diff --git a/CHANGELOG.md b/CHANGELOG.md
index c2cae65..c0b5ce1 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,6 +5,23 @@ entry points (`.`, `./three`) are frozen for 1.x, while the **scene subpaths** (
 `./splat`, `./model`) are a preview tier whose options may change in any release. Entries below say
 which tier they touch, because that is what tells you whether an upgrade can move your pixels.
 
+## 1.37.1 — 2026-10-07
+
+### Depth cursor: hybrid anchor keeps the line of sight, not the foot
+
+- 1.37.0's `'hybrid'` held the sprite's foot on the glass while the pointer was still. When the
+  depth under a still pointer changed (content animating under a resting mouse, or the first
+  frames after load), the sprite then rose along the display NORMAL. For an off-axis viewer that
+  pulls it off the pointer (27 px in the runtime's off-axis capture).
+- It now keeps the line of sight from the last pointer move, and sits on that line at the current
+  depth:
+  - **head moves:** the sprite stays put (it parallaxes, as in 1.37.0);
+  - **depth changes:** the sprite slides along that line, so it stays on the click point for the
+    viewer who placed it;
+  - **stop frame:** still continuous.
+- Matches the runtime's `XR_DXR_cursor_depth` v3 rule. Tests cover it, including an off-axis
+  depth-change case and a head moving nearer; each mutant is caught.
+
 ## 1.37.0 — 2026-10-07
 
 Driven by a tester's run on a head-tracked panel (the depth cursor shipped in 1.36.0). Additive
diff --git a/js/inline3d-cursor-depth.js b/js/inline3d-cursor-depth.js
index 3e9267c..638220f 100644
--- a/js/inline3d-cursor-depth.js
+++ b/js/inline3d-cursor-depth.js
@@ -34,8 +34,11 @@
 //      'world'  — C = S - f (1 - t) eyeToCanvas, straight in front of the pointer's canvas point:
 //                 parallaxes like content, drifts ~mm off the pointer from an off-axis viewer;
 //      'hybrid' (default) — 'screen' while the pointer moves (exact aim), and world-FIXED while it
-//                 is still (correct parallax): the foot F of the last moving placement on the glass
-//                 is kept, and C = F - f (1 - t) eyeToCanvas. Continuous at the stop frame.
+//                 is still (correct parallax): the line of sight at the last pointer move (E0 → S0)
+//                 is kept, and the sprite sits on it at the current depth — the point whose
+//                 distance in front of the glass is (1 - t) eyeToCanvas. A head move leaves it
+//                 put; a depth change slides it along that line, so it stays on the click point
+//                 for the viewer who placed it. Continuous at the stop frame.
 //    The height is scaled by t either way, so the apparent size is constant.
 
 import { CURSOR_ANCHOR_MODES } from './inline3d-cursor-option.js';
@@ -220,14 +223,14 @@ export class CursorDepthPlacer {
     this.tuning = tuning;
     this.anchor = anchor;
     this.filter = {};
-    this._foot = null; // hybrid: the world-fixed foot on the glass while the pointer is still
+    this._line = null; // hybrid: the line of sight at the last pointer move { E, S, D }
     this._last = null; // [u, v] of the previous active frame
   }
 
