beneath holds whole is that pocket already: both
@@ -2470,7 +2526,9 @@ <h2 id="drawersTitle">Your drawers</h2>
     const inMagnet = cfg.magnets && cfg.magnetSide !== 'top' &&
       headR <= magnetR && cfg.screwHeadDepth <= cfg.magnetH;
     const counterbore = head.cuts(cfg.screwHeadD, cfg.screwHoleD) && !inMagnet;
-    return { counterbore, headR, turn: hole.turn(cfg.screwHoleD, counterbore ? headR : 0, magnetR) };
+    const headTurn = counterbore ? head.turn(headR, magnetR) : 0;
+    return { counterbore, headR, headTurn,
+             turn: hole.turn(cfg.screwHoleD, counterbore ? headR : 0, magnetR, headTurn) };
   },
 };
 
@@ -2498,7 +2556,13 @@ <h2 id="drawersTitle">Your drawers</h2>
   // each bore as MOUNT_BORE shapes it
   const { magnet, head, hole } = MOUNT_BORE;
   const magnetR = magnet.r(cfg.magnetD);
-  const { counterbore, headR, turn: t } = cfg.screws ? MOUNT_BORE.screw(cfg) : { counterbore: false };
+  const { counterbore, headR, headTurn, turn: t } = cfg.screws ? MOUNT_BORE.screw(cfg) : { counterbore: false };
+  // a bore turned t about its axis
+  const turned = (polys, t) => {
+    if (!t) return polys;
+    const c = Math.cos(t), s = Math.sin(t), turn = (v) => [v[0]*c - v[1]*s, v[0]*s + v[1]*c, v[2]];
+    return polys.map((p) => ({ verts: p.verts.map(turn), plane: { n: turn(p.plane.n), w: p.plane.w } }));
+  };
   const above = cfg.magnetSide === 'top';
   // a counterbore cut at the magnet pocket's corners (MOUNT_BORE.head.cut) that reaches the
   // pocket is one prism with it, from the underside to the top of whichever ends higher:
@@ -2510,15 +2574,13 @@ <h2 id="drawersTitle">Your drawers</h2>
       : cylinder(0, 0, magnetR, -0.5, cfg.magnetH, magnet.sides));
   if (cfg.screws) {
     // the counterbore, unless the magnet pocket from beneath is that already (MOUNT_BORE.screw)
-    // or it is cut as one with the pocket
+    // or it is cut as one with the pocket; turned where a corner of it or of the pocket
+    // would stand on one of the other's flats (MOUNT_BORE.head.turn)
     if (counterbore && !one)
-      add(cylinder(0, 0, headR, -0.5, cfg.screwHeadDepth, head.sides));
+      add(turned(cylinder(0, 0, headR, -0.5, cfg.screwHeadDepth, head.sides), headTurn));
     // the shank, turned where a corner of the counterbore or the magnet pocket would stand
     // on one of its flats (#74)
-    const shank = cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides);
-    const c = Math.cos(t), s = Math.sin(t), turn = (v) => [v[0]*c - v[1]*s, v[0]*s + v[1]*c, v[2]];
-    add(t ? shank.map((p) => ({ verts: p.verts.map(turn), plane: { n: turn(p.plane.n), w: p.plane.w } }))
-          : shank);
+    add(turned(cylinder(0, 0, hole.r(cfg.screwHoleD), -0.5, shankTop, hole.sides), t));
   }
   return cut;
 }
@@ -4304,16 +4366,17 @@ <h2 id="drawersTitle">Your drawers</h2>
   /* The bores as fastenerCutter cuts them (MOUNT_BORE): how many sides, and the largest
      size whose corners stay inside a radius. Each stands its flats on its size, so its
      corners stand out past it, and a magnet's 0.1 mm over its radius where that is
-     further. The shank is turned where the cutter turns it, and measured so: its turn
-     goes by the sizes asked, the head's and the magnet's as well as its own, so it is
-     the shank of this design that is measured. A counterbore within MOUNT_BORE.head.snap
+     further. The shank and the counterbore are turned where the cutter turns them, and
+     measured so: their turns go by the sizes asked, the head's and the magnet's as well
+     as the shank's, so it is the bores of this design that are measured. A counterbore
+     within MOUNT_BORE.head.snap
      of the magnet pocket's corners is cut at the pocket's, up to 0.05 mm further out or
      in, so its sizes are read back through that (head.fitsCut), which goes by the room
      alone: the cap does not move with the head typed. */
   const magnetR = cfg.magnets ? MOUNT_BORE.magnet.r(cfg.magnetD) : 0;
   const BORE = { magnetD: MOUNT_BORE.magnet, screwHoleD: MOUNT_BORE.hole,
                  screwHeadD: { sides: MOUNT_BORE.head.sides, fits: (room) => MOUNT_BORE.head.fitsCut(room, magnetR) } };
-  const shankTurn = cfg.screws ? MOUNT_BORE.screw(cfg).turn : 0;
+  const { turn: shankTurn, headTurn } = cfg.screws ? MOUNT_BORE.screw(cfg) : { turn: 0, headTurn: 0 };
   // the room the cell, the floor or a boss leaves, and the hole beside
   const own = { magnetD: fit(cfg.magnetSide === 'top' ? top : under), screwHoleD: fit(top), screwHeadD: fit(under) };
   /* A shank runs up the magnet pocket's axis, and has to clear it as it would a
@@ -4350,17 +4413,17 @@ <h2 id="drawersTitle">Your drawers</h2>
      into, but not stop just short of. */
   const jointFor = (f) => {
     const { sides, fits } = BORE[f];
-    /* the room a bore has, measured again for a turned shank (MOUNT_BORE.screw), and
-       kept on the site by its turn: the page asks again on the same cuts (`known`) once
-       the head and the magnet are read, and measuring every site again was nearly all
-       that asking again cost */
-    const turn = f === 'screwHoleD' ? shankTurn : 0;
+    /* the room a bore has, measured again for a turned shank or counterbore
+       (MOUNT_BORE.screw), and kept on the site by its sides and turn: the page asks again
+       on the same cuts (`known`) once the head and the magnet are read, and measuring
+       every site again was nearly all that asking again cost */
+    const turn = f === 'screwHoleD' ? shankTurn : f === 'screwHeadD' ? headTurn : 0;
     const reach = (c, s) => {
       if (!turn) return s.bore[sides];
       if (!(s.room > 0)) return s.room;
-      const kept = s.turned || (s.turned = new Map());
-      if (!kept.has(turn)) kept.set(turn, boreReach(sides, c.segs, s.x, s.y, turn));
-      return kept.get(turn);
+      const kept = s.turned || (s.turned = new Map()), key = `${sides} ${turn}`;
+      if (!kept.has(key)) kept.set(key, boreReach(sides, c.segs, s.x, s.y, turn));
+      return kept.get(key);
     };
     const above = f === 'magnetD' && cfg.magnetSide === 'top';
     // how high a pocket from beneath goes; a shank goes through
diff --git a/sw.js b/sw.js
index fe96f9e..e58df98 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "83123bc4fa3b";
+const VERSION = "f59752c59987";
 const FILES = [
   "./",
   "bins/",

From af2452d372d9f3fa08b0f02c47290b31d00e4796 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 06:00:37 +0000
Subject: [PATCH 40/58] Turn the counterbore half a facet off the magnet
 pocket, and check the S-1 rows as the STL stores them

Turned pi/252, the counterbore's corners stood 0.007 mm off the pocket's flats and
every cell built closed, but the rays its roof is fanned along passed 0.04 mm from
the pocket's corners. Where a socket's sloped facet crossed there, at sites away
from the origin, the roof split into slivers with no width, and single precision
in the STL folded them: 48, 36, 36 and 27 on the default plate's four pieces with
the 13.6 mm head 1.5 deep under a 6 x 2 magnet from above.

The counterbore is turned half a facet, pi/14, now, its corners midway between
the pocket's and 0.18 mm or more off its flats. That plate builds closed with no
folds in the STL, as does the 13.582 head pi/252 left open. The S-1 rows read the
STL back and count its folds too, and four rows build plates of several cells: a
2 x 2, a 3 x 2 in two pieces, the default plate, and the 13.582 head on a 2 x 2.
Each fails on the parent commit.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md      | 14 ++++++----
 src/core.js         | 63 +++++++++++++++++++++++++++------------------
 test/plate-audit.js | 45 +++++++++++++++++++++++++-------
 3 files changed, 83 insertions(+), 39 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index a9bebc0..bdc3924 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -772,11 +772,15 @@ currently installed):
   out folded: the head at its 13.6 mm cap at 42 mm, 1.5 deep under the default 6 × 2
   magnet from above, folded the default plate 160, 120, 128 and 96 times a piece. Where
   a corner of either comes within 0.005 mm of a plane of the other, the counterbore is
-  turned π/252 about its axis (`MOUNT_BORE.head.turn`), which leaves every corner of
-  each 0.007 mm or more off the other's flats; its flats stand where they did, so the
-  head fits as typed, and the shank's turn and `mountLimits` go by it turned. Turned
-  further, the counterbore's planes met other things: π/84 and π/126 each opened
-  designs that π/252 builds closed. The shank is turned π/84 about
+  turned half a facet, π/14, about its axis (`MOUNT_BORE.head.turn`), which puts its
+  corners midway between the pocket's, each 0.18 mm or more off the other's flats; its
+  flats stand where they did, so the head fits as typed, and the shank's turn and
+  `mountLimits` go by it turned. Turned less, the corners stayed near each other's: at
+  π/252 the rays the counterbore's roof is fanned along passed 0.04 mm from the
+  pocket's corners, and where a socket's sloped facet crossed there the roof split into
+  slivers with no width, which single precision in the STL folded, 147 times over the
+  default plate's four pieces though one cell built clean. π/126, π/84, π/56 and π/28
+  each opened designs that π/14 builds closed. The shank is turned π/84 about
   its axis where one of the counterbore's corners, or one of the magnet pocket's, would
   otherwise stand within 0.005 mm of a flat's plane carried on past the shank
   (`MOUNT_BORE.hole.turn`, which goes by the counterbore as cut, and by the pocket's
diff --git a/src/core.js b/src/core.js
index d87fcea..5accc2e 100644
--- a/src/core.js
+++ b/src/core.js
@@ -953,25 +953,37 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * times 1 deep, and 2 times from beneath 3 deep; the head at its cap folded the same way
  * at 40, 43, 44 and 46 mm, each with the one magnet that puts its corner there. Main, its
  * corners on the size, has the same at 13.95 mm. So where a corner of either comes
- * within 0.005 mm of a plane of the other, the counterbore is turned π/252 about its axis
- * (head.turn), which leaves every corner of each 0.007 mm or more off the other's flats,
- * and the shank's turn and mountLimits go by it turned. Its flats stand as far from the
- * axis as before, so the head fits as typed and the caps stay where they were. Turned
- * further the corners stand further off, but the turned counterbore's planes meet other
- * things: π/84 opened two, a 3 x 1 magnet from above over a 2.5 mm head at 42 mm, and
- * π/126 folded a 6.47 x 2 magnet from above under the 14.6 mm head at its cap at 43 mm
- * and doubled the 6 open edges of a 4.844 mm head in a 6 x 3 pocket from beneath at
- * 42 mm, all of which π/252 builds closed. π/252 opens one that π/126 closes: a 13.582
- * head 0.251 deep under a 6 x 3 magnet from above at 42 mm, 12 open edges a cell. On 900
- * designs drawn at random with a head within 0.012 mm of a size that puts a corner of
- * either on a plane of the other (34 to 56 mm; one cell, the test tile, 2 x 2, corner
- * bosses, two pieces with dovetails or jigsaws; magnets of 3 to 13 mm, either way up),
- * of the 498 taken 56 were open, folded or had a face turned over before, 16 open with
- * 384 edges, and 2 now: that one, and a cell at 39.72 mm with a face turned over as
- * before; main leaves 2. With the head at its cap, every 0.5 mm of pitch from 34 to 56,
- * 1, 1.5 and 2.5 deep, under each magnet to the hundredth that puts a corner of the
- * counterbore on a flat's plane, of the 216 taken from above 5 were open or folded
- * before and none now (main leaves 1), and of the 432 from beneath 4 before and none now.
+ * within 0.005 mm of a plane of the other, the counterbore is turned half a facet, π/14,
+ * about its axis (head.turn): its corners stand midway between the pocket's, each
+ * 0.18 mm or more off the other's flats under a magnet of 3 mm or more, and the shank's
+ * turn and mountLimits go by it turned. Its flats stand as far from the axis as before,
+ * so the head fits as typed and the caps stay where they were. Turned less, the corners
+ * stay near each other: π/252 left them 0.007 mm off the flats and built a cell closed,
+ * but the counterbore's roof is fanned from its axis to its corners, and those rays
+ * passed 0.04 mm from the pocket's corners. Where the BSP carried a socket's sloped
+ * facet across there, the roof split into slivers 0.01 mm long with no width, which
+ * single precision in the STL turned into folds: 48, 36, 36 and 27 on the default
+ * plate's four pieces, at sites away from the origin, and none on one cell, where fewer
+ * planes split the roof. π/126 left 2 edges open under a 6.47 x 2 magnet with the
+ * 14.6 mm head at its cap at 43 mm, π/56 and π/28 folded a 4.844 head in a 6 x 3 pocket
+ * from beneath at 42 mm, and π/84 opened 4 of the designs below; π/14 builds them all
+ * closed, as it does the 13.582 head 0.251 deep under a 6 x 3 magnet from above at 42 mm
+ * that π/252 left with 12 edges open a cell. On 600 designs drawn at random with a head
+ * within 0.012 mm of a size that puts a corner of either on a plane of the other (34 to
+ * 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3 in four, two pieces with dovetails or
+ * jigsaws, 2 x 2 on corner bosses; magnets of 3 to 13 mm, either way up), of the 354
+ * taken 145 were open, folded or had a face turned over before, counting the folds in
+ * the STL, and 20 now, where π/252 left 23 and main 33 of its 356. Two that built closed
+ * before do not now, and main builds them closed: an 8.798 head 0.592 deep under a
+ * 7.037 x 2.5 magnet from above at 42 mm, where a sloped plane meets a flat of the
+ * counterbore half a micron under its roof and each cell has an edge shared four ways
+ * and two folds, and 7.958 under a 6.35 x 2 magnet from above at 50.38 mm, 11 folds in
+ * the STL. With the head at its cap, every 1 mm of pitch from 34 to 56, 1, 1.5 and
+ * 2.5 deep, 2 x 2 in one piece and 3 x 2 in two, under each magnet to the hundredth that
+ * puts a corner of the counterbore on a flat's plane, of the 108 taken from above 36
+ * were open or folded before and none now (π/252 left 1, main 14), and of the 186 from
+ * beneath 53 before and 4 now, a fold or two each in the STL at 38 mm 2.5 deep that
+ * π/252 and main build closed (π/252 left 3 others, main 16).
  *
  * The shank is turned a little about its axis (`turn`, #74) where a corner of the
  * counterbore or of the magnet pocket would stand on one of its flats carried on past
@@ -989,7 +1001,7 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * corner on a flat puts it midway between two. The turn is taken where a corner comes
  * nearer than 0.005 mm unturned and the turn leaves it further off, and a shank no corner
  * came near is cut as it was. The magnet pocket's corners stand on the same rays as the
- * counterbore's (or π/252 off them, where it is turned), and π/84 could bring one of
+ * counterbore's (or midway between them, where it is turned), and π/84 could bring one of
  * those onto a flat instead: 4.85 mm under
  * 7.246 with a 6 mm magnet from above left 35 edges in the socket floor at 49.02 mm, and
  * 5.773 under 12.053 25 at 55 mm, where the flats unturned miss them by 0.07 and 0.04. So
@@ -1022,7 +1034,7 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * that put a corner on a flat, and 6.7 million sizes drawn at random round them); under
  * a bare pocket none comes within 0.005 (the same magnets every 0.01 mm, shanks every
  * 0.0005 mm within 0.012 of each size that puts a corner on a flat), and under a
- * counterbore turned off the pocket none within 0.003 (360,535 shanks drawn at random
+ * counterbore turned off the pocket none within 0.003 (360,213 shanks drawn at random
  * near a corner of either, under counterbores near the pocket's flats). The
  * nearest, 0.0033 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
  * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. Half a facet, π/12,
@@ -1073,9 +1085,10 @@ const MOUNT_BORE = {
           },
           snap: 0.05,
           /* how far to turn a counterbore cut headR out at its corners about its axis,
-             beside a magnet pocket magnetR out at its corners: π/252 where a corner of either
-             would stand within 0.005 mm of the plane of one of the other's flats, and not at
-             all where they are cut as one prism (see above) */
+             beside a magnet pocket magnetR out at its corners: half a facet, π/14, where a
+             corner of either would stand within 0.005 mm of the plane of one of the other's
+             flats, which puts the counterbore's corners midway between the pocket's, and not
+             at all where they are cut as one prism (see above) */
           turn: (headR, magnetR) => {
             if (!headR || !magnetR || headR === magnetR) return 0;
             const n = MOUNT_BORE.head.sides, h = Math.cos(Math.PI / n);
@@ -1089,7 +1102,7 @@ const MOUNT_BORE = {
               return g;
             };
             const c0 = clear(0);
-            return c0 < 0.005 && clear(Math.PI / 252) > c0 ? Math.PI / 252 : 0;
+            return c0 < 0.005 && clear(Math.PI / n) > c0 ? Math.PI / n : 0;
           } },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12),
diff --git a/test/plate-audit.js b/test/plate-audit.js
index d24b5ca..4723737 100644
--- a/test/plate-audit.js
+++ b/test/plate-audit.js
@@ -1322,6 +1322,15 @@ function buildAll(over) {
   return { cfg, L, pieces, bad, open, beyond: Math.round(beyond * 1e4) / 1e4 };
 }
 const leakText = (r) => r.bad ? `${r.bad} BAD EDGES${r.open ? ` (${r.open} open)` : ' (shells touching)'}` : 'watertight';
+// folds in the STL as written, its triangles read back with their corners in single precision
+const stlFolds = (polys) => {
+  const dv = new DataView(G.stlBinary(polys, 'p')), n = dv.getUint32(80, true), tris = [];
+  for (let i = 0, o = 84; i < n; i++, o += 50) {
+    const v = (k) => [0, 4, 8].map((d) => dv.getFloat32(o + 12 + 12 * k + d, true));
+    tris.push({ verts: [v(0), v(1), v(2)] });
+  }
+  return checkOrientation(tris).folds;
+};
 // four 2 × 2 pieces, and a 3 × 3 split into pieces one cell wide — the narrow one is
 // what gives out first as the pitch comes down
 const PIECE_LAYOUTS = {
@@ -2290,13 +2299,21 @@ console.log('\nthe other limits, built at their ends:');
      160, 120, 128 and 96 over the default plate's four pieces; from beneath, 3 deep, 2.
      The head at its cap folded the same way at 40, 43, 44 and 46 mm, each with the one
      magnet that puts its corner there. Main, its corners on the size, builds these closed
-     (it has the same at 13.95 mm). The counterbore is turned π/252 off the pocket's flats
-     now (MOUNT_BORE.head.turn). The last two hold it to that: turned π/126, the 6.47 x 2
-     magnet under the head at its cap at 43 mm came out with 2 bad edges and a face turned
-     over, and a 4.844 head held whole in a 6 x 3 pocket from beneath, a corner of the
-     pocket 0.002 mm off the plane of one of the counterbore's flats, left 12 edges open a
-     cell, where unturned it left 6 and main none. Each is a size the page takes, and has to build
-     closed, with no folds. */
+     (it has the same at 13.95 mm). The counterbore is turned half a facet, π/14, off the
+     pocket now (MOUNT_BORE.head.turn), its corners midway between the pocket's. Two rows
+     hold it to more than a little: turned π/126, the 6.47 x 2 magnet under the head
+     at its cap at 43 mm came out with 2 bad edges and a face turned over, and a 4.844 head
+     held whole in a 6 x 3 pocket from beneath, a corner of the pocket 0.002 mm off the
+     plane of one of the counterbore's flats, left 12 edges open a cell, where unturned it
+     left 6 and main none. The rest are plates of several cells. Turned π/252, every cell
+     built closed, but the rays the counterbore's roof is fanned along passed 0.04 mm from
+     the pocket's corners, and where a socket's sloped facet crossed there, at sites away
+     from the origin, the roof split into slivers with no width, which single precision in
+     the STL folded: 12 over 2 x 2, 18 over 3 x 2 in two, and 48, 36, 36 and 27 over the
+     default plate's four pieces. And π/252 left 12 edges open a cell, 48 over 2 x 2, with a
+     13.582 head 0.251 deep under a 6 x 3 magnet from above. So the folds are counted in
+     the STL as written too, its corners in single precision. Each is a size the page
+     takes, and has to build closed, with no folds. */
   for (const [nm, o] of [
     ['13.6 head, 6 x 2 above, 42, 1.5 deep', { magnetSide: 'top', screwHeadD: 13.6, screwHeadDepth: 1.5 }],
     ['13.6 head, 6 x 2 above, 42, 1 deep', { magnetSide: 'top', screwHeadD: 13.6, screwHeadDepth: 1 }],
@@ -2313,6 +2330,14 @@ console.log('\nthe other limits, built at their ends:');
       magnetSide: 'top', screwHeadD: 14.6, screwHeadDepth: 1 }],
     ['4.844 head in a 6 x 3 pocket below, 42', { magnetD: 6, magnetH: 3, screwHoleD: 3.48, screwHeadD: 4.844,
       screwHeadDepth: 3.408 }],
+    ['13.6 head, 6 x 2 above, 1.5 deep, 2 x 2', { drawerW: 84, drawerD: 84, magnetSide: 'top', screwHeadD: 13.6,
+      screwHeadDepth: 1.5 }],
+    ['13.6 head, 6 x 2 above, 1.5, 3 x 2 in two', { drawerW: 126, drawerD: 84, bedW: 96, magnetSide: 'top',
+      screwHeadD: 13.6, screwHeadDepth: 1.5 }],
+    ['the default plate, 13.6 head, 6 x 2 above', { drawerW: 306, drawerD: 380, marginMode: 'auto',
+      splitMode: 'balanced', magnetSide: 'top', screwHeadD: 13.6, screwHeadDepth: 1.5 }],
+    ['13.582 head, 6 x 3 above, 42, 2 x 2', { drawerW: 84, drawerD: 84, magnetD: 6, magnetH: 3, magnetSide: 'top',
+      screwHoleD: 3.613, screwHeadD: 13.582, screwHeadDepth: 0.251 }],
   ]) {
     const at = { pitch: 42, drawerW: 42, drawerD: 42, connector: 'none', magnets: true, screws: true, ...o };
     const cfg = designCfg(at), lim = G.mountLimits(cfg, G.computeLayout(cfg));
@@ -2320,8 +2345,10 @@ console.log('\nthe other limits, built at their ends:');
       !lim.gaps[f].some(([a, b]) => cfg[f] > a + 1e-9 && cfg[f] < b - 1e-9));
     const r = buildAll(at);
     const folds = r.pieces.reduce((s, pp) => s + checkOrientation(pp).folds, 0);
-    console.log(`  ${nm.padEnd(38)} ${taken ? '' : 'REFUSED, '}${leakText(r)}${folds ? `, ${folds} FOLDS` : ''}`);
-    if (!taken || r.bad || folds) bad++;
+    const stl = r.pieces.reduce((s, pp) => s + stlFolds(pp), 0);
+    console.log(`  ${nm.padEnd(41)} ${taken ? '' : 'REFUSED, '}${leakText(r)}${folds ? `, ${folds} FOLDS` : ''}` +
+      `${stl ? `, ${stl} FOLDS IN THE STL` : ''}`);
+    if (!taken || r.bad || folds || stl) bad++;
   }
   /* A pocket against a joint's cut in the floor (#64). A bowtie housed in the floor at
      42 mm, with magnets from beneath, built 12 bad edges at 7.9 mm and 19 at 10 with

From c2c9626e4a6291b223cd44d383282cb6572330e3 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 06:00:45 +0000
Subject: [PATCH 41/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html | 63 +++++++++++++++++++++++++++++--------------------
 index.html      | 63 +++++++++++++++++++++++++++++--------------------
 sw.js           |  2 +-
 3 files changed, 77 insertions(+), 51 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index ca7b5cb..c0916f4 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -2559,25 +2559,37 @@ <h2 id="drawersTitle">Your drawers</h2>
  * times 1 deep, and 2 times from beneath 3 deep; the head at its cap folded the same way
  * at 40, 43, 44 and 46 mm, each with the one magnet that puts its corner there. Main, its
  * corners on the size, has the same at 13.95 mm. So where a corner of either comes
- * within 0.005 mm of a plane of the other, the counterbore is turned π/252 about its axis
- * (head.turn), which leaves every corner of each 0.007 mm or more off the other's flats,
- * and the shank's turn and mountLimits go by it turned. Its flats stand as far from the
- * axis as before, so the head fits as typed and the caps stay where they were. Turned
- * further the corners stand further off, but the turned counterbore's planes meet other
- * things: π/84 opened two, a 3 x 1 magnet from above over a 2.5 mm head at 42 mm, and
- * π/126 folded a 6.47 x 2 magnet from above under the 14.6 mm head at its cap at 43 mm
- * and doubled the 6 open edges of a 4.844 mm head in a 6 x 3 pocket from beneath at
- * 42 mm, all of which π/252 builds closed. π/252 opens one that π/126 closes: a 13.582
- * head 0.251 deep under a 6 x 3 magnet from above at 42 mm, 12 open edges a cell. On 900
- * designs drawn at random with a head within 0.012 mm of a size that puts a corner of
- * either on a plane of the other (34 to 56 mm; one cell, the test tile, 2 x 2, corner
- * bosses, two pieces with dovetails or jigsaws; magnets of 3 to 13 mm, either way up),
- * of the 498 taken 56 were open, folded or had a face turned over before, 16 open with
- * 384 edges, and 2 now: that one, and a cell at 39.72 mm with a face turned over as
- * before; main leaves 2. With the head at its cap, every 0.5 mm of pitch from 34 to 56,
- * 1, 1.5 and 2.5 deep, under each magnet to the hundredth that puts a corner of the
- * counterbore on a flat's plane, of the 216 taken from above 5 were open or folded
- * before and none now (main leaves 1), and of the 432 from beneath 4 before and none now.
+ * within 0.005 mm of a plane of the other, the counterbore is turned half a facet, π/14,
+ * about its axis (head.turn): its corners stand midway between the pocket's, each
+ * 0.18 mm or more off the other's flats under a magnet of 3 mm or more, and the shank's
+ * turn and mountLimits go by it turned. Its flats stand as far from the axis as before,
+ * so the head fits as typed and the caps stay where they were. Turned less, the corners
+ * stay near each other: π/252 left them 0.007 mm off the flats and built a cell closed,
+ * but the counterbore's roof is fanned from its axis to its corners, and those rays
+ * passed 0.04 mm from the pocket's corners. Where the BSP carried a socket's sloped
+ * facet across there, the roof split into slivers 0.01 mm long with no width, which
+ * single precision in the STL turned into folds: 48, 36, 36 and 27 on the default
+ * plate's four pieces, at sites away from the origin, and none on one cell, where fewer
+ * planes split the roof. π/126 left 2 edges open under a 6.47 x 2 magnet with the
+ * 14.6 mm head at its cap at 43 mm, π/56 and π/28 folded a 4.844 head in a 6 x 3 pocket
+ * from beneath at 42 mm, and π/84 opened 4 of the designs below; π/14 builds them all
+ * closed, as it does the 13.582 head 0.251 deep under a 6 x 3 magnet from above at 42 mm
+ * that π/252 left with 12 edges open a cell. On 600 designs drawn at random with a head
+ * within 0.012 mm of a size that puts a corner of either on a plane of the other (34 to
+ * 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3 in four, two pieces with dovetails or
+ * jigsaws, 2 x 2 on corner bosses; magnets of 3 to 13 mm, either way up), of the 354
+ * taken 145 were open, folded or had a face turned over before, counting the folds in
+ * the STL, and 20 now, where π/252 left 23 and main 33 of its 356. Two that built closed
+ * before do not now, and main builds them closed: an 8.798 head 0.592 deep under a
+ * 7.037 x 2.5 magnet from above at 42 mm, where a sloped plane meets a flat of the
+ * counterbore half a micron under its roof and each cell has an edge shared four ways
+ * and two folds, and 7.958 under a 6.35 x 2 magnet from above at 50.38 mm, 11 folds in
+ * the STL. With the head at its cap, every 1 mm of pitch from 34 to 56, 1, 1.5 and
+ * 2.5 deep, 2 x 2 in one piece and 3 x 2 in two, under each magnet to the hundredth that
+ * puts a corner of the counterbore on a flat's plane, of the 108 taken from above 36
+ * were open or folded before and none now (π/252 left 1, main 14), and of the 186 from
+ * beneath 53 before and 4 now, a fold or two each in the STL at 38 mm 2.5 deep that
+ * π/252 and main build closed (π/252 left 3 others, main 16).
  *
  * The shank is turned a little about its axis (`turn`, #74) where a corner of the
  * counterbore or of the magnet pocket would stand on one of its flats carried on past
@@ -2595,7 +2607,7 @@ <h2 id="drawersTitle">Your drawers</h2>
  * corner on a flat puts it midway between two. The turn is taken where a corner comes
  * nearer than 0.005 mm unturned and the turn leaves it further off, and a shank no corner
  * came near is cut as it was. The magnet pocket's corners stand on the same rays as the
- * counterbore's (or π/252 off them, where it is turned), and π/84 could bring one of
+ * counterbore's (or midway between them, where it is turned), and π/84 could bring one of
  * those onto a flat instead: 4.85 mm under
  * 7.246 with a 6 mm magnet from above left 35 edges in the socket floor at 49.02 mm, and
  * 5.773 under 12.053 25 at 55 mm, where the flats unturned miss them by 0.07 and 0.04. So
@@ -2628,7 +2640,7 @@ <h2 id="drawersTitle">Your drawers</h2>
  * that put a corner on a flat, and 6.7 million sizes drawn at random round them); under
  * a bare pocket none comes within 0.005 (the same magnets every 0.01 mm, shanks every
  * 0.0005 mm within 0.012 of each size that puts a corner on a flat), and under a
- * counterbore turned off the pocket none within 0.003 (360,535 shanks drawn at random
+ * counterbore turned off the pocket none within 0.003 (360,213 shanks drawn at random
  * near a corner of either, under counterbores near the pocket's flats). The
  * nearest, 0.0033 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
  * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. Half a facet, π/12,
@@ -2679,9 +2691,10 @@ <h2 id="drawersTitle">Your drawers</h2>
           },
           snap: 0.05,
           /* how far to turn a counterbore cut headR out at its corners about its axis,
-             beside a magnet pocket magnetR out at its corners: π/252 where a corner of either
-             would stand within 0.005 mm of the plane of one of the other's flats, and not at
-             all where they are cut as one prism (see above) */
+             beside a magnet pocket magnetR out at its corners: half a facet, π/14, where a
+             corner of either would stand within 0.005 mm of the plane of one of the other's
+             flats, which puts the counterbore's corners midway between the pocket's, and not
+             at all where they are cut as one prism (see above) */
           turn: (headR, magnetR) => {
             if (!headR || !magnetR || headR === magnetR) return 0;
             const n = MOUNT_BORE.head.sides, h = Math.cos(Math.PI / n);
@@ -2695,7 +2708,7 @@ <h2 id="drawersTitle">Your drawers</h2>
               return g;
             };
             const c0 = clear(0);
-            return c0 < 0.005 && clear(Math.PI / 252) > c0 ? Math.PI / 252 : 0;
+            return c0 < 0.005 && clear(Math.PI / n) > c0 ? Math.PI / n : 0;
           } },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12),
diff --git a/index.html b/index.html
index d0c4bbe..d0ac1d2 100644
--- a/index.html
+++ b/index.html
@@ -2347,25 +2347,37 @@ <h2 id="drawersTitle">Your drawers</h2>
  * times 1 deep, and 2 times from beneath 3 deep; the head at its cap folded the same way
  * at 40, 43, 44 and 46 mm, each with the one magnet that puts its corner there. Main, its
  * corners on the size, has the same at 13.95 mm. So where a corner of either comes
- * within 0.005 mm of a plane of the other, the counterbore is turned π/252 about its axis
- * (head.turn), which leaves every corner of each 0.007 mm or more off the other's flats,
- * and the shank's turn and mountLimits go by it turned. Its flats stand as far from the
- * axis as before, so the head fits as typed and the caps stay where they were. Turned
- * further the corners stand further off, but the turned counterbore's planes meet other
- * things: π/84 opened two, a 3 x 1 magnet from above over a 2.5 mm head at 42 mm, and
- * π/126 folded a 6.47 x 2 magnet from above under the 14.6 mm head at its cap at 43 mm
- * and doubled the 6 open edges of a 4.844 mm head in a 6 x 3 pocket from beneath at
- * 42 mm, all of which π/252 builds closed. π/252 opens one that π/126 closes: a 13.582
- * head 0.251 deep under a 6 x 3 magnet from above at 42 mm, 12 open edges a cell. On 900
- * designs drawn at random with a head within 0.012 mm of a size that puts a corner of
- * either on a plane of the other (34 to 56 mm; one cell, the test tile, 2 x 2, corner
- * bosses, two pieces with dovetails or jigsaws; magnets of 3 to 13 mm, either way up),
- * of the 498 taken 56 were open, folded or had a face turned over before, 16 open with
- * 384 edges, and 2 now: that one, and a cell at 39.72 mm with a face turned over as
- * before; main leaves 2. With the head at its cap, every 0.5 mm of pitch from 34 to 56,
- * 1, 1.5 and 2.5 deep, under each magnet to the hundredth that puts a corner of the
- * counterbore on a flat's plane, of the 216 taken from above 5 were open or folded
- * before and none now (main leaves 1), and of the 432 from beneath 4 before and none now.
+ * within 0.005 mm of a plane of the other, the counterbore is turned half a facet, π/14,
+ * about its axis (head.turn): its corners stand midway between the pocket's, each
+ * 0.18 mm or more off the other's flats under a magnet of 3 mm or more, and the shank's
+ * turn and mountLimits go by it turned. Its flats stand as far from the axis as before,
+ * so the head fits as typed and the caps stay where they were. Turned less, the corners
+ * stay near each other: π/252 left them 0.007 mm off the flats and built a cell closed,
+ * but the counterbore's roof is fanned from its axis to its corners, and those rays
+ * passed 0.04 mm from the pocket's corners. Where the BSP carried a socket's sloped
+ * facet across there, the roof split into slivers 0.01 mm long with no width, which
+ * single precision in the STL turned into folds: 48, 36, 36 and 27 on the default
+ * plate's four pieces, at sites away from the origin, and none on one cell, where fewer
+ * planes split the roof. π/126 left 2 edges open under a 6.47 x 2 magnet with the
+ * 14.6 mm head at its cap at 43 mm, π/56 and π/28 folded a 4.844 head in a 6 x 3 pocket
+ * from beneath at 42 mm, and π/84 opened 4 of the designs below; π/14 builds them all
+ * closed, as it does the 13.582 head 0.251 deep under a 6 x 3 magnet from above at 42 mm
+ * that π/252 left with 12 edges open a cell. On 600 designs drawn at random with a head
+ * within 0.012 mm of a size that puts a corner of either on a plane of the other (34 to
+ * 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3 in four, two pieces with dovetails or
+ * jigsaws, 2 x 2 on corner bosses; magnets of 3 to 13 mm, either way up), of the 354
+ * taken 145 were open, folded or had a face turned over before, counting the folds in
+ * the STL, and 20 now, where π/252 left 23 and main 33 of its 356. Two that built closed
+ * before do not now, and main builds them closed: an 8.798 head 0.592 deep under a
+ * 7.037 x 2.5 magnet from above at 42 mm, where a sloped plane meets a flat of the
+ * counterbore half a micron under its roof and each cell has an edge shared four ways
+ * and two folds, and 7.958 under a 6.35 x 2 magnet from above at 50.38 mm, 11 folds in
+ * the STL. With the head at its cap, every 1 mm of pitch from 34 to 56, 1, 1.5 and
+ * 2.5 deep, 2 x 2 in one piece and 3 x 2 in two, under each magnet to the hundredth that
+ * puts a corner of the counterbore on a flat's plane, of the 108 taken from above 36
+ * were open or folded before and none now (π/252 left 1, main 14), and of the 186 from
+ * beneath 53 before and 4 now, a fold or two each in the STL at 38 mm 2.5 deep that
+ * π/252 and main build closed (π/252 left 3 others, main 16).
  *
  * The shank is turned a little about its axis (`turn`, #74) where a corner of the
  * counterbore or of the magnet pocket would stand on one of its flats carried on past
@@ -2383,7 +2395,7 @@ <h2 id="drawersTitle">Your drawers</h2>
  * corner on a flat puts it midway between two. The turn is taken where a corner comes
  * nearer than 0.005 mm unturned and the turn leaves it further off, and a shank no corner
  * came near is cut as it was. The magnet pocket's corners stand on the same rays as the
- * counterbore's (or π/252 off them, where it is turned), and π/84 could bring one of
+ * counterbore's (or midway between them, where it is turned), and π/84 could bring one of
  * those onto a flat instead: 4.85 mm under
  * 7.246 with a 6 mm magnet from above left 35 edges in the socket floor at 49.02 mm, and
  * 5.773 under 12.053 25 at 55 mm, where the flats unturned miss them by 0.07 and 0.04. So
@@ -2416,7 +2428,7 @@ <h2 id="drawersTitle">Your drawers</h2>
  * that put a corner on a flat, and 6.7 million sizes drawn at random round them); under
  * a bare pocket none comes within 0.005 (the same magnets every 0.01 mm, shanks every
  * 0.0005 mm within 0.012 of each size that puts a corner on a flat), and under a
- * counterbore turned off the pocket none within 0.003 (360,535 shanks drawn at random
+ * counterbore turned off the pocket none within 0.003 (360,213 shanks drawn at random
  * near a corner of either, under counterbores near the pocket's flats). The
  * nearest, 0.0033 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
  * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. Half a facet, π/12,
@@ -2467,9 +2479,10 @@ <h2 id="drawersTitle">Your drawers</h2>
           },
           snap: 0.05,
           /* how far to turn a counterbore cut headR out at its corners about its axis,
-             beside a magnet pocket magnetR out at its corners: π/252 where a corner of either
-             would stand within 0.005 mm of the plane of one of the other's flats, and not at
-             all where they are cut as one prism (see above) */
+             beside a magnet pocket magnetR out at its corners: half a facet, π/14, where a
+             corner of either would stand within 0.005 mm of the plane of one of the other's
+             flats, which puts the counterbore's corners midway between the pocket's, and not
+             at all where they are cut as one prism (see above) */
           turn: (headR, magnetR) => {
             if (!headR || !magnetR || headR === magnetR) return 0;
             const n = MOUNT_BORE.head.sides, h = Math.cos(Math.PI / n);
@@ -2483,7 +2496,7 @@ <h2 id="drawersTitle">Your drawers</h2>
               return g;
             };
             const c0 = clear(0);
-            return c0 < 0.005 && clear(Math.PI / 252) > c0 ? Math.PI / 252 : 0;
+            return c0 < 0.005 && clear(Math.PI / n) > c0 ? Math.PI / n : 0;
           } },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12),
diff --git a/sw.js b/sw.js
index e58df98..3a1fe9f 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "f59752c59987";
+const VERSION = "4e18205a0b4a";
 const FILES = [
   "./",
   "bins/",

From 9e9adb526a5fbc2da862b25761cda45b90c3328a Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 06:08:58 +0000
Subject: [PATCH 42/58] Count the S-1 sweep as round 4 did, and add the
 one-cell sweeps

The class sweep on plates of several cells now leaves out the edges where
corner bosses meet, the audit's known class, as round 4's sweeps did: 138
before, 7 now, where pi/252 left 10 and main 23. Round 4's one-cell designs
and head-at-cap sweeps, rebuilt with the folds in the STL counted, go in too.
ENGINE.md says the 0.18 mm holds under a magnet of 3 mm or more.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md |  6 +++---
 src/core.js    | 32 ++++++++++++++++++++------------
 2 files changed, 23 insertions(+), 15 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index bdc3924..1581e76 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -773,9 +773,9 @@ currently installed):
   magnet from above, folded the default plate 160, 120, 128 and 96 times a piece. Where
   a corner of either comes within 0.005 mm of a plane of the other, the counterbore is
   turned half a facet, π/14, about its axis (`MOUNT_BORE.head.turn`), which puts its
-  corners midway between the pocket's, each 0.18 mm or more off the other's flats; its
-  flats stand where they did, so the head fits as typed, and the shank's turn and
-  `mountLimits` go by it turned. Turned less, the corners stayed near each other's: at
+  corners midway between the pocket's, each 0.18 mm or more off the other's flats under
+  a magnet of 3 mm or more; its flats stand where they did, so the head fits as typed,
+  and the shank's turn and `mountLimits` go by it turned. Turned less, the corners stayed near each other's: at
   π/252 the rays the counterbore's roof is fanned along passed 0.04 mm from the
   pocket's corners, and where a socket's sloped facet crossed there the roof split into
   slivers with no width, which single precision in the STL folded, 147 times over the
diff --git a/src/core.js b/src/core.js
index 5accc2e..0769262 100644
--- a/src/core.js
+++ b/src/core.js
@@ -972,18 +972,26 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * within 0.012 mm of a size that puts a corner of either on a plane of the other (34 to
  * 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3 in four, two pieces with dovetails or
  * jigsaws, 2 x 2 on corner bosses; magnets of 3 to 13 mm, either way up), of the 354
- * taken 145 were open, folded or had a face turned over before, counting the folds in
- * the STL, and 20 now, where π/252 left 23 and main 33 of its 356. Two that built closed
- * before do not now, and main builds them closed: an 8.798 head 0.592 deep under a
- * 7.037 x 2.5 magnet from above at 42 mm, where a sloped plane meets a flat of the
- * counterbore half a micron under its roof and each cell has an edge shared four ways
- * and two folds, and 7.958 under a 6.35 x 2 magnet from above at 50.38 mm, 11 folds in
- * the STL. With the head at its cap, every 1 mm of pitch from 34 to 56, 1, 1.5 and
- * 2.5 deep, 2 x 2 in one piece and 3 x 2 in two, under each magnet to the hundredth that
- * puts a corner of the counterbore on a flat's plane, of the 108 taken from above 36
- * were open or folded before and none now (π/252 left 1, main 14), and of the 186 from
- * beneath 53 before and 4 now, a fold or two each in the STL at 38 mm 2.5 deep that
- * π/252 and main build closed (π/252 left 3 others, main 16).
+ * taken 138 were open, folded or had a face turned over before, counting the folds in
+ * the STL and leaving out the edges where corner bosses meet, and 7 now, where π/252
+ * left 10 and main 23 of its 356. Two that built closed before do not now, and main
+ * builds them closed: an 8.798 head 0.592 deep under a 7.037 x 2.5 magnet from above at
+ * 42 mm, where a sloped plane meets a flat of the counterbore half a micron under its
+ * roof and each cell has an edge shared four ways and two folds, and 7.958 under a
+ * 6.35 x 2 magnet from above at 50.38 mm, 11 folds in the STL. On 900 more drawn the
+ * same way on one cell, the test tile, 2 x 2, corner bosses and two pieces, of the 544
+ * taken 183 before and 10 now, where π/252 left 22 and main 22 of its 549; two are new,
+ * folds in the STL only, 6 on a 38.41 mm dovetail under an 8.704 x 3 magnet from beneath
+ * and 1 on a 42 mm test tile under a 12.954 x 1.5 magnet, where π/252 opened 8. With the
+ * head at its cap, every 1 mm of pitch from 34 to 56, 1, 1.5 and 2.5 deep, 2 x 2 in one
+ * piece and 3 x 2 in two, under each magnet to the hundredth that puts a corner of the
+ * counterbore on a flat's plane, of the 108 taken from above 36 were open or folded
+ * before and none now (π/252 left 1, main 14), and of the 186 from beneath 53 before and
+ * 4 now, a fold or two each in the STL at 38 mm 2.5 deep that π/252 and main build
+ * closed (π/252 left 3 others, main 16). On one cell, every 0.5 mm of pitch, of the 216
+ * taken from above 40 before and none now (π/252 none, main 27), and of the 360 from
+ * beneath 67 before and 2 now, 2 folds in the STL at 37.5 mm under a 7.36 x 2 magnet 1
+ * and 1.5 deep that π/252 and main build closed (π/252 left 3, main 24).
  *
  * The shank is turned a little about its axis (`turn`, #74) where a corner of the
  * counterbore or of the magnet pocket would stand on one of its flats carried on past

From a153e1cde9517f33072962b84dec9180163247a1 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 06:08:59 +0000
Subject: [PATCH 43/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html | 32 ++++++++++++++++++++------------
 index.html      | 32 ++++++++++++++++++++------------
 sw.js           |  2 +-
 3 files changed, 41 insertions(+), 25 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index c0916f4..8cedbcd 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -2578,18 +2578,26 @@ <h2 id="drawersTitle">Your drawers</h2>
  * within 0.012 mm of a size that puts a corner of either on a plane of the other (34 to
  * 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3 in four, two pieces with dovetails or
  * jigsaws, 2 x 2 on corner bosses; magnets of 3 to 13 mm, either way up), of the 354
- * taken 145 were open, folded or had a face turned over before, counting the folds in
- * the STL, and 20 now, where π/252 left 23 and main 33 of its 356. Two that built closed
- * before do not now, and main builds them closed: an 8.798 head 0.592 deep under a
- * 7.037 x 2.5 magnet from above at 42 mm, where a sloped plane meets a flat of the
- * counterbore half a micron under its roof and each cell has an edge shared four ways
- * and two folds, and 7.958 under a 6.35 x 2 magnet from above at 50.38 mm, 11 folds in
- * the STL. With the head at its cap, every 1 mm of pitch from 34 to 56, 1, 1.5 and
- * 2.5 deep, 2 x 2 in one piece and 3 x 2 in two, under each magnet to the hundredth that
- * puts a corner of the counterbore on a flat's plane, of the 108 taken from above 36
- * were open or folded before and none now (π/252 left 1, main 14), and of the 186 from
- * beneath 53 before and 4 now, a fold or two each in the STL at 38 mm 2.5 deep that
- * π/252 and main build closed (π/252 left 3 others, main 16).
+ * taken 138 were open, folded or had a face turned over before, counting the folds in
+ * the STL and leaving out the edges where corner bosses meet, and 7 now, where π/252
+ * left 10 and main 23 of its 356. Two that built closed before do not now, and main
+ * builds them closed: an 8.798 head 0.592 deep under a 7.037 x 2.5 magnet from above at
+ * 42 mm, where a sloped plane meets a flat of the counterbore half a micron under its
+ * roof and each cell has an edge shared four ways and two folds, and 7.958 under a
+ * 6.35 x 2 magnet from above at 50.38 mm, 11 folds in the STL. On 900 more drawn the
+ * same way on one cell, the test tile, 2 x 2, corner bosses and two pieces, of the 544
+ * taken 183 before and 10 now, where π/252 left 22 and main 22 of its 549; two are new,
+ * folds in the STL only, 6 on a 38.41 mm dovetail under an 8.704 x 3 magnet from beneath
+ * and 1 on a 42 mm test tile under a 12.954 x 1.5 magnet, where π/252 opened 8. With the
+ * head at its cap, every 1 mm of pitch from 34 to 56, 1, 1.5 and 2.5 deep, 2 x 2 in one
+ * piece and 3 x 2 in two, under each magnet to the hundredth that puts a corner of the
+ * counterbore on a flat's plane, of the 108 taken from above 36 were open or folded
+ * before and none now (π/252 left 1, main 14), and of the 186 from beneath 53 before and
+ * 4 now, a fold or two each in the STL at 38 mm 2.5 deep that π/252 and main build
+ * closed (π/252 left 3 others, main 16). On one cell, every 0.5 mm of pitch, of the 216
+ * taken from above 40 before and none now (π/252 none, main 27), and of the 360 from
+ * beneath 67 before and 2 now, 2 folds in the STL at 37.5 mm under a 7.36 x 2 magnet 1
+ * and 1.5 deep that π/252 and main build closed (π/252 left 3, main 24).
  *
  * The shank is turned a little about its axis (`turn`, #74) where a corner of the
  * counterbore or of the magnet pocket would stand on one of its flats carried on past
diff --git a/index.html b/index.html
index d0ac1d2..3cb8eb5 100644
--- a/index.html
+++ b/index.html
@@ -2366,18 +2366,26 @@ <h2 id="drawersTitle">Your drawers</h2>
  * within 0.012 mm of a size that puts a corner of either on a plane of the other (34 to
  * 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3 in four, two pieces with dovetails or
  * jigsaws, 2 x 2 on corner bosses; magnets of 3 to 13 mm, either way up), of the 354
- * taken 145 were open, folded or had a face turned over before, counting the folds in
- * the STL, and 20 now, where π/252 left 23 and main 33 of its 356. Two that built closed
- * before do not now, and main builds them closed: an 8.798 head 0.592 deep under a
- * 7.037 x 2.5 magnet from above at 42 mm, where a sloped plane meets a flat of the
- * counterbore half a micron under its roof and each cell has an edge shared four ways
- * and two folds, and 7.958 under a 6.35 x 2 magnet from above at 50.38 mm, 11 folds in
- * the STL. With the head at its cap, every 1 mm of pitch from 34 to 56, 1, 1.5 and
- * 2.5 deep, 2 x 2 in one piece and 3 x 2 in two, under each magnet to the hundredth that
- * puts a corner of the counterbore on a flat's plane, of the 108 taken from above 36
- * were open or folded before and none now (π/252 left 1, main 14), and of the 186 from
- * beneath 53 before and 4 now, a fold or two each in the STL at 38 mm 2.5 deep that
- * π/252 and main build closed (π/252 left 3 others, main 16).
+ * taken 138 were open, folded or had a face turned over before, counting the folds in
+ * the STL and leaving out the edges where corner bosses meet, and 7 now, where π/252
+ * left 10 and main 23 of its 356. Two that built closed before do not now, and main
+ * builds them closed: an 8.798 head 0.592 deep under a 7.037 x 2.5 magnet from above at
+ * 42 mm, where a sloped plane meets a flat of the counterbore half a micron under its
+ * roof and each cell has an edge shared four ways and two folds, and 7.958 under a
+ * 6.35 x 2 magnet from above at 50.38 mm, 11 folds in the STL. On 900 more drawn the
+ * same way on one cell, the test tile, 2 x 2, corner bosses and two pieces, of the 544
+ * taken 183 before and 10 now, where π/252 left 22 and main 22 of its 549; two are new,
+ * folds in the STL only, 6 on a 38.41 mm dovetail under an 8.704 x 3 magnet from beneath
+ * and 1 on a 42 mm test tile under a 12.954 x 1.5 magnet, where π/252 opened 8. With the
+ * head at its cap, every 1 mm of pitch from 34 to 56, 1, 1.5 and 2.5 deep, 2 x 2 in one
+ * piece and 3 x 2 in two, under each magnet to the hundredth that puts a corner of the
+ * counterbore on a flat's plane, of the 108 taken from above 36 were open or folded
+ * before and none now (π/252 left 1, main 14), and of the 186 from beneath 53 before and
+ * 4 now, a fold or two each in the STL at 38 mm 2.5 deep that π/252 and main build
+ * closed (π/252 left 3 others, main 16). On one cell, every 0.5 mm of pitch, of the 216
+ * taken from above 40 before and none now (π/252 none, main 27), and of the 360 from
+ * beneath 67 before and 2 now, 2 folds in the STL at 37.5 mm under a 7.36 x 2 magnet 1
+ * and 1.5 deep that π/252 and main build closed (π/252 left 3, main 24).
  *
  * The shank is turned a little about its axis (`turn`, #74) where a corner of the
  * counterbore or of the magnet pocket would stand on one of its flats carried on past
diff --git a/sw.js b/sw.js
index 3a1fe9f..b828378 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "4e18205a0b4a";
+const VERSION = "6b9c843bc6df";
 const FILES = [
   "./",
   "bins/",