   update(views, hint, nowSec) {
     const inactive = { active: false, position: null, basis: null, height: 0, disparity: 0, targetDisparity: 0 };
     if (!views || views.length < 2 || !hint) {
-      this._foot = null;
+      this._line = null;
       this._last = null;
       return inactive;
     }
@@ -235,7 +238,7 @@ export class CursorDepthPlacer {
     const b = asView(views[views.length - 1]);
     const g = solveCursorGeometry(a, b, hint.u, hint.v);
     if (!g) {
-      this._foot = null;
+      this._line = null;
       this._last = null;
       return inactive;
     }
@@ -255,12 +258,14 @@ export class CursorDepthPlacer {
     } else if (this.anchor === 'hybrid') {
       const last = this._last;
       const moved =
-        reprimed || !this._foot || !last || Math.abs(hint.u - last[0]) > POINTER_STILL_EPS || Math.abs(hint.v - last[1]) > POINTER_STILL_EPS;
+        reprimed || !this._line || !last || Math.abs(hint.u - last[0]) > POINTER_STILL_EPS || Math.abs(hint.v - last[1]) > POINTER_STILL_EPS;
       if (moved) {
-        // The foot of the on-ray placement on the glass, along the normal: C = F - f·(1-t)·eyeToCanvas.
-        this._foot = addScaled(onRay, fw, -out);
+        this._line = { E: g.eye, S: g.canvasPoint, D: g.eyeToCanvas };
       } else {
-        position = addScaled(this._foot, fw, out);
+        // On the kept line E0 → S0, the point (1 - t)·eyeToCanvas in front of the glass.
+        const L = this._line;
+        const k = 1 - ((1 - t) * g.eyeToCanvas) / L.D;
+        position = addScaled(L.E, sub(L.S, L.E), k);
         anchored = true;
       }
     }
diff --git a/package.json b/package.json
index 4811046..4d525ab 100644
--- a/package.json
+++ b/package.json
@@ -1,6 +1,6 @@
 {
   "name": "@displayxr/inline3d",
-  "version": "1.37.0",
+  "version": "1.37.1",
   "description": "Turn any HTML <canvas> into a 3D window on a spatial display, inside an ordinary web page, for the DisplayXR Browser. Dependency-free; progressive enhancement (falls back to plain 2D everywhere else).",
   "type": "module",
   "types": "./index.d.ts",
diff --git a/test/cursor-depth.test.mjs b/test/cursor-depth.test.mjs
index dfa27f0..88e01b9 100644
--- a/test/cursor-depth.test.mjs
+++ b/test/cursor-depth.test.mjs
@@ -373,3 +373,48 @@ test('DepthCursor: margin option + pointerScope window (over overlay DOM, page-w
     delete globalThis.document;
   }
 });
+
+test('anchor hybrid: depth changing under a STILL pointer slides along the kept line of sight (no drift off the click point)', () => {
+  // Off-axis viewer (10 cm up, 6 cm right): the case where lifting along the display normal
+  // would pull the sprite visibly off the pointer.
+  const views = [kooima([0.06 - 0.032, 0.1, 0.6]), kooima([0.06 + 0.032, 0.1, 0.6])];
+  const hybrid = new CursorDepthPlacer();
+  const world = new CursorDepthPlacer(T, { anchor: 'world' });
+  // Frame 1: nothing under the pointer yet — anchored on the glass.
+  const a0 = hybrid.update(views, { u: 0.4, v: 0.6, nearestPoint: null }, 1.0);
+  world.update(views, { u: 0.4, v: 0.6, nearestPoint: null }, 1.0);
+  const E0 = a0.geometry.eye, S0 = a0.geometry.canvasPoint;
+  // Content appears under the still pointer; let the filter rise.
+  let h, w;
+  for (let i = 1; i <= 40; i++) {
+    h = hybrid.update(views, { u: 0.4, v: 0.6, nearestPoint: [0, 0, 0.12] }, 1.0 + i * 0.016);
+    w = world.update(views, { u: 0.4, v: 0.6, nearestPoint: [0, 0, 0.12] }, 1.0 + i * 0.016);
+  }
+  assert.equal(h.anchored, true);
+  assert.ok(h.position[2] > 0.1, 'it rose');
+  // Projected from E0 onto the glass, the hybrid sprite is still exactly on the click point S0 …
+  const onGlass = (e, p) => { const k = e[2] / (e[2] - p[2]); return [e[0] + (p[0] - e[0]) * k, e[1] + (p[1] - e[1]) * k]; };
+  near3(onGlass(E0, h.position), [S0[0], S0[1]], 1e-6);
+  // … while lifting along the normal (world) lands visibly off it for this viewer.
+  const off = onGlass(E0, w.position);
+  assert.ok(Math.hypot(off[0] - S0[0], off[1] - S0[1]) > 0.005, 'world drifts > 5 mm here');
+  // And it is at the same depth as the world placement (only the line differs).
+  near(h.position[2], w.position[2], 1e-6);
+});
+
+test('anchor hybrid: a still pointer + the head moving NEARER keeps the sprite at the depth the content needs', () => {
+  const hint = { u: 0.45, v: 0.5, nearestPoint: [0, 0, 0.1] };
+  const at = (z) => [kooima([-0.032, 0, z]), kooima([0.032, 0, z])];
+  const hybrid = new CursorDepthPlacer();
+  const world = new CursorDepthPlacer(T, { anchor: 'world' });
+  hybrid.update(at(0.6), hint, 1.0);
+  world.update(at(0.6), hint, 1.0);
+  let h, w;
+  for (let i = 1; i <= 60; i++) {
+    h = hybrid.update(at(0.5), hint, 1.0 + i * 0.016); // 10 cm nearer, pointer still
+    w = world.update(at(0.5), hint, 1.0 + i * 0.016);
+  }
+  assert.equal(h.anchored, true);
+  near(h.position[2], w.position[2], 1e-6); // same distance in front of the glass as the world placement
+  assert.ok(h.position[2] > 0.1, 'still in front of the content');
+});