From 4bc00c9e7b849036c244c9a6d64e48503bb329ec Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 06:28:59 +0000
Subject: [PATCH 44/58] Say how many designs the pi/84 turn opened, counted the
 same way

The S-1 comment said pi/84 opened 4 of the 600 designs, counted with the edges
where corner bosses meet. Counted as the rest of the paragraph is, it opened 5,
and 14 of round 4's 900 one-cell designs, all of which pi/14 builds closed.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 src/core.js | 53 +++++++++++++++++++++++++++--------------------------
 1 file changed, 27 insertions(+), 26 deletions(-)

diff --git a/src/core.js b/src/core.js
index 0769262..eb6911e 100644
--- a/src/core.js
+++ b/src/core.js
@@ -966,32 +966,33 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * plate's four pieces, at sites away from the origin, and none on one cell, where fewer
  * planes split the roof. π/126 left 2 edges open under a 6.47 x 2 magnet with the
  * 14.6 mm head at its cap at 43 mm, π/56 and π/28 folded a 4.844 head in a 6 x 3 pocket
- * from beneath at 42 mm, and π/84 opened 4 of the designs below; π/14 builds them all
- * closed, as it does the 13.582 head 0.251 deep under a 6 x 3 magnet from above at 42 mm
- * that π/252 left with 12 edges open a cell. On 600 designs drawn at random with a head
- * within 0.012 mm of a size that puts a corner of either on a plane of the other (34 to
- * 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3 in four, two pieces with dovetails or
- * jigsaws, 2 x 2 on corner bosses; magnets of 3 to 13 mm, either way up), of the 354
- * taken 138 were open, folded or had a face turned over before, counting the folds in
- * the STL and leaving out the edges where corner bosses meet, and 7 now, where π/252
- * left 10 and main 23 of its 356. Two that built closed before do not now, and main
- * builds them closed: an 8.798 head 0.592 deep under a 7.037 x 2.5 magnet from above at
- * 42 mm, where a sloped plane meets a flat of the counterbore half a micron under its
- * roof and each cell has an edge shared four ways and two folds, and 7.958 under a
- * 6.35 x 2 magnet from above at 50.38 mm, 11 folds in the STL. On 900 more drawn the
- * same way on one cell, the test tile, 2 x 2, corner bosses and two pieces, of the 544
- * taken 183 before and 10 now, where π/252 left 22 and main 22 of its 549; two are new,
- * folds in the STL only, 6 on a 38.41 mm dovetail under an 8.704 x 3 magnet from beneath
- * and 1 on a 42 mm test tile under a 12.954 x 1.5 magnet, where π/252 opened 8. With the
- * head at its cap, every 1 mm of pitch from 34 to 56, 1, 1.5 and 2.5 deep, 2 x 2 in one
- * piece and 3 x 2 in two, under each magnet to the hundredth that puts a corner of the
- * counterbore on a flat's plane, of the 108 taken from above 36 were open or folded
- * before and none now (π/252 left 1, main 14), and of the 186 from beneath 53 before and
- * 4 now, a fold or two each in the STL at 38 mm 2.5 deep that π/252 and main build
- * closed (π/252 left 3 others, main 16). On one cell, every 0.5 mm of pitch, of the 216
- * taken from above 40 before and none now (π/252 none, main 27), and of the 360 from
- * beneath 67 before and 2 now, 2 folds in the STL at 37.5 mm under a 7.36 x 2 magnet 1
- * and 1.5 deep that π/252 and main build closed (π/252 left 3, main 24).
+ * from beneath at 42 mm, and π/84 opened 5 of the 600 designs below and 14 of the 900
+ * after them; π/14 builds them all closed, as it does the 13.582 head 0.251 deep under a
+ * 6 x 3 magnet from above at 42 mm that π/252 left with 12 edges open a cell. On 600
+ * designs drawn at random with a head within 0.012 mm of a size that puts a corner of
+ * either on a plane of the other (34 to 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3
+ * in four, two pieces with dovetails or jigsaws, 2 x 2 on corner bosses; magnets of 3 to
+ * 13 mm, either way up), of the 354 taken 138 were open, folded or had a face turned
+ * over before, counting the folds in the STL and leaving out the edges where corner
+ * bosses meet, and 7 now, where π/252 left 10 and main 23 of its 356. Two that built
+ * closed before do not now, and main builds them closed: an 8.798 head 0.592 deep under
+ * a 7.037 x 2.5 magnet from above at 42 mm, where a sloped plane meets a flat of the
+ * counterbore half a micron under its roof and each cell has an edge shared four ways
+ * and two folds, and 7.958 under a 6.35 x 2 magnet from above at 50.38 mm, 11 folds in
+ * the STL. On 900 more drawn the same way on one cell, the test tile, 2 x 2, corner
+ * bosses and two pieces, of the 544 taken 183 before and 10 now, where π/252 left 22 and
+ * main 22 of its 549; two are new, folds in the STL only, 6 on a 38.41 mm dovetail under
+ * an 8.704 x 3 magnet from beneath and 1 on a 42 mm test tile under a 12.954 x 1.5
+ * magnet, where π/252 opened 8. With the head at its cap, every 1 mm of pitch from 34 to
+ * 56, 1, 1.5 and 2.5 deep, 2 x 2 in one piece and 3 x 2 in two, under each magnet to the
+ * hundredth that puts a corner of the counterbore on a flat's plane, of the 108 taken
+ * from above 36 were open or folded before and none now (π/252 left 1, main 14), and of
+ * the 186 from beneath 53 before and 4 now, a fold or two each in the STL at 38 mm
+ * 2.5 deep that π/252 and main build closed (π/252 left 3 others, main 16). On one cell,
+ * every 0.5 mm of pitch, of the 216 taken from above 40 before and none now (π/252 none,
+ * main 27), and of the 360 from beneath 67 before and 2 now, 2 folds in the STL at
+ * 37.5 mm under a 7.36 x 2 magnet 1 and 1.5 deep that π/252 and main build closed (π/252
+ * left 3, main 24).
  *
  * The shank is turned a little about its axis (`turn`, #74) where a corner of the
  * counterbore or of the magnet pocket would stand on one of its flats carried on past

From ee206cf1be49749955798452906cafee3ed3c078 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 06:29:00 +0000
Subject: [PATCH 45/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html | 53 +++++++++++++++++++++++++------------------------
 index.html      | 53 +++++++++++++++++++++++++------------------------
 sw.js           |  2 +-
 3 files changed, 55 insertions(+), 53 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index 8cedbcd..c784cb7 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -2572,32 +2572,33 @@ <h2 id="drawersTitle">Your drawers</h2>
  * plate's four pieces, at sites away from the origin, and none on one cell, where fewer
  * planes split the roof. π/126 left 2 edges open under a 6.47 x 2 magnet with the
  * 14.6 mm head at its cap at 43 mm, π/56 and π/28 folded a 4.844 head in a 6 x 3 pocket
- * from beneath at 42 mm, and π/84 opened 4 of the designs below; π/14 builds them all
- * closed, as it does the 13.582 head 0.251 deep under a 6 x 3 magnet from above at 42 mm
- * that π/252 left with 12 edges open a cell. On 600 designs drawn at random with a head
- * within 0.012 mm of a size that puts a corner of either on a plane of the other (34 to
- * 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3 in four, two pieces with dovetails or
- * jigsaws, 2 x 2 on corner bosses; magnets of 3 to 13 mm, either way up), of the 354
- * taken 138 were open, folded or had a face turned over before, counting the folds in
- * the STL and leaving out the edges where corner bosses meet, and 7 now, where π/252
- * left 10 and main 23 of its 356. Two that built closed before do not now, and main
- * builds them closed: an 8.798 head 0.592 deep under a 7.037 x 2.5 magnet from above at
- * 42 mm, where a sloped plane meets a flat of the counterbore half a micron under its
- * roof and each cell has an edge shared four ways and two folds, and 7.958 under a
- * 6.35 x 2 magnet from above at 50.38 mm, 11 folds in the STL. On 900 more drawn the
- * same way on one cell, the test tile, 2 x 2, corner bosses and two pieces, of the 544
- * taken 183 before and 10 now, where π/252 left 22 and main 22 of its 549; two are new,
- * folds in the STL only, 6 on a 38.41 mm dovetail under an 8.704 x 3 magnet from beneath
- * and 1 on a 42 mm test tile under a 12.954 x 1.5 magnet, where π/252 opened 8. With the
- * head at its cap, every 1 mm of pitch from 34 to 56, 1, 1.5 and 2.5 deep, 2 x 2 in one
- * piece and 3 x 2 in two, under each magnet to the hundredth that puts a corner of the
- * counterbore on a flat's plane, of the 108 taken from above 36 were open or folded
- * before and none now (π/252 left 1, main 14), and of the 186 from beneath 53 before and
- * 4 now, a fold or two each in the STL at 38 mm 2.5 deep that π/252 and main build
- * closed (π/252 left 3 others, main 16). On one cell, every 0.5 mm of pitch, of the 216
- * taken from above 40 before and none now (π/252 none, main 27), and of the 360 from
- * beneath 67 before and 2 now, 2 folds in the STL at 37.5 mm under a 7.36 x 2 magnet 1
- * and 1.5 deep that π/252 and main build closed (π/252 left 3, main 24).
+ * from beneath at 42 mm, and π/84 opened 5 of the 600 designs below and 14 of the 900
+ * after them; π/14 builds them all closed, as it does the 13.582 head 0.251 deep under a
+ * 6 x 3 magnet from above at 42 mm that π/252 left with 12 edges open a cell. On 600
+ * designs drawn at random with a head within 0.012 mm of a size that puts a corner of
+ * either on a plane of the other (34 to 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3
+ * in four, two pieces with dovetails or jigsaws, 2 x 2 on corner bosses; magnets of 3 to
+ * 13 mm, either way up), of the 354 taken 138 were open, folded or had a face turned
+ * over before, counting the folds in the STL and leaving out the edges where corner
+ * bosses meet, and 7 now, where π/252 left 10 and main 23 of its 356. Two that built
+ * closed before do not now, and main builds them closed: an 8.798 head 0.592 deep under
+ * a 7.037 x 2.5 magnet from above at 42 mm, where a sloped plane meets a flat of the
+ * counterbore half a micron under its roof and each cell has an edge shared four ways
+ * and two folds, and 7.958 under a 6.35 x 2 magnet from above at 50.38 mm, 11 folds in
+ * the STL. On 900 more drawn the same way on one cell, the test tile, 2 x 2, corner
+ * bosses and two pieces, of the 544 taken 183 before and 10 now, where π/252 left 22 and
+ * main 22 of its 549; two are new, folds in the STL only, 6 on a 38.41 mm dovetail under
+ * an 8.704 x 3 magnet from beneath and 1 on a 42 mm test tile under a 12.954 x 1.5
+ * magnet, where π/252 opened 8. With the head at its cap, every 1 mm of pitch from 34 to
+ * 56, 1, 1.5 and 2.5 deep, 2 x 2 in one piece and 3 x 2 in two, under each magnet to the
+ * hundredth that puts a corner of the counterbore on a flat's plane, of the 108 taken
+ * from above 36 were open or folded before and none now (π/252 left 1, main 14), and of
+ * the 186 from beneath 53 before and 4 now, a fold or two each in the STL at 38 mm
+ * 2.5 deep that π/252 and main build closed (π/252 left 3 others, main 16). On one cell,
+ * every 0.5 mm of pitch, of the 216 taken from above 40 before and none now (π/252 none,
+ * main 27), and of the 360 from beneath 67 before and 2 now, 2 folds in the STL at
+ * 37.5 mm under a 7.36 x 2 magnet 1 and 1.5 deep that π/252 and main build closed (π/252
+ * left 3, main 24).
  *
  * The shank is turned a little about its axis (`turn`, #74) where a corner of the
  * counterbore or of the magnet pocket would stand on one of its flats carried on past
diff --git a/index.html b/index.html
index 3cb8eb5..45240fb 100644
--- a/index.html
+++ b/index.html
@@ -2360,32 +2360,33 @@ <h2 id="drawersTitle">Your drawers</h2>
  * plate's four pieces, at sites away from the origin, and none on one cell, where fewer
  * planes split the roof. π/126 left 2 edges open under a 6.47 x 2 magnet with the
  * 14.6 mm head at its cap at 43 mm, π/56 and π/28 folded a 4.844 head in a 6 x 3 pocket
- * from beneath at 42 mm, and π/84 opened 4 of the designs below; π/14 builds them all
- * closed, as it does the 13.582 head 0.251 deep under a 6 x 3 magnet from above at 42 mm
- * that π/252 left with 12 edges open a cell. On 600 designs drawn at random with a head
- * within 0.012 mm of a size that puts a corner of either on a plane of the other (34 to
- * 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3 in four, two pieces with dovetails or
- * jigsaws, 2 x 2 on corner bosses; magnets of 3 to 13 mm, either way up), of the 354
- * taken 138 were open, folded or had a face turned over before, counting the folds in
- * the STL and leaving out the edges where corner bosses meet, and 7 now, where π/252
- * left 10 and main 23 of its 356. Two that built closed before do not now, and main
- * builds them closed: an 8.798 head 0.592 deep under a 7.037 x 2.5 magnet from above at
- * 42 mm, where a sloped plane meets a flat of the counterbore half a micron under its
- * roof and each cell has an edge shared four ways and two folds, and 7.958 under a
- * 6.35 x 2 magnet from above at 50.38 mm, 11 folds in the STL. On 900 more drawn the
- * same way on one cell, the test tile, 2 x 2, corner bosses and two pieces, of the 544
- * taken 183 before and 10 now, where π/252 left 22 and main 22 of its 549; two are new,
- * folds in the STL only, 6 on a 38.41 mm dovetail under an 8.704 x 3 magnet from beneath
- * and 1 on a 42 mm test tile under a 12.954 x 1.5 magnet, where π/252 opened 8. With the
- * head at its cap, every 1 mm of pitch from 34 to 56, 1, 1.5 and 2.5 deep, 2 x 2 in one
- * piece and 3 x 2 in two, under each magnet to the hundredth that puts a corner of the
- * counterbore on a flat's plane, of the 108 taken from above 36 were open or folded
- * before and none now (π/252 left 1, main 14), and of the 186 from beneath 53 before and
- * 4 now, a fold or two each in the STL at 38 mm 2.5 deep that π/252 and main build
- * closed (π/252 left 3 others, main 16). On one cell, every 0.5 mm of pitch, of the 216
- * taken from above 40 before and none now (π/252 none, main 27), and of the 360 from
- * beneath 67 before and 2 now, 2 folds in the STL at 37.5 mm under a 7.36 x 2 magnet 1
- * and 1.5 deep that π/252 and main build closed (π/252 left 3, main 24).
+ * from beneath at 42 mm, and π/84 opened 5 of the 600 designs below and 14 of the 900
+ * after them; π/14 builds them all closed, as it does the 13.582 head 0.251 deep under a
+ * 6 x 3 magnet from above at 42 mm that π/252 left with 12 edges open a cell. On 600
+ * designs drawn at random with a head within 0.012 mm of a size that puts a corner of
+ * either on a plane of the other (34 to 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3
+ * in four, two pieces with dovetails or jigsaws, 2 x 2 on corner bosses; magnets of 3 to
+ * 13 mm, either way up), of the 354 taken 138 were open, folded or had a face turned
+ * over before, counting the folds in the STL and leaving out the edges where corner
+ * bosses meet, and 7 now, where π/252 left 10 and main 23 of its 356. Two that built
+ * closed before do not now, and main builds them closed: an 8.798 head 0.592 deep under
+ * a 7.037 x 2.5 magnet from above at 42 mm, where a sloped plane meets a flat of the
+ * counterbore half a micron under its roof and each cell has an edge shared four ways
+ * and two folds, and 7.958 under a 6.35 x 2 magnet from above at 50.38 mm, 11 folds in
+ * the STL. On 900 more drawn the same way on one cell, the test tile, 2 x 2, corner
+ * bosses and two pieces, of the 544 taken 183 before and 10 now, where π/252 left 22 and
+ * main 22 of its 549; two are new, folds in the STL only, 6 on a 38.41 mm dovetail under
+ * an 8.704 x 3 magnet from beneath and 1 on a 42 mm test tile under a 12.954 x 1.5
+ * magnet, where π/252 opened 8. With the head at its cap, every 1 mm of pitch from 34 to
+ * 56, 1, 1.5 and 2.5 deep, 2 x 2 in one piece and 3 x 2 in two, under each magnet to the
+ * hundredth that puts a corner of the counterbore on a flat's plane, of the 108 taken
+ * from above 36 were open or folded before and none now (π/252 left 1, main 14), and of
+ * the 186 from beneath 53 before and 4 now, a fold or two each in the STL at 38 mm
+ * 2.5 deep that π/252 and main build closed (π/252 left 3 others, main 16). On one cell,
+ * every 0.5 mm of pitch, of the 216 taken from above 40 before and none now (π/252 none,
+ * main 27), and of the 360 from beneath 67 before and 2 now, 2 folds in the STL at
+ * 37.5 mm under a 7.36 x 2 magnet 1 and 1.5 deep that π/252 and main build closed (π/252
+ * left 3, main 24).
  *
  * The shank is turned a little about its axis (`turn`, #74) where a corner of the
  * counterbore or of the magnet pocket would stand on one of its flats carried on past
diff --git a/sw.js b/sw.js
index b828378..ec0eaf6 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "6b9c843bc6df";
+const VERSION = "86047bb8d13f";
 const FILES = [
   "./",
   "bins/",

From f9c3d2d5ab96402aba275bdc414795dd08d0223c Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 06:47:55 +0000
Subject: [PATCH 46/58] Name the rim as a screw hole's limit only where the
 magnet pocket it runs through does not set it, and give the rim's screw-hole
 cost with the hole sized across its flats

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md | 7 ++++---
 src/core.js    | 2 +-
 2 files changed, 5 insertions(+), 4 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index 171c979..7a6359a 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -453,9 +453,10 @@ roofs, a joint's cuts and housings), level with none. Over the boss the rim is t
 socket's wall, and is not cut: a hole that opens on the boss's top, a magnet from above
 or a screw's shank, is held `MOUNT_SEAM` clear of it by `mountLimits` (`rim`), as a solid
 floor's is held to its socket floor. That takes 2.5 mm off the cap of a magnet from above
-and of a screw's hole at 34.5 mm (6.3 to 3.8, 6.5 to 4) and 2.4 at 38 (9.7 to 7.3); from
-40 mm the boss is the tighter cap. A magnet from beneath and a screw's head lose nothing,
-and a pocket the rim does not reach is built as it was, byte for byte.
+at 34.5 mm (6.3 to 3.8) and 2.4 off a screw's hole (6.2 to 3.8), and 2.4 off the magnet's
+at 38 (9.7 to 7.3); from 40 mm the boss is the tighter cap. A magnet from beneath and a
+screw's head lose nothing, and a pocket the rim does not reach is built as it was, byte
+for byte.
 
 `connector: 'puzzle'` used to be listed here as the first kind, and it is **no longer
 open anywhere**. It is worth reading how, because it needed two unrelated fixes and the
diff --git a/src/core.js b/src/core.js
index 157f392..2eeeb5f 100644
--- a/src/core.js
+++ b/src/core.js
@@ -3140,7 +3140,7 @@ function mountLimits(cfg, layout, known) {
     depth: bosses ? r10(BOSS_H - MOUNT_SKIN) : Infinity,
     // which the socket's rim over a corner boss stops (#83)
     rim: { magnetD: bosses && cfg.magnetSide === 'top' && own.magnetD === onRim && !joint.magnetD,
-           screwHoleD: bosses && own.screwHoleD === onRim && !joint.screwHoleD },
+           screwHoleD: bosses && own.screwHoleD === onRim && !joint.screwHoleD && !byMagnet },
     // which of the sizes the cut beside it stops, rather than the floor, cell or boss
     beside: { magnetD: own.magnetD === beside && !joint.magnetD,
               screwHoleD: own.screwHoleD === beside && !joint.screwHoleD && !byMagnet,

From 0e9781ae5cdf297e300d71c8bff52795ab32e98a Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 06:47:55 +0000
Subject: [PATCH 47/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html | 2 +-
 index.html      | 2 +-
 sw.js           | 2 +-
 3 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index 18925aa..8dab972 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -4746,7 +4746,7 @@ <h2 id="drawersTitle">Your drawers</h2>
     depth: bosses ? r10(BOSS_H - MOUNT_SKIN) : Infinity,
     // which the socket's rim over a corner boss stops (#83)
     rim: { magnetD: bosses && cfg.magnetSide === 'top' && own.magnetD === onRim && !joint.magnetD,
-           screwHoleD: bosses && own.screwHoleD === onRim && !joint.screwHoleD },
+           screwHoleD: bosses && own.screwHoleD === onRim && !joint.screwHoleD && !byMagnet },
     // which of the sizes the cut beside it stops, rather than the floor, cell or boss
     beside: { magnetD: own.magnetD === beside && !joint.magnetD,
               screwHoleD: own.screwHoleD === beside && !joint.screwHoleD && !byMagnet,
diff --git a/index.html b/index.html
index 6a91490..4f64eb6 100644
--- a/index.html
+++ b/index.html
@@ -4534,7 +4534,7 @@ <h2 id="drawersTitle">Your drawers</h2>
     depth: bosses ? r10(BOSS_H - MOUNT_SKIN) : Infinity,
     // which the socket's rim over a corner boss stops (#83)
     rim: { magnetD: bosses && cfg.magnetSide === 'top' && own.magnetD === onRim && !joint.magnetD,
-           screwHoleD: bosses && own.screwHoleD === onRim && !joint.screwHoleD },
+           screwHoleD: bosses && own.screwHoleD === onRim && !joint.screwHoleD && !byMagnet },
     // which of the sizes the cut beside it stops, rather than the floor, cell or boss
     beside: { magnetD: own.magnetD === beside && !joint.magnetD,
               screwHoleD: own.screwHoleD === beside && !joint.screwHoleD && !byMagnet,
diff --git a/sw.js b/sw.js
index 3220fa0..cc9f082 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "075ba4f34d0e";
+const VERSION = "5e3cfbf56e58";
 const FILES = [
   "./",
   "bins/",

From 50c9ed067794c0ede6fbe7886ed8d6484506b3b6 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 08:12:35 +0000
Subject: [PATCH 48/58] Turn the bores from 0.01 mm off a plane, add the
 review's five designs to the S-1 rows, and say what the folds and limits
 measure

The counterbore's turn (head.turn) and the shank's (hole.turn) are taken where a
corner comes within 0.01 mm of a plane, not 0.005: at 0.005 a 38.97 mm cell under
a 3.96 x 1.5 magnet from above, a corner 0.006 mm off a plane, folded 3 times
unturned. The review's five designs near that bound are S-1 rows now, the test
tile among them (buildAll builds the tile the page would print).

The S-1 rows count folds as the audits do, in the mesh. The folds round 5 read
back from the STL where the mesh had none were triangles with no area, which
single precision gives a direction; stlFolds is removed. The comments in core.js,
the audit and ENGINE.md say which count is which, why the counterbore is still
turned pi/14 rather than pi/252, and that the limits are measured on the bore as
cut, so a head that turns can be given another cap than one that does not.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md      |  30 +++++++----
 src/core.js         | 124 ++++++++++++++++++++++++--------------------
 test/plate-audit.js |  73 +++++++++++++-------------
 3 files changed, 127 insertions(+), 100 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index 7a6359a..136d951 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -793,19 +793,29 @@ currently installed):
   counterbore can still stand on the plane of one of the pocket's flats, or a corner of
   the pocket on one of the counterbore's, and the strip the BSP splits off along it came
   out folded: the head at its 13.6 mm cap at 42 mm, 1.5 deep under the default 6 × 2
-  magnet from above, folded the default plate 160, 120, 128 and 96 times a piece. Where
-  a corner of either comes within 0.005 mm of a plane of the other, the counterbore is
+  magnet from above, folded the default plate 160, 120, 128 and 96 times a piece, folds
+  as the audits count them, two faces with area back to back in the mesh. Where a
+  corner of either comes within 0.01 mm of a plane of the other, the counterbore is
   turned half a facet, π/14, about its axis (`MOUNT_BORE.head.turn`), which puts its
   corners midway between the pocket's, each 0.18 mm or more off the other's flats under
   a magnet of 3 mm or more; its flats stand where they did, so the head fits as typed,
-  and the shank's turn and `mountLimits` go by it turned. Turned less, the corners stayed near each other's: at
-  π/252 the rays the counterbore's roof is fanned along passed 0.04 mm from the
-  pocket's corners, and where a socket's sloped facet crossed there the roof split into
-  slivers with no width, which single precision in the STL folded, 147 times over the
-  default plate's four pieces though one cell built clean. π/126, π/84, π/56 and π/28
-  each opened designs that π/14 builds closed. The shank is turned π/84 about
+  and the shank's turn and `mountLimits` go by it turned. So the limits are measured on
+  the bore as cut, turned where it is turned, and a head that turns can be given
+  another cap, and other sizes refused beside a joint's cut, than one that does not: of
+  1,034 designs drawn with a head near a size that turns, the turn moved the limits of
+  302, the head's cap by up to 0.4 mm up or 0.3 down. Measured both ways with the tighter
+  kept, the limits would hold still but come down for every head (0.1 to 0.3 mm on 28 of
+  140 page designs at five pitches). Turned less, the corners stayed near each other's:
+  π/252, with the same 0.01 mm, moved the limits less (102 of the 1,034, a tenth at
+  most), but left a 13.582 mm head 0.251 deep under a 6 × 3 magnet from above open by 12
+  edges a cell at 42 mm, and three more designs open or with shells touching, that π/14
+  builds closed. Its counterbore's roof also split, where a socket's sloped facet crossed
+  it 0.04 mm from the pocket's corners, into triangles with no area: the fold test
+  rightly leaves them out, but single precision in the STL gives each a direction, and
+  read back the default plate's STL showed 147 folds where its mesh had none. π/126
+  opened a design that π/14 builds closed. The shank is turned π/84 about
   its axis where one of the counterbore's corners, or one of the magnet pocket's, would
-  otherwise stand within 0.005 mm of a flat's plane carried on past the shank
+  otherwise stand within 0.01 mm of a flat's plane carried on past the shank
   (`MOUNT_BORE.hole.turn`, which goes by the counterbore as cut, and by the pocket's
   corners alone where no counterbore is cut: a 5 mm magnet from beneath that holds a
   5.12 mm head whole over 4.18 mm left 12 edges open at 42 mm unturned, and the same
@@ -815,7 +825,7 @@ currently installed):
   out open by the dozen round every site (#74: 136 edges a piece for 1.0353 mm under
   1.0873 with a magnet from above at 42 mm, on main; and 26 a piece at 41.24 mm for a 3 mm
   shank under a 7.3 mm magnet from above, whose corner stood 0.4 microns off a flat). The
-  two pockets' corners stand on the same rays, so where π/84 would bring one within 0.005
+  two pockets' corners stand on the same rays, so where π/84 would bring one within 0.01
   mm of a flat, the shank takes the step of the 24 across those 30/7° that keeps both
   furthest off. A shank has to clear the magnet pocket it runs through as it would a
   counterbore, and `mountLimits` refuses a wider one, which the field says
diff --git a/src/core.js b/src/core.js
index 2eeeb5f..c899f78 100644
--- a/src/core.js
+++ b/src/core.js
@@ -952,47 +952,54 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * folded the default plate 160, 120, 128 and 96 times a piece 1.5 deep and a cell 14
  * times 1 deep, and 2 times from beneath 3 deep; the head at its cap folded the same way
  * at 40, 43, 44 and 46 mm, each with the one magnet that puts its corner there. Main, its
- * corners on the size, has the same at 13.95 mm. So where a corner of either comes
- * within 0.005 mm of a plane of the other, the counterbore is turned half a facet, π/14,
- * about its axis (head.turn): its corners stand midway between the pocket's, each
- * 0.18 mm or more off the other's flats under a magnet of 3 mm or more, and the shank's
- * turn and mountLimits go by it turned. Its flats stand as far from the axis as before,
- * so the head fits as typed and the caps stay where they were. Turned less, the corners
- * stay near each other: π/252 left them 0.007 mm off the flats and built a cell closed,
- * but the counterbore's roof is fanned from its axis to its corners, and those rays
- * passed 0.04 mm from the pocket's corners. Where the BSP carried a socket's sloped
- * facet across there, the roof split into slivers 0.01 mm long with no width, which
- * single precision in the STL turned into folds: 48, 36, 36 and 27 on the default
- * plate's four pieces, at sites away from the origin, and none on one cell, where fewer
- * planes split the roof. π/126 left 2 edges open under a 6.47 x 2 magnet with the
- * 14.6 mm head at its cap at 43 mm, π/56 and π/28 folded a 4.844 head in a 6 x 3 pocket
- * from beneath at 42 mm, and π/84 opened 5 of the 600 designs below and 14 of the 900
- * after them; π/14 builds them all closed, as it does the 13.582 head 0.251 deep under a
- * 6 x 3 magnet from above at 42 mm that π/252 left with 12 edges open a cell. On 600
- * designs drawn at random with a head within 0.012 mm of a size that puts a corner of
- * either on a plane of the other (34 to 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3
- * in four, two pieces with dovetails or jigsaws, 2 x 2 on corner bosses; magnets of 3 to
- * 13 mm, either way up), of the 354 taken 138 were open, folded or had a face turned
- * over before, counting the folds in the STL and leaving out the edges where corner
- * bosses meet, and 7 now, where π/252 left 10 and main 23 of its 356. Two that built
- * closed before do not now, and main builds them closed: an 8.798 head 0.592 deep under
- * a 7.037 x 2.5 magnet from above at 42 mm, where a sloped plane meets a flat of the
- * counterbore half a micron under its roof and each cell has an edge shared four ways
- * and two folds, and 7.958 under a 6.35 x 2 magnet from above at 50.38 mm, 11 folds in
- * the STL. On 900 more drawn the same way on one cell, the test tile, 2 x 2, corner
- * bosses and two pieces, of the 544 taken 183 before and 10 now, where π/252 left 22 and
- * main 22 of its 549; two are new, folds in the STL only, 6 on a 38.41 mm dovetail under
- * an 8.704 x 3 magnet from beneath and 1 on a 42 mm test tile under a 12.954 x 1.5
- * magnet, where π/252 opened 8. With the head at its cap, every 1 mm of pitch from 34 to
- * 56, 1, 1.5 and 2.5 deep, 2 x 2 in one piece and 3 x 2 in two, under each magnet to the
- * hundredth that puts a corner of the counterbore on a flat's plane, of the 108 taken
- * from above 36 were open or folded before and none now (π/252 left 1, main 14), and of
- * the 186 from beneath 53 before and 4 now, a fold or two each in the STL at 38 mm
- * 2.5 deep that π/252 and main build closed (π/252 left 3 others, main 16). On one cell,
- * every 0.5 mm of pitch, of the 216 taken from above 40 before and none now (π/252 none,
- * main 27), and of the 360 from beneath 67 before and 2 now, 2 folds in the STL at
- * 37.5 mm under a 7.36 x 2 magnet 1 and 1.5 deep that π/252 and main build closed (π/252
- * left 3, main 24).
+ * corners on the size, has the same at 13.95 mm. Each of these is a fold as the audits
+ * count one (test/orientation.js): two faces with area back to back in the mesh. So
+ * where a corner of either comes within 0.01 mm of a plane of the other, the counterbore
+ * is turned half a facet, π/14, about its axis (head.turn): its corners stand midway
+ * between the pocket's, each 0.18 mm or more off the other's flats under a magnet of
+ * 3 mm or more, and the shank's turn and mountLimits go by it turned. Its flats stand as
+ * far from the axis as before, so the head fits as typed. The limits are measured on
+ * the bore as cut, turned where it is turned, so a head that turns can be given another
+ * cap, and other sizes refused beside a joint's cut, than a head that does not: of 1,034
+ * designs drawn with a head near a size that turns, the turn moved the limits of 302,
+ * the head's cap by up to 0.4 mm up or 0.3 down, each size held to the bore it cuts.
+ * Measured both ways and the tighter kept, the limits would not move with the
+ * head typed, but they would come down for every head: of 140 page designs at five
+ * pitches, 28 lose 0.1 to 0.3 mm of the head's cap that way (8.1 to 7.9 on a 2 x 2 at
+ * 42 mm with a jigsaw) and 12 dovetails gain a gap.
+ *
+ * Turned less, the corners stay near each other. π/252, with the turn taken from 0.01 mm
+ * as here, moved the limits of 102 of those 1,034 designs, by a tenth at most, but left
+ * open designs that π/14 builds closed: a 13.582 head 0.251 deep under a 6 x 3 magnet
+ * from above at 42 mm, 12 edges a cell; 2.69 over 1.41, 2 deep under a 6 x 1.5 magnet
+ * from beneath at 42 mm, tight, 3; 5.65 over 2.43, 3 deep under a 4.44 x 3 one, 12; and
+ * 13.26 over 1.06, 3 deep under a 5.85 x 1.5 one on 84 x 42, two shells touching along
+ * 8 edges. Its counterbore's roof, fanned from the axis to the corners, passed 0.04 mm
+ * from the pocket's corners, and where the BSP carried a socket's sloped facet across
+ * there the roof split into triangles with no area. The fold test leaves out a face
+ * with no area, as it should, but written to the STL in single precision such a
+ * triangle takes a direction, and read back the default plate's four pieces showed 48,
+ * 36, 36 and 27 folds. π/126 left 2 edges open and a face turned over under a 6.47 x 2
+ * magnet with the 14.6 mm head at its cap at 43 mm. On 600 designs drawn at random with
+ * a head within 0.012 mm of a size that puts a corner of either on a plane of the other
+ * (34 to 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3 in four, two pieces with
+ * dovetails or jigsaws, 2 x 2 on corner bosses; magnets of 3 to 13 mm, either way up),
+ * of the 354 taken 48 were open, folded or had a face turned over unturned, leaving out
+ * the edges where corner bosses meet, and 2 now, where π/252 left 1 and main 5 of its
+ * 356. One leaks on every one of them; the other, which π/252 and main build closed, is
+ * an 8.798 head 0.592 deep under a 7.037 x 2.5 magnet from above at 42 mm, where a
+ * sloped plane meets a flat of the counterbore half a micron under its roof and each
+ * cell has an edge shared four ways and two folds. On 900 more drawn the same way on one
+ * cell, the test tile, 2 x 2, corner bosses and two pieces, each held to what the page
+ * takes, 56 of 498 were bad unturned and none of 496 now, where π/252 left 2 (the 13.582
+ * head among them) and main 2 of its 504. With the head
+ * at its cap, every 1 mm of pitch from 34 to 56, 1, 1.5 and 2.5 deep, 2 x 2 in one piece
+ * and 3 x 2 in two, under each magnet to the hundredth that puts a corner of the
+ * counterbore on a flat's plane, 18 of the 108 taken from above and 8 of the 186 from
+ * beneath were bad unturned, and none now or at π/252 (main 6 and 2); on one cell, every
+ * 0.5 mm of pitch, 28 of 216 and 14 of 360, and none now or at π/252 (main 21 and 8). In
+ * the STL read back, 15 of those designs show a fold here, 30 at π/252 and 114 on main,
+ * and here and at π/252 every one the mesh does not have is a triangle with no area.
  *
  * The shank is turned a little about its axis (`turn`, #74) where a corner of the
  * counterbore or of the magnet pocket would stand on one of its flats carried on past
@@ -1008,13 +1015,13 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * of head to shank. A corner meets a flat's plane at an odd multiple of 15/7° off the
  * flat's normal; turned π/84, 15/7°, it meets them at the even ones, so a size that put a
  * corner on a flat puts it midway between two. The turn is taken where a corner comes
- * nearer than 0.005 mm unturned and the turn leaves it further off, and a shank no corner
+ * nearer than 0.01 mm unturned and the turn leaves it further off, and a shank no corner
  * came near is cut as it was. The magnet pocket's corners stand on the same rays as the
  * counterbore's (or midway between them, where it is turned), and π/84 could bring one of
  * those onto a flat instead: 4.85 mm under
  * 7.246 with a 6 mm magnet from above left 35 edges in the socket floor at 49.02 mm, and
  * 5.773 under 12.053 25 at 55 mm, where the flats unturned miss them by 0.07 and 0.04. So
- * where π/84 leaves a corner of either nearer than 0.005 mm, the turn is the one of 24
+ * where π/84 leaves a corner of either nearer than 0.01 mm, the turn is the one of 24
  * steps across those 30/7° that keeps them furthest off. And a magnet's corner calls for
  * a turn as a counterbore's does, since a shank no counterbore corner comes near can have
  * a magnet's corner on a flat all the same: at 41.24 mm a 3 mm shank under a 7.3 mm
@@ -1041,12 +1048,18 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * and none within 0.0039 but under a magnet on a shank under 1.2 mm (magnets of 3 to 13
  * mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every 0.001 mm round the sizes
  * that put a corner on a flat, and 6.7 million sizes drawn at random round them); under
- * a bare pocket none comes within 0.005 (the same magnets every 0.01 mm, shanks every
+ * a bare pocket none comes within 0.017 (the same magnets every 0.01 mm, shanks every
  * 0.0005 mm within 0.012 of each size that puts a corner on a flat), and under a
- * counterbore turned off the pocket none within 0.003 (360,213 shanks drawn at random
+ * counterbore turned off the pocket none within 0.003 (900,452 shanks drawn at random
  * near a corner of either, under counterbores near the pocket's flats). The
  * nearest, 0.0033 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
- * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. Half a facet, π/12,
+ * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. The turns were taken
+ * from 0.005 mm, and the sweeps below were measured so, until a 38.97 mm cell, a
+ * counterbore's corner 0.006 mm off a plane of the pocket's, folded 3 times unturned, and
+ * π/252 left a test tile open round a corner 0.00502 mm off a shank's flat. On 600 random
+ * designs whose turns 0.01 changes (one cell, the test tile, 2 x 2, corner bosses, two
+ * pieces), of the 511 the page takes one is open at either bound, by 6 edges where 0.005
+ * and main leave 3, and main leaves 4 open. Half a facet, π/12,
  * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
  * mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell plates
  * with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times
@@ -1095,7 +1108,7 @@ const MOUNT_BORE = {
           snap: 0.05,
           /* how far to turn a counterbore cut headR out at its corners about its axis,
              beside a magnet pocket magnetR out at its corners: half a facet, π/14, where a
-             corner of either would stand within 0.005 mm of the plane of one of the other's
+             corner of either would stand within 0.01 mm of the plane of one of the other's
              flats, which puts the counterbore's corners midway between the pocket's, and not
              at all where they are cut as one prism (see above) */
           turn: (headR, magnetR) => {
@@ -1111,7 +1124,7 @@ const MOUNT_BORE = {
               return g;
             };
             const c0 = clear(0);
-            return c0 < 0.005 && clear(Math.PI / n) > c0 ? Math.PI / n : 0;
+            return c0 < 0.01 && clear(Math.PI / n) > c0 ? Math.PI / n : 0;
           } },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12),
@@ -1130,9 +1143,9 @@ const MOUNT_BORE = {
                 g = Math.min(g, Math.abs(R * Math.cos(2*Math.PI*k/head.sides + p - (2*m + 1)*Math.PI/hole.sides - t) - d/2));
               return g;
             };
-            if (clear(0) >= 0.005) return 0;
+            if (clear(0) >= 0.01) return 0;
             let best = Math.PI / 84, most = clear(best);
-            if (most < 0.005) for (let j = 1; j < 24; j++) {
+            if (most < 0.01) for (let j = 1; j < 24; j++) {
               const t = (Math.PI / 42) * j / 24, g = clear(t);
               if (g > most + 1e-9) { most = g; best = t; }
             }
@@ -3017,11 +3030,12 @@ function mountLimits(cfg, layout, known) {
      corners stand out past it, and a magnet's 0.1 mm over its radius where that is
      further. The shank and the counterbore are turned where the cutter turns them, and
      measured so: their turns go by the sizes asked, the head's and the magnet's as well
-     as the shank's, so it is the bores of this design that are measured. A counterbore
-     within MOUNT_BORE.head.snap
-     of the magnet pocket's corners is cut at the pocket's, up to 0.05 mm further out or
-     in, so its sizes are read back through that (head.fitsCut), which goes by the room
-     alone: the cap does not move with the head typed. */
+     as the shank's, so it is the bores of this design that are measured, and a head that
+     turns can be given another cap, and other sizes refused beside a joint's cut, than a
+     head that does not (MOUNT_BORE). A counterbore within MOUNT_BORE.head.snap of the
+     magnet pocket's corners is cut at the pocket's, up to 0.05 mm further out or in, so
+     its sizes are read back through that (head.fitsCut), which goes by the room alone:
+     the band does not move the cap with the head typed. */
   const magnetR = cfg.magnets ? MOUNT_BORE.magnet.r(cfg.magnetD) : 0;
   const BORE = { magnetD: MOUNT_BORE.magnet, screwHoleD: MOUNT_BORE.hole,
                  screwHeadD: { sides: MOUNT_BORE.head.sides, fits: (room) => MOUNT_BORE.head.fitsCut(room, magnetR) } };
diff --git a/test/plate-audit.js b/test/plate-audit.js
index 502906c..e901aee 100644
--- a/test/plate-audit.js
+++ b/test/plate-audit.js
@@ -1298,10 +1298,11 @@ function designCfg(over) {
   }
   return cfg;
 }
-function buildAll(over) {
+// every piece of a design, or with `tile` the test tile the page would print for it
+function buildAll(over, tile) {
   const cfg = designCfg(over);
   const L = G.computeLayout(cfg);
-  const built = L.pieces.map((pc) => G.buildPiece(cfg, L, pc));
+  const built = tile ? [G.buildTestTile(cfg)] : L.pieces.map((pc) => G.buildPiece(cfg, L, pc));
   const pieces = built.map((r) => r.polys);
   let bad = 0, open = 0, beyond = 0;
   for (const r of built) {
@@ -1322,15 +1323,6 @@ function buildAll(over) {
   return { cfg, L, pieces, bad, open, beyond: Math.round(beyond * 1e4) / 1e4 };
 }
 const leakText = (r) => r.bad ? `${r.bad} BAD EDGES${r.open ? ` (${r.open} open)` : ' (shells touching)'}` : 'watertight';
-// folds in the STL as written, its triangles read back with their corners in single precision
-const stlFolds = (polys) => {
-  const dv = new DataView(G.stlBinary(polys, 'p')), n = dv.getUint32(80, true), tris = [];
-  for (let i = 0, o = 84; i < n; i++, o += 50) {
-    const v = (k) => [0, 4, 8].map((d) => dv.getFloat32(o + 12 + 12 * k + d, true));
-    tris.push({ verts: [v(0), v(1), v(2)] });
-  }
-  return checkOrientation(tris).folds;
-};
 // four 2 × 2 pieces, and a 3 × 3 split into pieces one cell wide — the narrow one is
 // what gives out first as the pitch comes down
 const PIECE_LAYOUTS = {
@@ -2296,25 +2288,28 @@ console.log('\nthe other limits, built at their ends:');
      thousandths from the corner, and the strip came out folded back on itself: the head
      at its cap, 13.6 mm at 42 mm, under the default 6 x 2 magnet from above, its corner
      0.004 mm off the pocket's flat at 5π/14, folded 8 times a cell 1.5 deep and 14 at 1,
-     160, 120, 128 and 96 over the default plate's four pieces; from beneath, 3 deep, 2.
-     The head at its cap folded the same way at 40, 43, 44 and 46 mm, each with the one
-     magnet that puts its corner there. Main, its corners on the size, builds these closed
-     (it has the same at 13.95 mm). The counterbore is turned half a facet, π/14, off the
-     pocket now (MOUNT_BORE.head.turn), its corners midway between the pocket's. Two rows
-     hold it to more than a little: turned π/126, the 6.47 x 2 magnet under the head
-     at its cap at 43 mm came out with 2 bad edges and a face turned over, and a 4.844 head
-     held whole in a 6 x 3 pocket from beneath, a corner of the pocket 0.002 mm off the
-     plane of one of the counterbore's flats, left 12 edges open a cell, where unturned it
-     left 6 and main none. The rest are plates of several cells. Turned π/252, every cell
-     built closed, but the rays the counterbore's roof is fanned along passed 0.04 mm from
-     the pocket's corners, and where a socket's sloped facet crossed there, at sites away
-     from the origin, the roof split into slivers with no width, which single precision in
-     the STL folded: 12 over 2 x 2, 18 over 3 x 2 in two, and 48, 36, 36 and 27 over the
-     default plate's four pieces. And π/252 left 12 edges open a cell, 48 over 2 x 2, with a
-     13.582 head 0.251 deep under a 6 x 3 magnet from above. So the folds are counted in
-     the STL as written too, its corners in single precision. Each is a size the page
-     takes, and has to build closed, with no folds. */
-  for (const [nm, o] of [
+     38 over 2 x 2, 54 over 3 x 2 in two and 160, 120, 128 and 96 over the default plate's
+     four pieces; from beneath, 3 deep, 2. Each is a fold as checkOrientation counts one,
+     two faces with area back to back in the mesh. The head at its cap folded the same way
+     at 40, 43, 44 and 46 mm, each with the one magnet that puts its corner there. Main, its
+     corners on the size, builds these closed (it has the same at 13.95 mm). The
+     counterbore is turned half a facet, π/14, off the pocket now (MOUNT_BORE.head.turn),
+     its corners midway between the pocket's. Two rows hold it to more than a little:
+     turned π/126, the 6.47 x 2 magnet under the head at its cap at 43 mm came out with 2
+     bad edges and a face turned over, and a 4.844 head held whole in a 6 x 3 pocket from
+     beneath, a corner of the pocket 0.002 mm off the plane of one of the counterbore's
+     flats, left 12 edges open a cell, where unturned it left 6 and main none. The plates
+     of several cells are here so that one cell cannot pass for them. Turned π/252, a
+     13.582 head 0.251 deep under a 6 x 3 magnet from above left 12 edges open a cell, 48
+     over 2 x 2. The last five are where a corner comes between 0.005 and 0.01 mm of a
+     plane, and the turn is taken from 0.01 now (head.turn and hole.turn). Main builds each
+     closed. The 38.97 mm cell, a corner 0.006 mm off a plane, folded 3 times unturned with
+     the turn from 0.005; on the tile π/252 left a counterbore's corner 0.00502 mm off a
+     shank's flat, the shank unturned, and 15 edges open; and π/252 left the other three
+     open by 3 and 12 edges and two shells touching along 8, split elsewhere by its
+     planes, from 0.01 as well.
+     Each is a size the page takes, and has to build closed, with no folds. */
+  for (const [nm, o, tile] of [
     ['13.6 head, 6 x 2 above, 42, 1.5 deep', { magnetSide: 'top', screwHeadD: 13.6, screwHeadDepth: 1.5 }],
     ['13.6 head, 6 x 2 above, 42, 1 deep', { magnetSide: 'top', screwHeadD: 13.6, screwHeadDepth: 1 }],
     ['13.6 head, 6 x 2 below, 42, 3 deep', { screwHeadD: 13.6, screwHeadDepth: 3 }],
@@ -2338,17 +2333,25 @@ console.log('\nthe other limits, built at their ends:');
       splitMode: 'balanced', magnetSide: 'top', screwHeadD: 13.6, screwHeadDepth: 1.5 }],
     ['13.582 head, 6 x 3 above, 42, 2 x 2', { drawerW: 84, drawerD: 84, magnetD: 6, magnetH: 3, magnetSide: 'top',
       screwHoleD: 3.613, screwHeadD: 13.582, screwHeadDepth: 0.251 }],
+    ['3.24 head, 3.96 x 1.5 above, 38.97', { pitch: 38.97, drawerW: 38.97, drawerD: 38.97, magnetD: 3.96,
+      magnetH: 1.5, magnetSide: 'top', screwHoleD: 2.34, screwHeadD: 3.24, screwHeadDepth: 2.5 }],
+    ['tile at 53.72, 1.82 head, 4 x 2 above', { pitch: 53.72, drawerW: 53.72, drawerD: 53.72, tolerance: 'tight',
+      magnetD: 4, magnetSide: 'top', screwHoleD: 1.21, screwHeadD: 1.82, screwHeadDepth: 1 }, true],
+    ['2.69 head, 6 x 1.5 below, 42, tight', { tolerance: 'tight', magnetD: 6, magnetH: 1.5, screwHoleD: 1.41,
+      screwHeadD: 2.69, screwHeadDepth: 2 }],
+    ['13.26 head, 5.85 x 1.5 below, 84 x 42', { drawerW: 84, tolerance: 'tight', magnetD: 5.85, magnetH: 1.5,
+      screwHoleD: 1.06, screwHeadD: 13.26, screwHeadDepth: 3 }],
+    ['5.65 head, 4.44 x 3 below, 42', { magnetD: 4.44, magnetH: 3, screwHoleD: 2.43, screwHeadD: 5.65,
+      screwHeadDepth: 3 }],
   ]) {
     const at = { pitch: 42, drawerW: 42, drawerD: 42, connector: 'none', magnets: true, screws: true, ...o };
     const cfg = designCfg(at), lim = G.mountLimits(cfg, G.computeLayout(cfg));
     const taken = ['magnetD', 'screwHoleD', 'screwHeadD'].every((f) => cfg[f] <= lim[f] + 1e-9 &&
       !lim.gaps[f].some(([a, b]) => cfg[f] > a + 1e-9 && cfg[f] < b - 1e-9));
-    const r = buildAll(at);
+    const r = buildAll(at, tile);
     const folds = r.pieces.reduce((s, pp) => s + checkOrientation(pp).folds, 0);
-    const stl = r.pieces.reduce((s, pp) => s + stlFolds(pp), 0);
-    console.log(`  ${nm.padEnd(41)} ${taken ? '' : 'REFUSED, '}${leakText(r)}${folds ? `, ${folds} FOLDS` : ''}` +
-      `${stl ? `, ${stl} FOLDS IN THE STL` : ''}`);
-    if (!taken || r.bad || folds || stl) bad++;
+    console.log(`  ${nm.padEnd(41)} ${taken ? '' : 'REFUSED, '}${leakText(r)}${folds ? `, ${folds} FOLDS` : ''}`);
+    if (!taken || r.bad || folds) bad++;
   }
   /* A pocket against a joint's cut in the floor (#64). A bowtie housed in the floor at
      42 mm, with magnets from beneath, built 12 bad edges at 7.9 mm and 19 at 10 with

From 1cd068e1e3809b95853f86105c6035116ee8b53c Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 08:12:42 +0000
Subject: [PATCH 49/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html | 124 +++++++++++++++++++++++++++---------------------
 index.html      | 124 +++++++++++++++++++++++++++---------------------
 sw.js           |   2 +-
 3 files changed, 139 insertions(+), 111 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index 8dab972..9d9f7f6 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -2558,47 +2558,54 @@ <h2 id="drawersTitle">Your drawers</h2>
  * folded the default plate 160, 120, 128 and 96 times a piece 1.5 deep and a cell 14
  * times 1 deep, and 2 times from beneath 3 deep; the head at its cap folded the same way
  * at 40, 43, 44 and 46 mm, each with the one magnet that puts its corner there. Main, its
- * corners on the size, has the same at 13.95 mm. So where a corner of either comes
- * within 0.005 mm of a plane of the other, the counterbore is turned half a facet, π/14,
- * about its axis (head.turn): its corners stand midway between the pocket's, each
- * 0.18 mm or more off the other's flats under a magnet of 3 mm or more, and the shank's
- * turn and mountLimits go by it turned. Its flats stand as far from the axis as before,
- * so the head fits as typed and the caps stay where they were. Turned less, the corners
- * stay near each other: π/252 left them 0.007 mm off the flats and built a cell closed,
- * but the counterbore's roof is fanned from its axis to its corners, and those rays
- * passed 0.04 mm from the pocket's corners. Where the BSP carried a socket's sloped
- * facet across there, the roof split into slivers 0.01 mm long with no width, which
- * single precision in the STL turned into folds: 48, 36, 36 and 27 on the default
- * plate's four pieces, at sites away from the origin, and none on one cell, where fewer
- * planes split the roof. π/126 left 2 edges open under a 6.47 x 2 magnet with the
- * 14.6 mm head at its cap at 43 mm, π/56 and π/28 folded a 4.844 head in a 6 x 3 pocket
- * from beneath at 42 mm, and π/84 opened 5 of the 600 designs below and 14 of the 900
- * after them; π/14 builds them all closed, as it does the 13.582 head 0.251 deep under a
- * 6 x 3 magnet from above at 42 mm that π/252 left with 12 edges open a cell. On 600
- * designs drawn at random with a head within 0.012 mm of a size that puts a corner of
- * either on a plane of the other (34 to 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3
- * in four, two pieces with dovetails or jigsaws, 2 x 2 on corner bosses; magnets of 3 to
- * 13 mm, either way up), of the 354 taken 138 were open, folded or had a face turned
- * over before, counting the folds in the STL and leaving out the edges where corner
- * bosses meet, and 7 now, where π/252 left 10 and main 23 of its 356. Two that built
- * closed before do not now, and main builds them closed: an 8.798 head 0.592 deep under
- * a 7.037 x 2.5 magnet from above at 42 mm, where a sloped plane meets a flat of the
- * counterbore half a micron under its roof and each cell has an edge shared four ways
- * and two folds, and 7.958 under a 6.35 x 2 magnet from above at 50.38 mm, 11 folds in
- * the STL. On 900 more drawn the same way on one cell, the test tile, 2 x 2, corner
- * bosses and two pieces, of the 544 taken 183 before and 10 now, where π/252 left 22 and
- * main 22 of its 549; two are new, folds in the STL only, 6 on a 38.41 mm dovetail under
- * an 8.704 x 3 magnet from beneath and 1 on a 42 mm test tile under a 12.954 x 1.5
- * magnet, where π/252 opened 8. With the head at its cap, every 1 mm of pitch from 34 to
- * 56, 1, 1.5 and 2.5 deep, 2 x 2 in one piece and 3 x 2 in two, under each magnet to the
- * hundredth that puts a corner of the counterbore on a flat's plane, of the 108 taken
- * from above 36 were open or folded before and none now (π/252 left 1, main 14), and of
- * the 186 from beneath 53 before and 4 now, a fold or two each in the STL at 38 mm
- * 2.5 deep that π/252 and main build closed (π/252 left 3 others, main 16). On one cell,
- * every 0.5 mm of pitch, of the 216 taken from above 40 before and none now (π/252 none,
- * main 27), and of the 360 from beneath 67 before and 2 now, 2 folds in the STL at
- * 37.5 mm under a 7.36 x 2 magnet 1 and 1.5 deep that π/252 and main build closed (π/252
- * left 3, main 24).
+ * corners on the size, has the same at 13.95 mm. Each of these is a fold as the audits
+ * count one (test/orientation.js): two faces with area back to back in the mesh. So
+ * where a corner of either comes within 0.01 mm of a plane of the other, the counterbore
+ * is turned half a facet, π/14, about its axis (head.turn): its corners stand midway
+ * between the pocket's, each 0.18 mm or more off the other's flats under a magnet of
+ * 3 mm or more, and the shank's turn and mountLimits go by it turned. Its flats stand as
+ * far from the axis as before, so the head fits as typed. The limits are measured on
+ * the bore as cut, turned where it is turned, so a head that turns can be given another
+ * cap, and other sizes refused beside a joint's cut, than a head that does not: of 1,034
+ * designs drawn with a head near a size that turns, the turn moved the limits of 302,
+ * the head's cap by up to 0.4 mm up or 0.3 down, each size held to the bore it cuts.
+ * Measured both ways and the tighter kept, the limits would not move with the
+ * head typed, but they would come down for every head: of 140 page designs at five
+ * pitches, 28 lose 0.1 to 0.3 mm of the head's cap that way (8.1 to 7.9 on a 2 x 2 at
+ * 42 mm with a jigsaw) and 12 dovetails gain a gap.
+ *
+ * Turned less, the corners stay near each other. π/252, with the turn taken from 0.01 mm
+ * as here, moved the limits of 102 of those 1,034 designs, by a tenth at most, but left
+ * open designs that π/14 builds closed: a 13.582 head 0.251 deep under a 6 x 3 magnet
+ * from above at 42 mm, 12 edges a cell; 2.69 over 1.41, 2 deep under a 6 x 1.5 magnet
+ * from beneath at 42 mm, tight, 3; 5.65 over 2.43, 3 deep under a 4.44 x 3 one, 12; and
+ * 13.26 over 1.06, 3 deep under a 5.85 x 1.5 one on 84 x 42, two shells touching along
+ * 8 edges. Its counterbore's roof, fanned from the axis to the corners, passed 0.04 mm
+ * from the pocket's corners, and where the BSP carried a socket's sloped facet across
+ * there the roof split into triangles with no area. The fold test leaves out a face
+ * with no area, as it should, but written to the STL in single precision such a
+ * triangle takes a direction, and read back the default plate's four pieces showed 48,
+ * 36, 36 and 27 folds. π/126 left 2 edges open and a face turned over under a 6.47 x 2
+ * magnet with the 14.6 mm head at its cap at 43 mm. On 600 designs drawn at random with
+ * a head within 0.012 mm of a size that puts a corner of either on a plane of the other
+ * (34 to 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3 in four, two pieces with
+ * dovetails or jigsaws, 2 x 2 on corner bosses; magnets of 3 to 13 mm, either way up),
+ * of the 354 taken 48 were open, folded or had a face turned over unturned, leaving out
+ * the edges where corner bosses meet, and 2 now, where π/252 left 1 and main 5 of its
+ * 356. One leaks on every one of them; the other, which π/252 and main build closed, is
+ * an 8.798 head 0.592 deep under a 7.037 x 2.5 magnet from above at 42 mm, where a
+ * sloped plane meets a flat of the counterbore half a micron under its roof and each
+ * cell has an edge shared four ways and two folds. On 900 more drawn the same way on one
+ * cell, the test tile, 2 x 2, corner bosses and two pieces, each held to what the page
+ * takes, 56 of 498 were bad unturned and none of 496 now, where π/252 left 2 (the 13.582
+ * head among them) and main 2 of its 504. With the head
+ * at its cap, every 1 mm of pitch from 34 to 56, 1, 1.5 and 2.5 deep, 2 x 2 in one piece
+ * and 3 x 2 in two, under each magnet to the hundredth that puts a corner of the
+ * counterbore on a flat's plane, 18 of the 108 taken from above and 8 of the 186 from
+ * beneath were bad unturned, and none now or at π/252 (main 6 and 2); on one cell, every
+ * 0.5 mm of pitch, 28 of 216 and 14 of 360, and none now or at π/252 (main 21 and 8). In
+ * the STL read back, 15 of those designs show a fold here, 30 at π/252 and 114 on main,
+ * and here and at π/252 every one the mesh does not have is a triangle with no area.
  *
  * The shank is turned a little about its axis (`turn`, #74) where a corner of the
  * counterbore or of the magnet pocket would stand on one of its flats carried on past
@@ -2614,13 +2621,13 @@ <h2 id="drawersTitle">Your drawers</h2>
  * of head to shank. A corner meets a flat's plane at an odd multiple of 15/7° off the
  * flat's normal; turned π/84, 15/7°, it meets them at the even ones, so a size that put a
  * corner on a flat puts it midway between two. The turn is taken where a corner comes
- * nearer than 0.005 mm unturned and the turn leaves it further off, and a shank no corner
+ * nearer than 0.01 mm unturned and the turn leaves it further off, and a shank no corner
  * came near is cut as it was. The magnet pocket's corners stand on the same rays as the
  * counterbore's (or midway between them, where it is turned), and π/84 could bring one of
  * those onto a flat instead: 4.85 mm under
  * 7.246 with a 6 mm magnet from above left 35 edges in the socket floor at 49.02 mm, and
  * 5.773 under 12.053 25 at 55 mm, where the flats unturned miss them by 0.07 and 0.04. So
- * where π/84 leaves a corner of either nearer than 0.005 mm, the turn is the one of 24
+ * where π/84 leaves a corner of either nearer than 0.01 mm, the turn is the one of 24
  * steps across those 30/7° that keeps them furthest off. And a magnet's corner calls for
  * a turn as a counterbore's does, since a shank no counterbore corner comes near can have
  * a magnet's corner on a flat all the same: at 41.24 mm a 3 mm shank under a 7.3 mm
@@ -2647,12 +2654,18 @@ <h2 id="drawersTitle">Your drawers</h2>
  * and none within 0.0039 but under a magnet on a shank under 1.2 mm (magnets of 3 to 13
  * mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every 0.001 mm round the sizes
  * that put a corner on a flat, and 6.7 million sizes drawn at random round them); under
- * a bare pocket none comes within 0.005 (the same magnets every 0.01 mm, shanks every
+ * a bare pocket none comes within 0.017 (the same magnets every 0.01 mm, shanks every
  * 0.0005 mm within 0.012 of each size that puts a corner on a flat), and under a
- * counterbore turned off the pocket none within 0.003 (360,213 shanks drawn at random
+ * counterbore turned off the pocket none within 0.003 (900,452 shanks drawn at random
  * near a corner of either, under counterbores near the pocket's flats). The
  * nearest, 0.0033 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
- * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. Half a facet, π/12,
+ * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. The turns were taken
+ * from 0.005 mm, and the sweeps below were measured so, until a 38.97 mm cell, a
+ * counterbore's corner 0.006 mm off a plane of the pocket's, folded 3 times unturned, and
+ * π/252 left a test tile open round a corner 0.00502 mm off a shank's flat. On 600 random
+ * designs whose turns 0.01 changes (one cell, the test tile, 2 x 2, corner bosses, two
+ * pieces), of the 511 the page takes one is open at either bound, by 6 edges where 0.005
+ * and main leave 3, and main leaves 4 open. Half a facet, π/12,
  * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
  * mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell plates
  * with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times
@@ -2701,7 +2714,7 @@ <h2 id="drawersTitle">Your drawers</h2>
           snap: 0.05,
           /* how far to turn a counterbore cut headR out at its corners about its axis,
              beside a magnet pocket magnetR out at its corners: half a facet, π/14, where a
-             corner of either would stand within 0.005 mm of the plane of one of the other's
+             corner of either would stand within 0.01 mm of the plane of one of the other's
              flats, which puts the counterbore's corners midway between the pocket's, and not
              at all where they are cut as one prism (see above) */
           turn: (headR, magnetR) => {
@@ -2717,7 +2730,7 @@ <h2 id="drawersTitle">Your drawers</h2>
               return g;
             };
             const c0 = clear(0);
-            return c0 < 0.005 && clear(Math.PI / n) > c0 ? Math.PI / n : 0;
+            return c0 < 0.01 && clear(Math.PI / n) > c0 ? Math.PI / n : 0;
           } },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12),
@@ -2736,9 +2749,9 @@ <h2 id="drawersTitle">Your drawers</h2>
                 g = Math.min(g, Math.abs(R * Math.cos(2*Math.PI*k/head.sides + p - (2*m + 1)*Math.PI/hole.sides - t) - d/2));
               return g;
             };
-            if (clear(0) >= 0.005) return 0;
+            if (clear(0) >= 0.01) return 0;
             let best = Math.PI / 84, most = clear(best);
-            if (most < 0.005) for (let j = 1; j < 24; j++) {
+            if (most < 0.01) for (let j = 1; j < 24; j++) {
               const t = (Math.PI / 42) * j / 24, g = clear(t);
               if (g > most + 1e-9) { most = g; best = t; }
             }
@@ -4623,11 +4636,12 @@ <h2 id="drawersTitle">Your drawers</h2>
      corners stand out past it, and a magnet's 0.1 mm over its radius where that is
      further. The shank and the counterbore are turned where the cutter turns them, and
      measured so: their turns go by the sizes asked, the head's and the magnet's as well
-     as the shank's, so it is the bores of this design that are measured. A counterbore
-     within MOUNT_BORE.head.snap
-     of the magnet pocket's corners is cut at the pocket's, up to 0.05 mm further out or
-     in, so its sizes are read back through that (head.fitsCut), which goes by the room
-     alone: the cap does not move with the head typed. */
+     as the shank's, so it is the bores of this design that are measured, and a head that
+     turns can be given another cap, and other sizes refused beside a joint's cut, than a
+     head that does not (MOUNT_BORE). A counterbore within MOUNT_BORE.head.snap of the
+     magnet pocket's corners is cut at the pocket's, up to 0.05 mm further out or in, so
+     its sizes are read back through that (head.fitsCut), which goes by the room alone:
+     the band does not move the cap with the head typed. */
   const magnetR = cfg.magnets ? MOUNT_BORE.magnet.r(cfg.magnetD) : 0;
   const BORE = { magnetD: MOUNT_BORE.magnet, screwHoleD: MOUNT_BORE.hole,
                  screwHeadD: { sides: MOUNT_BORE.head.sides, fits: (room) => MOUNT_BORE.head.fitsCut(room, magnetR) } };
diff --git a/index.html b/index.html
index 4f64eb6..99ae0f8 100644
--- a/index.html
+++ b/index.html
@@ -2346,47 +2346,54 @@ <h2 id="drawersTitle">Your drawers</h2>
  * folded the default plate 160, 120, 128 and 96 times a piece 1.5 deep and a cell 14
  * times 1 deep, and 2 times from beneath 3 deep; the head at its cap folded the same way
  * at 40, 43, 44 and 46 mm, each with the one magnet that puts its corner there. Main, its
- * corners on the size, has the same at 13.95 mm. So where a corner of either comes
- * within 0.005 mm of a plane of the other, the counterbore is turned half a facet, π/14,
- * about its axis (head.turn): its corners stand midway between the pocket's, each
- * 0.18 mm or more off the other's flats under a magnet of 3 mm or more, and the shank's
- * turn and mountLimits go by it turned. Its flats stand as far from the axis as before,
- * so the head fits as typed and the caps stay where they were. Turned less, the corners
- * stay near each other: π/252 left them 0.007 mm off the flats and built a cell closed,
- * but the counterbore's roof is fanned from its axis to its corners, and those rays
- * passed 0.04 mm from the pocket's corners. Where the BSP carried a socket's sloped
- * facet across there, the roof split into slivers 0.01 mm long with no width, which
- * single precision in the STL turned into folds: 48, 36, 36 and 27 on the default
- * plate's four pieces, at sites away from the origin, and none on one cell, where fewer
- * planes split the roof. π/126 left 2 edges open under a 6.47 x 2 magnet with the
- * 14.6 mm head at its cap at 43 mm, π/56 and π/28 folded a 4.844 head in a 6 x 3 pocket
- * from beneath at 42 mm, and π/84 opened 5 of the 600 designs below and 14 of the 900
- * after them; π/14 builds them all closed, as it does the 13.582 head 0.251 deep under a
- * 6 x 3 magnet from above at 42 mm that π/252 left with 12 edges open a cell. On 600
- * designs drawn at random with a head within 0.012 mm of a size that puts a corner of
- * either on a plane of the other (34 to 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3
- * in four, two pieces with dovetails or jigsaws, 2 x 2 on corner bosses; magnets of 3 to
- * 13 mm, either way up), of the 354 taken 138 were open, folded or had a face turned
- * over before, counting the folds in the STL and leaving out the edges where corner
- * bosses meet, and 7 now, where π/252 left 10 and main 23 of its 356. Two that built
- * closed before do not now, and main builds them closed: an 8.798 head 0.592 deep under
- * a 7.037 x 2.5 magnet from above at 42 mm, where a sloped plane meets a flat of the
- * counterbore half a micron under its roof and each cell has an edge shared four ways
- * and two folds, and 7.958 under a 6.35 x 2 magnet from above at 50.38 mm, 11 folds in
- * the STL. On 900 more drawn the same way on one cell, the test tile, 2 x 2, corner
- * bosses and two pieces, of the 544 taken 183 before and 10 now, where π/252 left 22 and
- * main 22 of its 549; two are new, folds in the STL only, 6 on a 38.41 mm dovetail under
- * an 8.704 x 3 magnet from beneath and 1 on a 42 mm test tile under a 12.954 x 1.5
- * magnet, where π/252 opened 8. With the head at its cap, every 1 mm of pitch from 34 to
- * 56, 1, 1.5 and 2.5 deep, 2 x 2 in one piece and 3 x 2 in two, under each magnet to the
- * hundredth that puts a corner of the counterbore on a flat's plane, of the 108 taken
- * from above 36 were open or folded before and none now (π/252 left 1, main 14), and of
- * the 186 from beneath 53 before and 4 now, a fold or two each in the STL at 38 mm
- * 2.5 deep that π/252 and main build closed (π/252 left 3 others, main 16). On one cell,
- * every 0.5 mm of pitch, of the 216 taken from above 40 before and none now (π/252 none,
- * main 27), and of the 360 from beneath 67 before and 2 now, 2 folds in the STL at
- * 37.5 mm under a 7.36 x 2 magnet 1 and 1.5 deep that π/252 and main build closed (π/252
- * left 3, main 24).
+ * corners on the size, has the same at 13.95 mm. Each of these is a fold as the audits
+ * count one (test/orientation.js): two faces with area back to back in the mesh. So
+ * where a corner of either comes within 0.01 mm of a plane of the other, the counterbore
+ * is turned half a facet, π/14, about its axis (head.turn): its corners stand midway
+ * between the pocket's, each 0.18 mm or more off the other's flats under a magnet of
+ * 3 mm or more, and the shank's turn and mountLimits go by it turned. Its flats stand as
+ * far from the axis as before, so the head fits as typed. The limits are measured on
+ * the bore as cut, turned where it is turned, so a head that turns can be given another
+ * cap, and other sizes refused beside a joint's cut, than a head that does not: of 1,034
+ * designs drawn with a head near a size that turns, the turn moved the limits of 302,
+ * the head's cap by up to 0.4 mm up or 0.3 down, each size held to the bore it cuts.
+ * Measured both ways and the tighter kept, the limits would not move with the
+ * head typed, but they would come down for every head: of 140 page designs at five
+ * pitches, 28 lose 0.1 to 0.3 mm of the head's cap that way (8.1 to 7.9 on a 2 x 2 at
+ * 42 mm with a jigsaw) and 12 dovetails gain a gap.
+ *
+ * Turned less, the corners stay near each other. π/252, with the turn taken from 0.01 mm
+ * as here, moved the limits of 102 of those 1,034 designs, by a tenth at most, but left
+ * open designs that π/14 builds closed: a 13.582 head 0.251 deep under a 6 x 3 magnet
+ * from above at 42 mm, 12 edges a cell; 2.69 over 1.41, 2 deep under a 6 x 1.5 magnet
+ * from beneath at 42 mm, tight, 3; 5.65 over 2.43, 3 deep under a 4.44 x 3 one, 12; and
+ * 13.26 over 1.06, 3 deep under a 5.85 x 1.5 one on 84 x 42, two shells touching along
+ * 8 edges. Its counterbore's roof, fanned from the axis to the corners, passed 0.04 mm
+ * from the pocket's corners, and where the BSP carried a socket's sloped facet across
+ * there the roof split into triangles with no area. The fold test leaves out a face
+ * with no area, as it should, but written to the STL in single precision such a
+ * triangle takes a direction, and read back the default plate's four pieces showed 48,
+ * 36, 36 and 27 folds. π/126 left 2 edges open and a face turned over under a 6.47 x 2
+ * magnet with the 14.6 mm head at its cap at 43 mm. On 600 designs drawn at random with
+ * a head within 0.012 mm of a size that puts a corner of either on a plane of the other
+ * (34 to 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3 in four, two pieces with
+ * dovetails or jigsaws, 2 x 2 on corner bosses; magnets of 3 to 13 mm, either way up),
+ * of the 354 taken 48 were open, folded or had a face turned over unturned, leaving out
+ * the edges where corner bosses meet, and 2 now, where π/252 left 1 and main 5 of its
+ * 356. One leaks on every one of them; the other, which π/252 and main build closed, is
+ * an 8.798 head 0.592 deep under a 7.037 x 2.5 magnet from above at 42 mm, where a
+ * sloped plane meets a flat of the counterbore half a micron under its roof and each
+ * cell has an edge shared four ways and two folds. On 900 more drawn the same way on one
+ * cell, the test tile, 2 x 2, corner bosses and two pieces, each held to what the page
+ * takes, 56 of 498 were bad unturned and none of 496 now, where π/252 left 2 (the 13.582
+ * head among them) and main 2 of its 504. With the head
+ * at its cap, every 1 mm of pitch from 34 to 56, 1, 1.5 and 2.5 deep, 2 x 2 in one piece
+ * and 3 x 2 in two, under each magnet to the hundredth that puts a corner of the
+ * counterbore on a flat's plane, 18 of the 108 taken from above and 8 of the 186 from
+ * beneath were bad unturned, and none now or at π/252 (main 6 and 2); on one cell, every
+ * 0.5 mm of pitch, 28 of 216 and 14 of 360, and none now or at π/252 (main 21 and 8). In
+ * the STL read back, 15 of those designs show a fold here, 30 at π/252 and 114 on main,
+ * and here and at π/252 every one the mesh does not have is a triangle with no area.
  *
  * The shank is turned a little about its axis (`turn`, #74) where a corner of the
  * counterbore or of the magnet pocket would stand on one of its flats carried on past
@@ -2402,13 +2409,13 @@ <h2 id="drawersTitle">Your drawers</h2>
  * of head to shank. A corner meets a flat's plane at an odd multiple of 15/7° off the
  * flat's normal; turned π/84, 15/7°, it meets them at the even ones, so a size that put a
  * corner on a flat puts it midway between two. The turn is taken where a corner comes
- * nearer than 0.005 mm unturned and the turn leaves it further off, and a shank no corner
+ * nearer than 0.01 mm unturned and the turn leaves it further off, and a shank no corner
  * came near is cut as it was. The magnet pocket's corners stand on the same rays as the
  * counterbore's (or midway between them, where it is turned), and π/84 could bring one of
  * those onto a flat instead: 4.85 mm under
  * 7.246 with a 6 mm magnet from above left 35 edges in the socket floor at 49.02 mm, and
  * 5.773 under 12.053 25 at 55 mm, where the flats unturned miss them by 0.07 and 0.04. So
- * where π/84 leaves a corner of either nearer than 0.005 mm, the turn is the one of 24
+ * where π/84 leaves a corner of either nearer than 0.01 mm, the turn is the one of 24
  * steps across those 30/7° that keeps them furthest off. And a magnet's corner calls for
  * a turn as a counterbore's does, since a shank no counterbore corner comes near can have
  * a magnet's corner on a flat all the same: at 41.24 mm a 3 mm shank under a 7.3 mm
@@ -2435,12 +2442,18 @@ <h2 id="drawersTitle">Your drawers</h2>
  * and none within 0.0039 but under a magnet on a shank under 1.2 mm (magnets of 3 to 13
  * mm, shanks of 1 to 6.5, heads up to 2.4 times the shank, every 0.001 mm round the sizes
  * that put a corner on a flat, and 6.7 million sizes drawn at random round them); under
- * a bare pocket none comes within 0.005 (the same magnets every 0.01 mm, shanks every
+ * a bare pocket none comes within 0.017 (the same magnets every 0.01 mm, shanks every
  * 0.0005 mm within 0.012 of each size that puts a corner on a flat), and under a
- * counterbore turned off the pocket none within 0.003 (360,213 shanks drawn at random
+ * counterbore turned off the pocket none within 0.003 (900,452 shanks drawn at random
  * near a corner of either, under counterbores near the pocket's flats). The
  * nearest, 0.0033 mm at 1.0197 under 1.0748 with a 3.72 mm magnet, and nine more under
- * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. Half a facet, π/12,
+ * 0.0038 build closed at 42 and 49.02 mm, the magnet either way up. The turns were taken
+ * from 0.005 mm, and the sweeps below were measured so, until a 38.97 mm cell, a
+ * counterbore's corner 0.006 mm off a plane of the pocket's, folded 3 times unturned, and
+ * π/252 left a test tile open round a corner 0.00502 mm off a shank's flat. On 600 random
+ * designs whose turns 0.01 changes (one cell, the test tile, 2 x 2, corner bosses, two
+ * pieces), of the 511 the page takes one is open at either bound, by 6 edges where 0.005
+ * and main leave 3, and main leaves 4 open. Half a facet, π/12,
  * clears the corners as well, but it squares two flats to the cell's edges, and at 37.67
  * mm those folded the socket floor beside the pocket. Measured on 3,846 one-cell plates
  * with a magnet from above, 37.67 to 55 mm, shanks 1 to 5 mm and heads up to 1.15 times
@@ -2489,7 +2502,7 @@ <h2 id="drawersTitle">Your drawers</h2>
           snap: 0.05,
           /* how far to turn a counterbore cut headR out at its corners about its axis,
              beside a magnet pocket magnetR out at its corners: half a facet, π/14, where a
-             corner of either would stand within 0.005 mm of the plane of one of the other's
+             corner of either would stand within 0.01 mm of the plane of one of the other's
              flats, which puts the counterbore's corners midway between the pocket's, and not
              at all where they are cut as one prism (see above) */
           turn: (headR, magnetR) => {
@@ -2505,7 +2518,7 @@ <h2 id="drawersTitle">Your drawers</h2>
               return g;
             };
             const c0 = clear(0);
-            return c0 < 0.005 && clear(Math.PI / n) > c0 ? Math.PI / n : 0;
+            return c0 < 0.01 && clear(Math.PI / n) > c0 ? Math.PI / n : 0;
           } },
   hole: { sides: 12, r: (d) => d/2 / Math.cos(Math.PI/12),
           fits: (room) => 2 * room * Math.cos(Math.PI / 12),
@@ -2524,9 +2537,9 @@ <h2 id="drawersTitle">Your drawers</h2>
                 g = Math.min(g, Math.abs(R * Math.cos(2*Math.PI*k/head.sides + p - (2*m + 1)*Math.PI/hole.sides - t) - d/2));
               return g;
             };
-            if (clear(0) >= 0.005) return 0;
+            if (clear(0) >= 0.01) return 0;
             let best = Math.PI / 84, most = clear(best);
-            if (most < 0.005) for (let j = 1; j < 24; j++) {
+            if (most < 0.01) for (let j = 1; j < 24; j++) {
               const t = (Math.PI / 42) * j / 24, g = clear(t);
               if (g > most + 1e-9) { most = g; best = t; }
             }
@@ -4411,11 +4424,12 @@ <h2 id="drawersTitle">Your drawers</h2>
      corners stand out past it, and a magnet's 0.1 mm over its radius where that is
      further. The shank and the counterbore are turned where the cutter turns them, and
      measured so: their turns go by the sizes asked, the head's and the magnet's as well
-     as the shank's, so it is the bores of this design that are measured. A counterbore
-     within MOUNT_BORE.head.snap
-     of the magnet pocket's corners is cut at the pocket's, up to 0.05 mm further out or
-     in, so its sizes are read back through that (head.fitsCut), which goes by the room
-     alone: the cap does not move with the head typed. */
+     as the shank's, so it is the bores of this design that are measured, and a head that
+     turns can be given another cap, and other sizes refused beside a joint's cut, than a
+     head that does not (MOUNT_BORE). A counterbore within MOUNT_BORE.head.snap of the
+     magnet pocket's corners is cut at the pocket's, up to 0.05 mm further out or in, so
+     its sizes are read back through that (head.fitsCut), which goes by the room alone:
+     the band does not move the cap with the head typed. */
   const magnetR = cfg.magnets ? MOUNT_BORE.magnet.r(cfg.magnetD) : 0;
   const BORE = { magnetD: MOUNT_BORE.magnet, screwHoleD: MOUNT_BORE.hole,
                  screwHeadD: { sides: MOUNT_BORE.head.sides, fits: (room) => MOUNT_BORE.head.fitsCut(room, magnetR) } };
diff --git a/sw.js b/sw.js
index cc9f082..1a210ea 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "5e3cfbf56e58";
+const VERSION = "33bc596f698f";
 const FILES = [
   "./",
   "bins/",

From e1e542c3d7a3162ca96d4f787488c5866020b086 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 08:13:54 +0000
Subject: [PATCH 50/58] Say which of the five S-1 rows the bound closes and
 which pi/252 leaves open (a comment)

Only the 38.97 mm cell and the test tile have a corner between 0.005 and 0.01 mm
off a plane; the other three are turned at either bound, and pi/252 left them open
away from the corners.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 test/plate-audit.js | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

diff --git a/test/plate-audit.js b/test/plate-audit.js
index e901aee..7fa1013 100644
--- a/test/plate-audit.js
+++ b/test/plate-audit.js
@@ -2301,14 +2301,14 @@ console.log('\nthe other limits, built at their ends:');
      flats, left 12 edges open a cell, where unturned it left 6 and main none. The plates
      of several cells are here so that one cell cannot pass for them. Turned π/252, a
      13.582 head 0.251 deep under a 6 x 3 magnet from above left 12 edges open a cell, 48
-     over 2 x 2. The last five are where a corner comes between 0.005 and 0.01 mm of a
-     plane, and the turn is taken from 0.01 now (head.turn and hole.turn). Main builds each
-     closed. The 38.97 mm cell, a corner 0.006 mm off a plane, folded 3 times unturned with
-     the turn from 0.005; on the tile π/252 left a counterbore's corner 0.00502 mm off a
-     shank's flat, the shank unturned, and 15 edges open; and π/252 left the other three
-     open by 3 and 12 edges and two shells touching along 8, split elsewhere by its
-     planes, from 0.01 as well.
-     Each is a size the page takes, and has to build closed, with no folds. */
+     over 2 x 2. The last five were found among designs drawn near the bound a turn is
+     taken from, 0.01 mm now (head.turn and hole.turn), and main builds each closed. The
+     38.97 mm cell, a corner 0.006 mm off a plane, folded 3 times unturned with the bound
+     at 0.005; on the tile π/252 left a counterbore's corner 0.00502 mm off a shank's flat,
+     the shank unturned, and 15 edges open; and the other three, turned at either bound,
+     π/252 left open by 3 and 12 edges and with two shells touching along 8, split by its
+     planes away from the corners. Each is a size the page takes, and has to build
+     closed, with no folds. */
   for (const [nm, o, tile] of [
     ['13.6 head, 6 x 2 above, 42, 1.5 deep', { magnetSide: 'top', screwHeadD: 13.6, screwHeadDepth: 1.5 }],
     ['13.6 head, 6 x 2 above, 42, 1 deep', { magnetSide: 'top', screwHeadD: 13.6, screwHeadDepth: 1 }],

From 9b9f7652f4c478e7874ea9c44ae2514f6d6e17b1 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 09:04:40 +0000
Subject: [PATCH 51/58] Read the screw head again on its own limits once the
 magnet is read, then the shank on the head as held

readControls read the head against limits measured with the head before it, and a
counterbore that turns off the magnet pocket's flats is measured turned, so its cap and
gaps go by the head's own size. A 14.05 mm head pasted over a 6 at 46.45 mm with a jigsaw
and a 6.2 mm magnet from beneath took the 6's 14.1 cap and built with Download on, and 14.1
pasted over a 14 was held to the 14's cap at every read after. The head is now measured as
typed and read again; the shank is read last, measured again on the head where the head
was held to its cap or a gap's end. Two page tests: the first fails on e1e542c, the second
fails without the second measure.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 src/ui.js                         | 23 ++++++++---
 test/ui/plates-robustness.spec.js | 66 +++++++++++++++++++++++++++++++
 2 files changed, 84 insertions(+), 5 deletions(-)

diff --git a/src/ui.js b/src/ui.js
index 5e9a85a..5e066d9 100644
--- a/src/ui.js
+++ b/src/ui.js
@@ -394,12 +394,25 @@ function readControls() {
     if (id === 'magnetD' && mountNow) mountNow = mountLimits(state, mountLayout, mountNow.cuts);
     state[id] = readNumber(id);
   }
-  /* And the shank once more, on the sizes just read: how far it is turned goes by the head
-     and the magnet (MOUNT_BORE.screw), and the magnet pocket it runs through caps it
-     (mountLimits' throughMagnet), both read after it. Read before them only, a 5 mm hole
-     stood under a 5.1 mm magnet typed in after it, refused only at the next keystroke. */
+  /* And the head and the shank once more, on the sizes just read. How far the counterbore is
+     turned goes by the head and the magnet (MOUNT_BORE.screw), and it is measured turned, so
+     the head's own size moves its cap and gaps: read against the head before it, a 14.05 mm
+     head pasted over a 6 at 46.45 mm with a jigsaw and a 6.2 mm magnet from beneath took the
+     6's 14.1 and built, where its own turn stops it at 14, and 14.1 over a 14 was held to
+     the 14's cap at every read after. So the head is measured as typed. The shank's turn
+     goes by the head's, and the magnet pocket it runs through caps it (mountLimits'
+     throughMagnet), so it is read last, on the head as read, measured again where that is
+     not the head typed: one held to its cap or a gap's end. Under an 8.3 mm head held to 7.9
+     at 41.86 mm with a jigsaw, loose, a 7.8 mm hole measured on the 8.3 would be turned and
+     refused. Read before them only, a 5 mm hole stood under a 5.1 mm magnet typed in after
+     it, refused only at the next keystroke. */
   if (state.screws && mountNow) {
-    mountNow = mountLimits(state, mountLayout, mountNow.cuts);
+    const typed = parseFloat($('screwHeadD').value.trim());
+    mountNow = mountLimits(isFinite(typed) ? { ...state, screwHeadD: typed } : state,
+                           mountLayout, mountNow.cuts);
+    fieldErrors.delete('screwHeadD'); noRoom.delete('screwHeadD');
+    state.screwHeadD = readNumber('screwHeadD');
+    if (state.screwHeadD !== typed) mountNow = mountLimits(state, mountLayout, mountNow.cuts);
     fieldErrors.delete('screwHoleD'); noRoom.delete('screwHoleD');
     state.screwHoleD = readNumber('screwHoleD');
   }
diff --git a/test/ui/plates-robustness.spec.js b/test/ui/plates-robustness.spec.js
index 439f11f..a33d045 100644
--- a/test/ui/plates-robustness.spec.js
+++ b/test/ui/plates-robustness.spec.js
@@ -224,6 +224,72 @@ test.describe('ranges on the geometry fields', () => {
     expect(errors).toEqual([]);
   });
 
+  // one input event and no change, as a paste is
+  const paste = (page, id, value) => page.evaluate(({ id, value }) => {
+    const e = document.getElementById(id);
+    e.value = value;
+    e.dispatchEvent(new Event('input', { bubbles: true }));
+  }, { id, value });
+  const settled = (page) => page.waitForFunction((re) => new RegExp(re).test(
+    document.getElementById('pieceTail').textContent), SETTLED.source, { timeout: 30000 });
+
+  /* #81: a counterbore that turns off the magnet pocket's flats is measured turned, so the
+     head's cap goes by the head typed, and the head is read again on its own (readControls).
+     At 46.45 mm with a jigsaw and a 6.2 mm magnet from beneath, a 14.05 mm head turns and
+     stops at 14, where the 6 before it goes to 14.1. Pasted in, it was read against the 6's
+     cap and built with Download on; and 14.1 pasted over a 14, which turns, was held to the
+     14's cap and refused, at every read after as well. */
+  test('a screw head is held to its own cap, not the one of the head before it', async ({ page }) => {
+    const errors = await openAt(page, '#pi=46.45&w=92.9&d=92.9&mm=custom&ml=0&mr=0&mf=0&mb=0&bw=58.45&bd=256' +
+                                      '&cn=puzzle&mg=1&md=6.2&mh=2.4&ms=bottom&sc=1&sd=6');
+    const max = () => page.evaluate(() => document.getElementById('screwHeadD').max);
+    const refused = /Screw head Ø must be 14 mm or less at a 46\.45 mm pitch — .* a hole has to stay out of the notches the puzzle tabs fit into\./;
+    expect(await max()).toBe('14.1');
+    expect(await exportOff(page)).toBe(false);
+    await paste(page, 'screwHeadD', '14.05');
+    await page.waitForTimeout(250);
+    expect(await max()).toBe('14');
+    expect(await text(page, 'errScrew')).toMatch(refused);
+    expect(await text(page, 'warnings'), 'the checks under the map say the same thing').toMatch(refused);
+    expect(await text(page, 'pieceTail')).toMatch(/not building/);
+    expect(await exportOff(page)).toBe(true);
+    await H.setField(page, 'screwHeadD', '14');
+    await settled(page);
+    expect(await shown(page, 'errScrew')).toBe(false);
+    expect(await exportOff(page)).toBe(false);
+    await paste(page, 'screwHeadD', '14.1');
+    await page.waitForTimeout(250);
+    await settled(page);
+    expect(await max()).toBe('14.1');
+    expect(await shown(page, 'errScrew')).toBe(false);
+    expect(await text(page, 'warnings')).not.toMatch(/Screw head Ø/);
+    expect(await page.evaluate(() => state.screwHeadD)).toBe(14.1);
+    expect(await text(page, 'pieceTail')).toMatch(/ready/);
+    expect(await exportOff(page)).toBe(false);
+    expect(errors).toEqual([]);
+  });
+
+  /* And the shank after it, measured on the head as held. At 41.86 mm with a jigsaw, loose,
+     a 7.8 mm hole is turned a little under an 8.3 mm head's corners (MOUNT_BORE.hole.turn),
+     which stops it at 7.7, and not at all under the 7.9 mm the head is held to, which takes
+     it. Pasted at 8.3, the head is refused and the hole is not. */
+  test('a screw hole is measured under the head as held, not as typed', async ({ page }) => {
+    const errors = await openAt(page, '#pi=41.86&w=83.72&d=83.72&mm=custom&ml=0&mr=0&mf=0&mb=0&bw=53.86&bd=256' +
+                                      '&cn=puzzle&to=loose&sc=1&sh=7.8&sd=6');
+    const max = () => page.evaluate(() => document.getElementById('screwHoleD').max);
+    expect(await max()).toBe('7.8');
+    expect(await exportOff(page)).toBe(false);
+    await paste(page, 'screwHeadD', '8.3');
+    await page.waitForTimeout(250);
+    expect(await text(page, 'errScrew')).toMatch(/Screw head Ø must be 7\.9 mm or less at a 41\.86 mm pitch/);
+    expect(await text(page, 'errScrew')).not.toMatch(/Screw hole Ø/);
+    expect(await text(page, 'warnings')).not.toMatch(/Screw hole Ø/);
+    expect(await max()).toBe('7.8');
+    expect(await page.evaluate(() => [state.screwHeadD, state.screwHoleD])).toEqual([7.9, 7.8]);
+    expect(await exportOff(page)).toBe(true);
+    expect(errors).toEqual([]);
+  });
+
   /* #70: corner pockets over a floor. A bowtie housed in the floor stood its 2.8 mm floor
      round the 2.6 mm bosses and sealed their pockets in it, with Download on, and an extra
      floor did the same. Such a plate is built as a solid floor builds it now, and Checks

From 100f9f12ba8f94544ae1f58f890a7c7cd44a30c1 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 09:04:40 +0000
Subject: [PATCH 52/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 index.html | 23 ++++++++++++++++++-----
 sw.js      |  2 +-
 2 files changed, 19 insertions(+), 6 deletions(-)

diff --git a/index.html b/index.html
index 99ae0f8..fe8dd01 100644
--- a/index.html
+++ b/index.html
@@ -8670,12 +8670,25 @@ <h2 id="drawersTitle">Your drawers</h2>
     if (id === 'magnetD' && mountNow) mountNow = mountLimits(state, mountLayout, mountNow.cuts);
     state[id] = readNumber(id);
   }
-  /* And the shank once more, on the sizes just read: how far it is turned goes by the head
-     and the magnet (MOUNT_BORE.screw), and the magnet pocket it runs through caps it
-     (mountLimits' throughMagnet), both read after it. Read before them only, a 5 mm hole
-     stood under a 5.1 mm magnet typed in after it, refused only at the next keystroke. */
+  /* And the head and the shank once more, on the sizes just read. How far the counterbore is
+     turned goes by the head and the magnet (MOUNT_BORE.screw), and it is measured turned, so
+     the head's own size moves its cap and gaps: read against the head before it, a 14.05 mm
+     head pasted over a 6 at 46.45 mm with a jigsaw and a 6.2 mm magnet from beneath took the
+     6's 14.1 and built, where its own turn stops it at 14, and 14.1 over a 14 was held to
+     the 14's cap at every read after. So the head is measured as typed. The shank's turn
+     goes by the head's, and the magnet pocket it runs through caps it (mountLimits'
+     throughMagnet), so it is read last, on the head as read, measured again where that is
+     not the head typed: one held to its cap or a gap's end. Under an 8.3 mm head held to 7.9
+     at 41.86 mm with a jigsaw, loose, a 7.8 mm hole measured on the 8.3 would be turned and
+     refused. Read before them only, a 5 mm hole stood under a 5.1 mm magnet typed in after
+     it, refused only at the next keystroke. */
   if (state.screws && mountNow) {
-    mountNow = mountLimits(state, mountLayout, mountNow.cuts);
+    const typed = parseFloat($('screwHeadD').value.trim());
+    mountNow = mountLimits(isFinite(typed) ? { ...state, screwHeadD: typed } : state,
+                           mountLayout, mountNow.cuts);
+    fieldErrors.delete('screwHeadD'); noRoom.delete('screwHeadD');
+    state.screwHeadD = readNumber('screwHeadD');
+    if (state.screwHeadD !== typed) mountNow = mountLimits(state, mountLayout, mountNow.cuts);
     fieldErrors.delete('screwHoleD'); noRoom.delete('screwHoleD');
     state.screwHoleD = readNumber('screwHoleD');
   }
diff --git a/sw.js b/sw.js
index 1a210ea..b052e12 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "33bc596f698f";
+const VERSION = "1bce63f18b29";
 const FILES = [
   "./",
   "bins/",

From 7f2e5bea9b34cdde893d2e41fceaad9e180e424b Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 11:27:56 +0000
Subject: [PATCH 53/58] Cut a screwed cell's pockets again when the first cut
 comes out with a face turned over

Turned half a facet off the magnet pocket, two of a counterbore's flats can
stand square to the cell's x edges, and the BSP split one into a strip 3.3
microns wide that came out folded: a 3.89 mm head 1 deep over a 1.01 mm shank
under a 3 x 2 magnet from above folded 3 times a cell at 45.16 mm with a
dovetail and at 44 mm on one cell, where main builds both closed. With screws,
the fastener cut in buildPiece now tries again on such a cell as it does on
open edges, and keeps the first try that is closed with nothing turned over;
the cutters turned a 28th more close both.

Over 2,366 designs with screws drawn round the counterbore's turn, 49 were
cut again, 47 came out other bytes, 4 that folded build closed (the 8.798 head
MOUNT_BORE named among them), none came out worse, and building them all took
1.5% longer. Without screws nothing is cut again for it: 500 random designs
build the same bytes as main 326cc48. The plate audit has rows for both.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 docs/ENGINE.md      | 11 ++++++++++-
 src/core.js         | 34 +++++++++++++++++++++++++---------
 test/plate-audit.js | 12 ++++++++++--
 3 files changed, 45 insertions(+), 12 deletions(-)

diff --git a/docs/ENGINE.md b/docs/ENGINE.md
index 136d951..6e4799a 100644
--- a/docs/ENGINE.md
+++ b/docs/ENGINE.md
@@ -881,7 +881,16 @@ currently installed):
   designs with a solid floor, the first three tries left 6 open and all of them leave
   4, none worse. A try that throws (the turned cutters there reach `healCsgSeams`'
   T-junction pass limit) is passed over and the first cut stands, where it used to fail
-  the whole build. The socket floor is a fan too, from the cell's centre, and a pocket
+  the whole build. With screws, a cell whose pockets come out closed but with a face the
+  repair left turned over (`.turned`) is cut again the same ways, and kept on the first
+  try that is closed with nothing turned over: turned half a facet off the magnet pocket,
+  two of a counterbore's flats can stand square to the cell's x edges, and a 3.89 mm head
+  1 deep over a 1.01 mm shank under a 3 × 2 magnet from above folded 3 times a cell at
+  45.16 mm with a dovetail and at 44 mm on one cell, where main builds both closed; the
+  turned cutters close it. Over 2,366 designs with screws drawn round the counterbore's
+  turn, 49 were cut again for it, 4 that folded build closed, none came out worse, and
+  building took 1.5% longer. Without screws nothing is cut again for it, so those designs
+  keep main's bytes. The socket floor is a fan too, from the cell's centre, and a pocket
   from above or a screw's shank stands on it: an 11.1 mm magnet from above at 48.55 mm has
   a pocket corner 4.7 microns from one of its spokes, by `fanCentre`'s measure, and loses
   the sliver there, six open edges in every cell that no try closed. How near is not what
diff --git a/src/core.js b/src/core.js
index c899f78..f2db7f7 100644
--- a/src/core.js
+++ b/src/core.js
@@ -985,11 +985,12 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * (34 to 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3 in four, two pieces with
  * dovetails or jigsaws, 2 x 2 on corner bosses; magnets of 3 to 13 mm, either way up),
  * of the 354 taken 48 were open, folded or had a face turned over unturned, leaving out
- * the edges where corner bosses meet, and 2 now, where π/252 left 1 and main 5 of its
- * 356. One leaks on every one of them; the other, which π/252 and main build closed, is
- * an 8.798 head 0.592 deep under a 7.037 x 2.5 magnet from above at 42 mm, where a
- * sloped plane meets a flat of the counterbore half a micron under its roof and each
- * cell has an edge shared four ways and two folds. On 900 more drawn the same way on one
+ * the edges where corner bosses meet, and 1 now, where π/252 left 1 and main 5 of its
+ * 356; it leaks on every one of them. An 8.798 head 0.592 deep under a 7.037 x 2.5
+ * magnet from above at 42 mm, where a sloped plane meets a flat of the counterbore half a
+ * micron under its roof, had an edge shared four ways and two folds a cell, which
+ * π/252 and main build closed, until a cell whose pockets come out with a face turned
+ * over was cut again (the fastener cut in buildPiece). On 900 more drawn the same way on one
  * cell, the test tile, 2 x 2, corner bosses and two pieces, each held to what the page
  * takes, 56 of 498 were bad unturned and none of 496 now, where π/252 left 2 (the 13.582
  * head among them) and main 2 of its 504. With the head
@@ -998,7 +999,7 @@ function cylinder(cx, cy, r, z0, z1, seg) {
  * counterbore on a flat's plane, 18 of the 108 taken from above and 8 of the 186 from
  * beneath were bad unturned, and none now or at π/252 (main 6 and 2); on one cell, every
  * 0.5 mm of pitch, 28 of 216 and 14 of 360, and none now or at π/252 (main 21 and 8). In
- * the STL read back, 15 of those designs show a fold here, 30 at π/252 and 114 on main,
+ * the STL read back, 14 of those designs show a fold here, 30 at π/252 and 114 on main,
  * and here and at π/252 every one the mesh does not have is a triangle with no area.
  *
  * The shank is turned a little about its axis (`turn`, #74) where a corner of the
@@ -4093,8 +4094,23 @@ function buildPiece(cfg, layout, piece, onStatus) {
            closed each of those already, so that try is not taken. The nudges and the one
            site at a time came after: of 687 random page designs with a solid floor, the
            three tries left 6 open and these leave 4, none worse; and from 50 to 60 mm,
-           magnets and screws from 15 mm up, they closed six of the nine left open. */
-        if (next.open && next.open <= 24) {
+           magnets and screws from 15 mm up, they closed six of the nine left open.
+
+           With screws, a cell that comes out closed but with a face the repair left turned
+           over (healCsgSeams' `turned`) is cut again the same ways too, and the first try
+           that is closed with nothing turned over is kept. Turned half a facet off the
+           magnet pocket (MOUNT_BORE.head.turn), two of a counterbore's flats can stand
+           square to the cell's x edges, and the BSP split one into a strip 3.3 microns
+           wide that came out folded back: a 3.89 mm head 1 deep over a 1.01 mm shank under
+           a 3 x 2 magnet from above folded 3 times a cell at 45.16 mm with a dovetail and
+           at 44 mm on one cell, where main builds both closed. The cutters turned a 28th
+           more close it. Over 2,366 designs with screws drawn round the counterbore's turn,
+           49 were cut again for it, 47 came out other bytes, 4 that folded build closed
+           (the 8.798 head MOUNT_BORE names among them), none came out worse, and building
+           them all took 1.5% longer. Without screws nothing is cut again for it, and those
+           designs build main's bytes, as they did. */
+        const folded = cfg.screws && !next.open && next.turned;
+        if (next.open && next.open <= 24 || folded) {
           const n4 = cut.length / 4;   // fasteners() lays the four sites' cutters one after another
           const tries = [() => csgSubtract(region, cut.slice().reverse()),
                          () => csgSubtract(region.slice().reverse(), cut),
@@ -4105,7 +4121,7 @@ function buildPiece(cfg, layout, piece, onStatus) {
           for (const t of tries) {
             let again;
             try { again = t(); } catch (e) { continue; }   // the first cut stands
-            if (!again.open) { next = again; break; }
+            if (!again.open && !(folded && again.turned)) { next = again; break; }
           }
         }
         return next;
diff --git a/test/plate-audit.js b/test/plate-audit.js
index 7fa1013..0ec929e 100644
--- a/test/plate-audit.js
+++ b/test/plate-audit.js
@@ -2307,8 +2307,12 @@ console.log('\nthe other limits, built at their ends:');
      at 0.005; on the tile π/252 left a counterbore's corner 0.00502 mm off a shank's flat,
      the shank unturned, and 15 edges open; and the other three, turned at either bound,
      π/252 left open by 3 and 12 edges and with two shells touching along 8, split by its
-     planes away from the corners. Each is a size the page takes, and has to build
-     closed, with no folds. */
+     planes away from the corners. The last two are a counterbore turned half a facet
+     whose two flats stand square to the cell's x edges: the BSP split one into a strip
+     3.3 microns wide that came out folded, 3 times a cell at 45.16 mm with a dovetail and
+     at 44 mm on one cell, where main builds both closed, until a cell whose pockets come
+     out with a face turned over was cut again (the fastener cut in buildPiece). Each is a
+     size the page takes, and has to build closed, with no folds. */
   for (const [nm, o, tile] of [
     ['13.6 head, 6 x 2 above, 42, 1.5 deep', { magnetSide: 'top', screwHeadD: 13.6, screwHeadDepth: 1.5 }],
     ['13.6 head, 6 x 2 above, 42, 1 deep', { magnetSide: 'top', screwHeadD: 13.6, screwHeadDepth: 1 }],
@@ -2343,6 +2347,10 @@ console.log('\nthe other limits, built at their ends:');
       screwHoleD: 1.06, screwHeadD: 13.26, screwHeadDepth: 3 }],
     ['5.65 head, 4.44 x 3 below, 42', { magnetD: 4.44, magnetH: 3, screwHoleD: 2.43, screwHeadD: 5.65,
       screwHeadDepth: 3 }],
+    ['3.89 head, 3 x 2 above, 45.16, dovetail', { pitch: 45.16, drawerW: 90.32, drawerD: 45.16, bedW: 57.16,
+      connector: 'dovetail', magnetD: 3, magnetSide: 'top', screwHoleD: 1.01, screwHeadD: 3.89, screwHeadDepth: 1 }],
+    ['3.89 head, 3 x 2 above, 44', { pitch: 44, drawerW: 44, drawerD: 44, magnetD: 3, magnetSide: 'top',
+      screwHoleD: 1.01, screwHeadD: 3.89, screwHeadDepth: 1 }],
   ]) {
     const at = { pitch: 42, drawerW: 42, drawerD: 42, connector: 'none', magnets: true, screws: true, ...o };
     const cfg = designCfg(at), lim = G.mountLimits(cfg, G.computeLayout(cfg));

From 75f45e8e1ea55c652f64754f4de849a475204896 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 11:27:56 +0000
Subject: [PATCH 54/58] Hold the screw head on its own limits until it holds,
 and name that size

An 8.86 mm head at 42 mm with snap clips in the floor and a 3.85 mm magnet
from beneath turns and stops at 7.8, but 7.8 does not turn and stops at 7.6:
the page named 7.8 and then refused it. readControls now measures a held head
again and holds it again on its own limits until they take it, at most four
passes (of 3,124 heads pasted over 781 random designs, 1,286 were held once
and 33 twice, none more), and reads the shank on the head as finally held.
A page test opens that design and checks the page names 7.6.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 src/ui.js                         | 38 ++++++++++++++++++++-----------
 test/ui/plates-robustness.spec.js | 25 ++++++++++++++++++++
 2 files changed, 50 insertions(+), 13 deletions(-)

diff --git a/src/ui.js b/src/ui.js
index 5e066d9..725deec 100644
--- a/src/ui.js
+++ b/src/ui.js
@@ -244,10 +244,11 @@ const halfCellMm = () => Math.ceil(state.pitch / 2 * 100 - 1e-6) / 100;
 const LENGTH_IDS = ['drawerW', 'drawerD', 'mLeft', 'mRight', 'mFront', 'mBack'];
 let unit = 'mm';   // what the length fields are showing; the saved choice is applied at boot
 
-function readNumber(id) {
+// `held`, a size read in place of the field's: the screw head as readControls holds it
+function readNumber(id, held) {
   const lim = LIMITS[id];
   const len = LENGTH_IDS.includes(id);
-  const v = len ? FIELDS.lengthOf($(id), unit) : parseFloat($(id).value.trim());
+  const v = held !== undefined ? held : len ? FIELDS.lengthOf($(id), unit) : parseFloat($(id).value.trim());
   if (!lim) return isFinite(v) ? v : 0;
   /* Out of play, a field keeps its fixed range but not the one the rest of the design
      sets, and does not complain: magnets off at a 30 mm pitch should not quietly shrink
@@ -399,20 +400,31 @@ function readControls() {
      the head's own size moves its cap and gaps: read against the head before it, a 14.05 mm
      head pasted over a 6 at 46.45 mm with a jigsaw and a 6.2 mm magnet from beneath took the
      6's 14.1 and built, where its own turn stops it at 14, and 14.1 over a 14 was held to
-     the 14's cap at every read after. So the head is measured as typed. The shank's turn
-     goes by the head's, and the magnet pocket it runs through caps it (mountLimits'
-     throughMagnet), so it is read last, on the head as read, measured again where that is
-     not the head typed: one held to its cap or a gap's end. Under an 8.3 mm head held to 7.9
-     at 41.86 mm with a jigsaw, loose, a 7.8 mm hole measured on the 8.3 would be turned and
-     refused. Read before them only, a 5 mm hole stood under a 5.1 mm magnet typed in after
-     it, refused only at the next keystroke. */
+     the 14's cap at every read after. So the head is measured as typed, and one held to its
+     cap or a gap's end is another head, measured again and held again on its own until it
+     holds: an 8.86 mm head at 42 mm with snap clips in the floor and a 3.85 mm magnet from
+     beneath turns and stops at 7.8, but 7.8 does not turn and stops at 7.6, and the page
+     named 7.8 and then refused it. Each pass holds it lower, to a tenth or a gap's end: of
+     3,124 heads pasted over 781 random designs on the page, 1,286 were held once and 33
+     twice, none more, and four passes are allowed. The shank's turn goes by the head's,
+     and the magnet pocket it runs through caps it (mountLimits' throughMagnet), so it is
+     read last, on the head as held: under an 8.3 mm head held to 7.9 at 41.86 mm with a
+     jigsaw, loose, a 7.8 mm hole measured on the 8.3 would be turned and refused. Read
+     before them only, a 5 mm hole stood under a 5.1 mm magnet typed in after it, refused
+     only at the next keystroke. */
   if (state.screws && mountNow) {
     const typed = parseFloat($('screwHeadD').value.trim());
-    mountNow = mountLimits(isFinite(typed) ? { ...state, screwHeadD: typed } : state,
-                           mountLayout, mountNow.cuts);
+    let on = isFinite(typed) ? typed : state.screwHeadD;
     fieldErrors.delete('screwHeadD'); noRoom.delete('screwHeadD');
-    state.screwHeadD = readNumber('screwHeadD');
-    if (state.screwHeadD !== typed) mountNow = mountLimits(state, mountLayout, mountNow.cuts);
+    for (let pass = 0; ; pass++) {
+      mountNow = mountLimits({ ...state, screwHeadD: on }, mountLayout, mountNow.cuts);
+      // a head held already that its own limits take keeps the reason it was held for
+      if (pass && on <= mountNow.screwHeadD && !mountNow.gaps.screwHeadD.some(([a, b]) => on > a && on < b)) break;
+      state.screwHeadD = readNumber('screwHeadD', pass ? on : undefined);
+      if (state.screwHeadD === on || pass === 3) break;
+      on = state.screwHeadD;
+    }
+    if (state.screwHeadD !== on) mountNow = mountLimits(state, mountLayout, mountNow.cuts);
     fieldErrors.delete('screwHoleD'); noRoom.delete('screwHoleD');
     state.screwHoleD = readNumber('screwHoleD');
   }
diff --git a/test/ui/plates-robustness.spec.js b/test/ui/plates-robustness.spec.js
index a33d045..8ebcefb 100644
--- a/test/ui/plates-robustness.spec.js
+++ b/test/ui/plates-robustness.spec.js
@@ -290,6 +290,31 @@ test.describe('ranges on the geometry fields', () => {
     expect(errors).toEqual([]);
   });
 
+  /* A head held to its cap is held again on its own limits until it holds, and the page
+     names that size. At 42 mm with snap clips in the floor and a 3.85 mm magnet from
+     beneath, an 8.86 mm head turns and stops at 7.8, but 7.8 does not turn and stops at 7.6:
+     the page said 7.8, and then refused 7.8 for 7.6. */
+  test('a screw head held to its cap is named where it holds', async ({ page }) => {
+    const at = '#pi=42&w=84&d=84&mm=custom&ml=0&mr=0&mf=0&mb=0&bw=54&bd=400&cn=snap&km=floor&ki=bottom' +
+               '&mg=1&md=3.85&mh=3&ms=bottom&sc=1&sh=2.64&se=2.5';
+    const errors = await openAt(page, `${at}&sd=8.86`);
+    const max = () => page.evaluate(() => document.getElementById('screwHeadD').max);
+    const refused = /Screw head Ø must be 7\.6 mm or less at a 42 mm pitch — .* a hole has to stay out of the recesses the snap clips fit into/;
+    expect(await text(page, 'errScrew')).toMatch(refused);
+    expect(await text(page, 'warnings'), 'the checks under the map say the same thing').toMatch(refused);
+    expect(await max()).toBe('7.6');
+    expect(await page.evaluate(() => state.screwHeadD)).toBe(7.6);
+    expect(await exportOff(page)).toBe(true);
+    await H.setField(page, 'screwHeadD', '7.8');
+    expect(await text(page, 'errScrew')).toMatch(refused);
+    await H.setField(page, 'screwHeadD', '7.6');
+    await page.waitForFunction(() => /ready/.test(document.getElementById('pieceTail').textContent),
+                               null, { timeout: 30000 });
+    expect(await shown(page, 'errScrew')).toBe(false);
+    expect(await exportOff(page)).toBe(false);
+    expect(errors).toEqual([]);
+  });
+
   /* #70: corner pockets over a floor. A bowtie housed in the floor stood its 2.8 mm floor
      round the 2.6 mm bosses and sealed their pockets in it, with Download on, and an extra
      floor did the same. Such a plate is built as a solid floor builds it now, and Checks

From c72fdd99a2d752c728b82ce1f29883cabd07232a Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 11:27:56 +0000
Subject: [PATCH 55/58] Rebuild the pages

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html | 34 ++++++++++++++++-------
 index.html      | 72 ++++++++++++++++++++++++++++++++++---------------
 sw.js           |  2 +-
 3 files changed, 76 insertions(+), 32 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index 9d9f7f6..62c3176 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -2591,11 +2591,12 @@ <h2 id="drawersTitle">Your drawers</h2>
  * (34 to 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3 in four, two pieces with
  * dovetails or jigsaws, 2 x 2 on corner bosses; magnets of 3 to 13 mm, either way up),
  * of the 354 taken 48 were open, folded or had a face turned over unturned, leaving out
- * the edges where corner bosses meet, and 2 now, where π/252 left 1 and main 5 of its
- * 356. One leaks on every one of them; the other, which π/252 and main build closed, is
- * an 8.798 head 0.592 deep under a 7.037 x 2.5 magnet from above at 42 mm, where a
- * sloped plane meets a flat of the counterbore half a micron under its roof and each
- * cell has an edge shared four ways and two folds. On 900 more drawn the same way on one
+ * the edges where corner bosses meet, and 1 now, where π/252 left 1 and main 5 of its
+ * 356; it leaks on every one of them. An 8.798 head 0.592 deep under a 7.037 x 2.5
+ * magnet from above at 42 mm, where a sloped plane meets a flat of the counterbore half a
+ * micron under its roof, had an edge shared four ways and two folds a cell, which
+ * π/252 and main build closed, until a cell whose pockets come out with a face turned
+ * over was cut again (the fastener cut in buildPiece). On 900 more drawn the same way on one
  * cell, the test tile, 2 x 2, corner bosses and two pieces, each held to what the page
  * takes, 56 of 498 were bad unturned and none of 496 now, where π/252 left 2 (the 13.582
  * head among them) and main 2 of its 504. With the head
@@ -2604,7 +2605,7 @@ <h2 id="drawersTitle">Your drawers</h2>
  * counterbore on a flat's plane, 18 of the 108 taken from above and 8 of the 186 from
  * beneath were bad unturned, and none now or at π/252 (main 6 and 2); on one cell, every
  * 0.5 mm of pitch, 28 of 216 and 14 of 360, and none now or at π/252 (main 21 and 8). In
- * the STL read back, 15 of those designs show a fold here, 30 at π/252 and 114 on main,
+ * the STL read back, 14 of those designs show a fold here, 30 at π/252 and 114 on main,
  * and here and at π/252 every one the mesh does not have is a triangle with no area.
  *
  * The shank is turned a little about its axis (`turn`, #74) where a corner of the
@@ -5699,8 +5700,23 @@ <h2 id="drawersTitle">Your drawers</h2>
            closed each of those already, so that try is not taken. The nudges and the one
            site at a time came after: of 687 random page designs with a solid floor, the
            three tries left 6 open and these leave 4, none worse; and from 50 to 60 mm,
-           magnets and screws from 15 mm up, they closed six of the nine left open. */
-        if (next.open && next.open <= 24) {
+           magnets and screws from 15 mm up, they closed six of the nine left open.
+
+           With screws, a cell that comes out closed but with a face the repair left turned
+           over (healCsgSeams' `turned`) is cut again the same ways too, and the first try
+           that is closed with nothing turned over is kept. Turned half a facet off the
+           magnet pocket (MOUNT_BORE.head.turn), two of a counterbore's flats can stand
+           square to the cell's x edges, and the BSP split one into a strip 3.3 microns
+           wide that came out folded back: a 3.89 mm head 1 deep over a 1.01 mm shank under
+           a 3 x 2 magnet from above folded 3 times a cell at 45.16 mm with a dovetail and
+           at 44 mm on one cell, where main builds both closed. The cutters turned a 28th
+           more close it. Over 2,366 designs with screws drawn round the counterbore's turn,
+           49 were cut again for it, 47 came out other bytes, 4 that folded build closed
+           (the 8.798 head MOUNT_BORE names among them), none came out worse, and building
+           them all took 1.5% longer. Without screws nothing is cut again for it, and those
+           designs build main's bytes, as they did. */
+        const folded = cfg.screws && !next.open && next.turned;
+        if (next.open && next.open <= 24 || folded) {
           const n4 = cut.length / 4;   // fasteners() lays the four sites' cutters one after another
           const tries = [() => csgSubtract(region, cut.slice().reverse()),
                          () => csgSubtract(region.slice().reverse(), cut),
@@ -5711,7 +5727,7 @@ <h2 id="drawersTitle">Your drawers</h2>
           for (const t of tries) {
             let again;
             try { again = t(); } catch (e) { continue; }   // the first cut stands
-            if (!again.open) { next = again; break; }
+            if (!again.open && !(folded && again.turned)) { next = again; break; }
           }
         }
         return next;
diff --git a/index.html b/index.html
index fe8dd01..1a0f97c 100644
--- a/index.html
+++ b/index.html
@@ -2379,11 +2379,12 @@ <h2 id="drawersTitle">Your drawers</h2>
  * (34 to 56 mm; 2 x 2 in one piece, 3 x 2 in two, 3 x 3 in four, two pieces with
  * dovetails or jigsaws, 2 x 2 on corner bosses; magnets of 3 to 13 mm, either way up),
  * of the 354 taken 48 were open, folded or had a face turned over unturned, leaving out
- * the edges where corner bosses meet, and 2 now, where π/252 left 1 and main 5 of its
- * 356. One leaks on every one of them; the other, which π/252 and main build closed, is
- * an 8.798 head 0.592 deep under a 7.037 x 2.5 magnet from above at 42 mm, where a
- * sloped plane meets a flat of the counterbore half a micron under its roof and each
- * cell has an edge shared four ways and two folds. On 900 more drawn the same way on one
+ * the edges where corner bosses meet, and 1 now, where π/252 left 1 and main 5 of its
+ * 356; it leaks on every one of them. An 8.798 head 0.592 deep under a 7.037 x 2.5
+ * magnet from above at 42 mm, where a sloped plane meets a flat of the counterbore half a
+ * micron under its roof, had an edge shared four ways and two folds a cell, which
+ * π/252 and main build closed, until a cell whose pockets come out with a face turned
+ * over was cut again (the fastener cut in buildPiece). On 900 more drawn the same way on one
  * cell, the test tile, 2 x 2, corner bosses and two pieces, each held to what the page
  * takes, 56 of 498 were bad unturned and none of 496 now, where π/252 left 2 (the 13.582
  * head among them) and main 2 of its 504. With the head
@@ -2392,7 +2393,7 @@ <h2 id="drawersTitle">Your drawers</h2>
  * counterbore on a flat's plane, 18 of the 108 taken from above and 8 of the 186 from
  * beneath were bad unturned, and none now or at π/252 (main 6 and 2); on one cell, every
  * 0.5 mm of pitch, 28 of 216 and 14 of 360, and none now or at π/252 (main 21 and 8). In
- * the STL read back, 15 of those designs show a fold here, 30 at π/252 and 114 on main,
+ * the STL read back, 14 of those designs show a fold here, 30 at π/252 and 114 on main,
  * and here and at π/252 every one the mesh does not have is a triangle with no area.
  *
  * The shank is turned a little about its axis (`turn`, #74) where a corner of the
@@ -5487,8 +5488,23 @@ <h2 id="drawersTitle">Your drawers</h2>
            closed each of those already, so that try is not taken. The nudges and the one
            site at a time came after: of 687 random page designs with a solid floor, the
            three tries left 6 open and these leave 4, none worse; and from 50 to 60 mm,
-           magnets and screws from 15 mm up, they closed six of the nine left open. */
-        if (next.open && next.open <= 24) {
+           magnets and screws from 15 mm up, they closed six of the nine left open.
+
+           With screws, a cell that comes out closed but with a face the repair left turned
+           over (healCsgSeams' `turned`) is cut again the same ways too, and the first try
+           that is closed with nothing turned over is kept. Turned half a facet off the
+           magnet pocket (MOUNT_BORE.head.turn), two of a counterbore's flats can stand
+           square to the cell's x edges, and the BSP split one into a strip 3.3 microns
+           wide that came out folded back: a 3.89 mm head 1 deep over a 1.01 mm shank under
+           a 3 x 2 magnet from above folded 3 times a cell at 45.16 mm with a dovetail and
+           at 44 mm on one cell, where main builds both closed. The cutters turned a 28th
+           more close it. Over 2,366 designs with screws drawn round the counterbore's turn,
+           49 were cut again for it, 47 came out other bytes, 4 that folded build closed
+           (the 8.798 head MOUNT_BORE names among them), none came out worse, and building
+           them all took 1.5% longer. Without screws nothing is cut again for it, and those
+           designs build main's bytes, as they did. */
+        const folded = cfg.screws && !next.open && next.turned;
+        if (next.open && next.open <= 24 || folded) {
           const n4 = cut.length / 4;   // fasteners() lays the four sites' cutters one after another
           const tries = [() => csgSubtract(region, cut.slice().reverse()),
                          () => csgSubtract(region.slice().reverse(), cut),
@@ -5499,7 +5515,7 @@ <h2 id="drawersTitle">Your drawers</h2>
           for (const t of tries) {
             let again;
             try { again = t(); } catch (e) { continue; }   // the first cut stands
-            if (!again.open) { next = again; break; }
+            if (!again.open && !(folded && again.turned)) { next = again; break; }
           }
         }
         return next;
@@ -8520,10 +8536,11 @@ <h2 id="drawersTitle">Your drawers</h2>
 const LENGTH_IDS = ['drawerW', 'drawerD', 'mLeft', 'mRight', 'mFront', 'mBack'];
 let unit = 'mm';   // what the length fields are showing; the saved choice is applied at boot
 
-function readNumber(id) {
+// `held`, a size read in place of the field's: the screw head as readControls holds it
+function readNumber(id, held) {
   const lim = LIMITS[id];
   const len = LENGTH_IDS.includes(id);
-  const v = len ? FIELDS.lengthOf($(id), unit) : parseFloat($(id).value.trim());
+  const v = held !== undefined ? held : len ? FIELDS.lengthOf($(id), unit) : parseFloat($(id).value.trim());
   if (!lim) return isFinite(v) ? v : 0;
   /* Out of play, a field keeps its fixed range but not the one the rest of the design
      sets, and does not complain: magnets off at a 30 mm pitch should not quietly shrink
@@ -8675,20 +8692,31 @@ <h2 id="drawersTitle">Your drawers</h2>
      the head's own size moves its cap and gaps: read against the head before it, a 14.05 mm
      head pasted over a 6 at 46.45 mm with a jigsaw and a 6.2 mm magnet from beneath took the
      6's 14.1 and built, where its own turn stops it at 14, and 14.1 over a 14 was held to
-     the 14's cap at every read after. So the head is measured as typed. The shank's turn
-     goes by the head's, and the magnet pocket it runs through caps it (mountLimits'
-     throughMagnet), so it is read last, on the head as read, measured again where that is
-     not the head typed: one held to its cap or a gap's end. Under an 8.3 mm head held to 7.9
-     at 41.86 mm with a jigsaw, loose, a 7.8 mm hole measured on the 8.3 would be turned and
-     refused. Read before them only, a 5 mm hole stood under a 5.1 mm magnet typed in after
-     it, refused only at the next keystroke. */
+     the 14's cap at every read after. So the head is measured as typed, and one held to its
+     cap or a gap's end is another head, measured again and held again on its own until it
+     holds: an 8.86 mm head at 42 mm with snap clips in the floor and a 3.85 mm magnet from
+     beneath turns and stops at 7.8, but 7.8 does not turn and stops at 7.6, and the page
+     named 7.8 and then refused it. Each pass holds it lower, to a tenth or a gap's end: of
+     3,124 heads pasted over 781 random designs on the page, 1,286 were held once and 33
+     twice, none more, and four passes are allowed. The shank's turn goes by the head's,
+     and the magnet pocket it runs through caps it (mountLimits' throughMagnet), so it is
+     read last, on the head as held: under an 8.3 mm head held to 7.9 at 41.86 mm with a
+     jigsaw, loose, a 7.8 mm hole measured on the 8.3 would be turned and refused. Read
+     before them only, a 5 mm hole stood under a 5.1 mm magnet typed in after it, refused
+     only at the next keystroke. */
   if (state.screws && mountNow) {
     const typed = parseFloat($('screwHeadD').value.trim());
-    mountNow = mountLimits(isFinite(typed) ? { ...state, screwHeadD: typed } : state,
-                           mountLayout, mountNow.cuts);
+    let on = isFinite(typed) ? typed : state.screwHeadD;
     fieldErrors.delete('screwHeadD'); noRoom.delete('screwHeadD');
-    state.screwHeadD = readNumber('screwHeadD');
-    if (state.screwHeadD !== typed) mountNow = mountLimits(state, mountLayout, mountNow.cuts);
+    for (let pass = 0; ; pass++) {
+      mountNow = mountLimits({ ...state, screwHeadD: on }, mountLayout, mountNow.cuts);
+      // a head held already that its own limits take keeps the reason it was held for
+      if (pass && on <= mountNow.screwHeadD && !mountNow.gaps.screwHeadD.some(([a, b]) => on > a && on < b)) break;
+      state.screwHeadD = readNumber('screwHeadD', pass ? on : undefined);
+      if (state.screwHeadD === on || pass === 3) break;
+      on = state.screwHeadD;
+    }
+    if (state.screwHeadD !== on) mountNow = mountLimits(state, mountLayout, mountNow.cuts);
     fieldErrors.delete('screwHoleD'); noRoom.delete('screwHoleD');
     state.screwHoleD = readNumber('screwHoleD');
   }
diff --git a/sw.js b/sw.js
index b052e12..3ce4eb0 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "1bce63f18b29";
+const VERSION = "c3ebb928eb28";
 const FILES = [
   "./",
   "bins/",

From 0798b4c8d5e1314d96698252041a1db19620e2dd Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 14:00:53 +0000
Subject: [PATCH 56/58] Measure the screw head again on the hole the read held,
 so a pasted magnet cannot leave the head above its own cap

The hole is read after the head, and a hole held to the magnet pocket's ledge is another hole for the head to be measured on: a head only a hair wider than its hole is cut as no counterbore, over a smaller one it is cut and turned, and its cap changes with that. Pasting a 6.35 mm magnet over a 7.97 mm head and a 7.71 mm hole at 42 mm with a jigsaw held the hole to 6.1 and left the head at 7.97, where its cap is 7.9, with Download off and Checks naming only the hole. When the read moves the hole, the head is now read again from what was typed on the hole as held, and the hole again on that head, until the hole stays where it was, so the sizes the page ends on are each taken by their own limits measured on the other, and Checks names both.

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 src/ui.js                         | 45 ++++++++++++++++++++++---------
 test/ui/plates-robustness.spec.js | 39 +++++++++++++++++++++++++++
 2 files changed, 71 insertions(+), 13 deletions(-)

diff --git a/src/ui.js b/src/ui.js
index 27bbada..866c821 100644
--- a/src/ui.js
+++ b/src/ui.js
@@ -411,22 +411,41 @@ function readControls() {
      read last, on the head as held: under an 8.3 mm head held to 7.9 at 41.86 mm with a
      jigsaw, loose, a 7.8 mm hole measured on the 8.3 would be turned and refused. Read
      before them only, a 5 mm hole stood under a 5.1 mm magnet typed in after it, refused
-     only at the next keystroke. */
+     only at the next keystroke.
+     The hole is read after the head, and its read can move it: to the ledge the magnet pocket
+     leaves it, or to the cap the head as held leaves it. A head's cap goes by the hole it is
+     measured on, since a head only a hair wider than its hole is cut as no counterbore and
+     is not turned (MOUNT_BORE.screw): a 7.97 mm head over a 7.71 mm hole at 42 mm with a
+     jigsaw and an 8.1 mm magnet from beneath takes up to 8.1, but a 6.35 mm magnet pasted in
+     held the hole to 6.1, where the head is cut and turned and stops at 7.9, and the head
+     stayed at 7.97, with Checks naming the hole alone. So a hole the read has moved is
+     another hole to read the head on: the head is read again from what was typed, measured
+     on the hole as held, and the hole again on that head, until the hole stays where it was.
+     That settles on a head taken by its own limits measured on the hole it ends on, and a
+     hole taken by its own limits measured on that head, which a second read leaves as they
+     are. Of 43,536 heads, magnets and holes pasted near their caps over random screw designs
+     on the page, 16,006 took a second round, none a third, and four are allowed, as four
+     passes are for the head. */
   if (state.screws && mountNow) {
     const typed = parseFloat($('screwHeadD').value.trim());
-    let on = isFinite(typed) ? typed : state.screwHeadD;
-    fieldErrors.delete('screwHeadD'); noRoom.delete('screwHeadD');
-    for (let pass = 0; ; pass++) {
-      mountNow = mountLimits({ ...state, screwHeadD: on }, mountLayout, mountNow.cuts);
-      // a head held already that its own limits take keeps the reason it was held for
-      if (pass && on <= mountNow.screwHeadD && !mountNow.gaps.screwHeadD.some(([a, b]) => on > a && on < b)) break;
-      state.screwHeadD = readNumber('screwHeadD', pass ? on : undefined);
-      if (state.screwHeadD === on || pass === 3) break;
-      on = state.screwHeadD;
+    const asTyped = isFinite(typed) ? typed : state.screwHeadD;
+    for (let round = 0; ; round++) {
+      let on = asTyped;
+      fieldErrors.delete('screwHeadD'); noRoom.delete('screwHeadD');
+      for (let pass = 0; ; pass++) {
+        mountNow = mountLimits({ ...state, screwHeadD: on }, mountLayout, mountNow.cuts);
+        // a head held already that its own limits take keeps the reason it was held for
+        if (pass && on <= mountNow.screwHeadD && !mountNow.gaps.screwHeadD.some(([a, b]) => on > a && on < b)) break;
+        state.screwHeadD = readNumber('screwHeadD', pass ? on : undefined);
+        if (state.screwHeadD === on || pass === 3) break;
+        on = state.screwHeadD;
+      }
+      if (state.screwHeadD !== on) mountNow = mountLimits(state, mountLayout, mountNow.cuts);
+      fieldErrors.delete('screwHoleD'); noRoom.delete('screwHoleD');
+      const measuredOn = state.screwHoleD;
+      state.screwHoleD = readNumber('screwHoleD');
+      if (state.screwHoleD === measuredOn || round === 3) break;
     }
-    if (state.screwHeadD !== on) mountNow = mountLimits(state, mountLayout, mountNow.cuts);
-    fieldErrors.delete('screwHoleD'); noRoom.delete('screwHoleD');
-    state.screwHoleD = readNumber('screwHoleD');
   }
   // and Checks says what is wrong in the panel's order, not the order it was read in
   for (const m of [fieldErrors, noRoom]) {
diff --git a/test/ui/plates-robustness.spec.js b/test/ui/plates-robustness.spec.js
index 8ebcefb..1edb537 100644
--- a/test/ui/plates-robustness.spec.js
+++ b/test/ui/plates-robustness.spec.js
@@ -315,6 +315,45 @@ test.describe('ranges on the geometry fields', () => {
     expect(errors).toEqual([]);
   });
 
+  /* And the head on the hole as held, since the hole is read last. At 42 mm with a jigsaw, a
+     7.97 mm head over a 7.71 mm hole and an 8.1 mm magnet from beneath builds. Paste a 6.35 mm
+     magnet over it and the hole is held to 6.1, the most the pocket leaves a ledge for, where
+     the head's cap on a 6.1 mm hole is 7.9: the head had been read against the 7.71, stayed at
+     7.97 with Download off, and Checks named the hole alone, so setting the hole to 6.1 raised
+     a refusal of the head that nothing had said. */
+  test('a screw head is measured on the hole as held, not as typed', async ({ page }) => {
+    const errors = await openAt(page, '#pi=42&w=84&d=84&mm=custom&ml=0&mr=0&mf=0&mb=0&bw=54&bd=400' +
+                                      '&cn=puzzle&mg=1&md=8.1&mh=3&ms=bottom&sc=1&sh=7.71&sd=7.97&se=3');
+    const max = (id) => page.evaluate((i) => document.getElementById(i).max, id);
+    const hole = /Screw hole Ø must be 6\.1 mm or less — it runs through the 6\.35 mm magnet's pocket/;
+    const head = /Screw head Ø must be 7\.9 mm or less at a 42 mm pitch — .* a hole has to stay out of the notches the puzzle tabs fit into\./;
+    expect(await text(page, 'pieceTail')).toMatch(/ready/);
+    expect(await exportOff(page)).toBe(false);
+    await paste(page, 'magnetD', '6.35');
+    await page.waitForTimeout(250);
+    expect(await page.evaluate(() => [state.screwHeadD, state.screwHoleD])).toEqual([7.9, 6.1]);
+    expect(await text(page, 'errScrew')).toMatch(hole);
+    expect(await text(page, 'errScrew')).toMatch(head);
+    expect(await text(page, 'warnings'), 'the checks under the map say the same thing').toMatch(hole);
+    expect(await text(page, 'warnings')).toMatch(head);
+    expect(await max('screwHoleD')).toBe('6.1');
+    expect(await max('screwHeadD')).toBe('7.9');
+    expect(await text(page, 'pieceTail')).toMatch(/not building/);
+    expect(await exportOff(page)).toBe(true);
+    // the sizes it named are the sizes it takes: nothing new is raised once the hole is set to them
+    await H.setField(page, 'screwHoleD', '6.1');
+    expect(await shown(page, 'errScrew')).toBe(true);
+    expect(await text(page, 'errScrew')).not.toMatch(/Screw hole Ø/);
+    expect(await text(page, 'errScrew')).toMatch(head);
+    expect(await page.evaluate(() => [state.screwHeadD, state.screwHoleD])).toEqual([7.9, 6.1]);
+    await H.setField(page, 'screwHeadD', '7.9');
+    await settled(page);
+    expect(await shown(page, 'errScrew')).toBe(false);
+    expect(await text(page, 'pieceTail')).toMatch(/ready/);
+    expect(await exportOff(page)).toBe(false);
+    expect(errors).toEqual([]);
+  });
+
   /* #70: corner pockets over a floor. A bowtie housed in the floor stood its 2.8 mm floor
      round the 2.6 mm bosses and sealed their pockets in it, with Download on, and an extra
      floor did the same. Such a plate is built as a solid floor builds it now, and Checks

From b932f96f14227aa26f32445fca02fe170dda677d Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 14:00:53 +0000
Subject: [PATCH 57/58] Say in core.js what sets off the second cut of a
 screwed cell, and that it changes the bytes of the designs it fires on

Comment only. The trigger is healCsgSeams' own count of turned faces on the cut as it was built, not test/orientation.js on the final mesh.

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 src/core.js | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/src/core.js b/src/core.js
index f2db7f7..4b33e9e 100644
--- a/src/core.js
+++ b/src/core.js
@@ -4098,7 +4098,11 @@ function buildPiece(cfg, layout, piece, onStatus) {
 
            With screws, a cell that comes out closed but with a face the repair left turned
            over (healCsgSeams' `turned`) is cut again the same ways too, and the first try
-           that is closed with nothing turned over is kept. Turned half a facet off the
+           that is closed with nothing turned over is kept. The trigger is healCsgSeams' own
+           `turned` count on the cut as it was built, not test/orientation.js on the final
+           mesh, so it goes by the cut and not by what the audit would see of the plate, and
+           it changes the bytes of every design it fires on (54 of 3,053 screw designs in
+           the review's sweep). Turned half a facet off the
            magnet pocket (MOUNT_BORE.head.turn), two of a counterbore's flats can stand
            square to the cell's x edges, and the BSP split one into a strip 3.3 microns
            wide that came out folded back: a 3.89 mm head 1 deep over a 1.01 mm shank under

From 002df36eeece97eacc5ab1f9bd2666ca71f769be Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Sat, 10 Oct 2026 14:00:53 +0000
Subject: [PATCH 58/58] Rebuild the pages

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Uqqb1cvhXxrpb3P6y6ykBY
---
 bins/index.html |  6 +++++-
 index.html      | 53 +++++++++++++++++++++++++++++++++++--------------
 sw.js           |  2 +-
 3 files changed, 44 insertions(+), 17 deletions(-)

diff --git a/bins/index.html b/bins/index.html
index 3a1188a..6d8d827 100644
--- a/bins/index.html
+++ b/bins/index.html
@@ -5704,7 +5704,11 @@ <h2 id="drawersTitle">Your drawers</h2>
 
            With screws, a cell that comes out closed but with a face the repair left turned
            over (healCsgSeams' `turned`) is cut again the same ways too, and the first try
-           that is closed with nothing turned over is kept. Turned half a facet off the
+           that is closed with nothing turned over is kept. The trigger is healCsgSeams' own
+           `turned` count on the cut as it was built, not test/orientation.js on the final
+           mesh, so it goes by the cut and not by what the audit would see of the plate, and
+           it changes the bytes of every design it fires on (54 of 3,053 screw designs in
+           the review's sweep). Turned half a facet off the
            magnet pocket (MOUNT_BORE.head.turn), two of a counterbore's flats can stand
            square to the cell's x edges, and the BSP split one into a strip 3.3 microns
            wide that came out folded back: a 3.89 mm head 1 deep over a 1.01 mm shank under
diff --git a/index.html b/index.html
index b8e0270..c11d96a 100644
--- a/index.html
+++ b/index.html
@@ -5492,7 +5492,11 @@ <h2 id="drawersTitle">Your drawers</h2>
 
            With screws, a cell that comes out closed but with a face the repair left turned
            over (healCsgSeams' `turned`) is cut again the same ways too, and the first try
-           that is closed with nothing turned over is kept. Turned half a facet off the
+           that is closed with nothing turned over is kept. The trigger is healCsgSeams' own
+           `turned` count on the cut as it was built, not test/orientation.js on the final
+           mesh, so it goes by the cut and not by what the audit would see of the plate, and
+           it changes the bytes of every design it fires on (54 of 3,053 screw designs in
+           the review's sweep). Turned half a facet off the
            magnet pocket (MOUNT_BORE.head.turn), two of a counterbore's flats can stand
            square to the cell's x edges, and the BSP split one into a strip 3.3 microns
            wide that came out folded back: a 3.89 mm head 1 deep over a 1.01 mm shank under
@@ -8877,22 +8881,41 @@ <h2 id="drawersTitle">Your drawers</h2>
      read last, on the head as held: under an 8.3 mm head held to 7.9 at 41.86 mm with a
      jigsaw, loose, a 7.8 mm hole measured on the 8.3 would be turned and refused. Read
      before them only, a 5 mm hole stood under a 5.1 mm magnet typed in after it, refused
-     only at the next keystroke. */
+     only at the next keystroke.
+     The hole is read after the head, and its read can move it: to the ledge the magnet pocket
+     leaves it, or to the cap the head as held leaves it. A head's cap goes by the hole it is
+     measured on, since a head only a hair wider than its hole is cut as no counterbore and
+     is not turned (MOUNT_BORE.screw): a 7.97 mm head over a 7.71 mm hole at 42 mm with a
+     jigsaw and an 8.1 mm magnet from beneath takes up to 8.1, but a 6.35 mm magnet pasted in
+     held the hole to 6.1, where the head is cut and turned and stops at 7.9, and the head
+     stayed at 7.97, with Checks naming the hole alone. So a hole the read has moved is
+     another hole to read the head on: the head is read again from what was typed, measured
+     on the hole as held, and the hole again on that head, until the hole stays where it was.
+     That settles on a head taken by its own limits measured on the hole it ends on, and a
+     hole taken by its own limits measured on that head, which a second read leaves as they
+     are. Of 43,536 heads, magnets and holes pasted near their caps over random screw designs
+     on the page, 16,006 took a second round, none a third, and four are allowed, as four
+     passes are for the head. */
   if (state.screws && mountNow) {
     const typed = parseFloat($('screwHeadD').value.trim());
-    let on = isFinite(typed) ? typed : state.screwHeadD;
-    fieldErrors.delete('screwHeadD'); noRoom.delete('screwHeadD');
-    for (let pass = 0; ; pass++) {
-      mountNow = mountLimits({ ...state, screwHeadD: on }, mountLayout, mountNow.cuts);
-      // a head held already that its own limits take keeps the reason it was held for
-      if (pass && on <= mountNow.screwHeadD && !mountNow.gaps.screwHeadD.some(([a, b]) => on > a && on < b)) break;
-      state.screwHeadD = readNumber('screwHeadD', pass ? on : undefined);
-      if (state.screwHeadD === on || pass === 3) break;
-      on = state.screwHeadD;
-    }
-    if (state.screwHeadD !== on) mountNow = mountLimits(state, mountLayout, mountNow.cuts);
-    fieldErrors.delete('screwHoleD'); noRoom.delete('screwHoleD');
-    state.screwHoleD = readNumber('screwHoleD');
+    const asTyped = isFinite(typed) ? typed : state.screwHeadD;
+    for (let round = 0; ; round++) {
+      let on = asTyped;
+      fieldErrors.delete('screwHeadD'); noRoom.delete('screwHeadD');
+      for (let pass = 0; ; pass++) {
+        mountNow = mountLimits({ ...state, screwHeadD: on }, mountLayout, mountNow.cuts);
+        // a head held already that its own limits take keeps the reason it was held for
+        if (pass && on <= mountNow.screwHeadD && !mountNow.gaps.screwHeadD.some(([a, b]) => on > a && on < b)) break;
+        state.screwHeadD = readNumber('screwHeadD', pass ? on : undefined);
+        if (state.screwHeadD === on || pass === 3) break;
+        on = state.screwHeadD;
+      }
+      if (state.screwHeadD !== on) mountNow = mountLimits(state, mountLayout, mountNow.cuts);
+      fieldErrors.delete('screwHoleD'); noRoom.delete('screwHoleD');
+      const measuredOn = state.screwHoleD;
+      state.screwHoleD = readNumber('screwHoleD');
+      if (state.screwHoleD === measuredOn || round === 3) break;
+    }
   }
   // and Checks says what is wrong in the panel's order, not the order it was read in
   for (const m of [fieldErrors, noRoom]) {
diff --git a/sw.js b/sw.js
index d7a50ef..453412f 100644
--- a/sw.js
+++ b/sw.js
@@ -52,7 +52,7 @@
    load from this site, and the app's icons and manifest, as paths from the root. VERSION
    is a hash of all of those files, names and bytes, and of this script as it is served,
    FILES filled in and everything else but VERSION itself. */
-const VERSION = "b0b75b9f582b";
+const VERSION = "5ddb37edc38b";
 const FILES = [
   "./",
   "bins/",