[MCA] Route rank eleven through anchored rich flats

agents.md

@@ -1,7 +1,7 @@
 # AGENTS.md — RS–MCA Resolution Protocol
 
-> **Updated:** 2026-07-29
-> **State snapshot:** `main@b13de8113a03f06b6fc22bbd2f289a8abcdf7e95`
+> **Updated:** 2026-08-13
+> **State snapshot:** `upstream/main@93fba1be3f3299b0ba4708d88715377bbb656e45`
 > **Supersedes:** all older priority lists in this file.
 
 Edit this workboard in place. Never append another “current focus”, “highest priority”, or competing task list.
@@ -80,6 +80,13 @@ At this snapshot:
 - The cumulative M31 rank-seven compiler now reaches `Q=147594` locally.  Its adjacent `Q=147595`, `k=4981` survivor is reduced to a varying proper-`G`, zero-excess cross-cofactor incidence terminal requiring an aggregate cap `2157928`; no v4 atom, higher-rank theorem, or row closure follows.
 - The KoalaBear equality-wall PR stack proves local normalization, a `Q=6,u=2` geometry reduction, and exclusion of 60 labelled `P3+C3` cases, but retains 405 labelled conic cases and lacks global ownership/add-back.  The separate column-far transverse-secant certificate is per fixed union only.  No large `U_paid` claimed by an abstract candidate-record compiler is banked; the live active value remains `null`.
 - The exact adjacent fixed-`G` Hahn relaxation has optimum `20737821.0968...`, above the list target, and its complementarity identity shows the proposed selection-gap hypothesis is target-equivalent.  This cuts the ordinary pairwise-distribution route without proving an unsafe list or moving the M31 row.
+- The affine-span transverse MCA compiler `thm:affine-span-mca` is refuted even under its printed direction-separation hypothesis.  An exact `GF(1009)` rank-one family has 31 pair-noncontained bad slopes against the claimed bound 23, with direction agreement `20<m=21`.  The corrected `thm:proper-subspace-mca` replaces its false extension factor, and the lifted-rank dichotomy isolates the full-lift branch.  There `W=C+<r_1>` has `d_1(W)=e` and every higher generalized weight MDS-sharp.  The punctured Johnson and Gram rungs lead to the exact-layer affine-line theorem, which pays every sparse-direction support `e<d`.  Beyond `d`, pair noncontainment caps the total common core of an affine explanation line; triple overlap synchronizes all top-third exact layers onto one global line, so its `N-m+1` cap is charged once.  Extending the exact suffix-minimum prefix with the mean-centered Gram cap, then absorbing one boundary layer by two top anchors and a second layer at residue two by an anchor/missed-set case split, leaves residual intervals `96151<=e<=1044238` on KoalaBear and `98232<=e<=1044241` on Mersenne-31.  At the first Mersenne residual, a normalized-direction Johnson count caps the boundary layer at `1450`; any unsafe family must then put at least `343071` slopes on the synchronized top line and give it a common core of size at least `m-2`.  That core absorbs every assigned pair of deficit at least `30791` into the same line, while the lower explanations form a punctured ordinary list of size at most `26`; the contradiction bound is `3535161<16777215`.  The fixed-cutoff generalization `h_0=65200` prices all intermediate exact layers and pays every Mersenne support through `e=101155`, directly through `101149` and by core absorption for the final six.  At the first wall `e=101156`, switching to `h_0=65258` and using residue two synchronizes both top boundary layers; the zero/one-top cases use an outside-core line cap or disjoint missed sets.  The largest of five exhaustive bounds is `16705799<16777215`.  Beyond that support, retaining every exact-layer direction class as an affine-line slot gives a global line bank; unsafe pigeonhole and total-core absorption pay all `23,649` supports through `e=124805`.  Recursive residual peeling then removes each forced parameterized affine line and either reaches the exact weighted prefix or violates the pairwise `K-1` intersection ceiling for the peeled inside cores.  Exact replay pays another `5,393` supports through `e=130198`, with at most five lines.  Bounding all removed lines jointly from their shared core budget gives a convex endpoint charge and pays 21 further supports through `e=130219`.  Retaining every forced total-core lower bound in that convex maximization pays `e=130220,130221`; both rows terminate after 38 lines with inside-core packing lower bound `142893`.  Splitting each subsequent selected line at actual core `e+10-65450` gives either weighted-prefix core absorption or a capped convex charge.  This pays `e=130222..130225`, with 14 lines on the first two rows and 70 on the last two.  Restoring each selected slot's exact-layer owner gives the inside-core bound `u>=ceil((lambda*h-e)/(lambda-1))`; with the capped-core branch, three lines pay every support `e=130226..130236`.  At adjacent `e=130237`, the bank forces only size-two shift-pair slots with inside core `807`; first-order packing reaches only `65529<e`.  A weight-`(1,5,5)` degree-264 interpolation kernel has dimension at least `938`; the capped bank still forces 2,705 distinct polynomial-pair cores, while two coprime kernel members have at most `52^2=2704` common pairs.  Thus every unsafe survivor forces a positive-`(Y,Z)`-degree common interpolation factor.  The full 7,583-line ledger and cofactor Bezout put at least 4,982 pairs on that factor; their core incidence forces the received pair onto it at least 126,188 times, leaving at most 4,049 inside exceptions.  The Mersenne residual starts at `e=130237`, with this near-total factor's classification open.  The adjacent KoalaBear cap loses its positive mean-centered denominator.  Neither remaining residual is an unsafe certificate.  The ordinary affine-span LIST theorem, common-core cancellation, directional Johnson compiler, gauge equivalence, and the selector-free all-LineRay error-affine-core set-pair theorem are not refuted by the example.
+- In the first Mersenne full-lift residual, the degree-one common-factor branch is now an exact `F`-rational projective star.  Polynomial-section parameterization and an ordinary Johnson cap of `802` exclude every nonconstant-coefficient linear factor against the `4982` captured sections.  This identifies the primitive-star shape but does not pay its population; the complementary factor branch has `(Y,Z)` degree at least two.
+- The same kernel's 938-dimensional quotient forces the primitive full gcd to have weight-`(1,5,5)` degree at most `217`, hence `(Y,Z)` degree at most `43`.  In the higher-degree branch this improves the factor mass to at least `5083` sections and `126266` inside points, leaving at most `3971` exceptions; reducible gcds remain allowed.
+- Base-field descent now removes geometric field-of-definition ambiguity from that branch.  Since the Mersenne characteristic exceeds 43, conjugation and Bezout leave at least `5079` selected pairs on `F(X)`-defined components; one absolutely irreducible base-field component carries at least `132`, while their union has at most `3974` inside exceptions.
+- The post-#1165 support-transverse refinement replaces the global final factor `L` by the exact selected-support margin `theta>=L`.  Its arbitrary-rank codeword gauge pays every intrinsic post-near KoalaBear family through affine error rank 9 by `110390969172308040`, with slack `164589758939087047`, conditional only on the separately pinned `2w` near-rational theorem.  At error ranks 10, 11, and 12, an over-budget family yields an actual identical support on which the original direction differs from a reconstructed codeword in at most `12`, `387`, or `12049` coordinates.  This is a direct distinct-slope route cut with zero active-v4 ledger movement; it does not transport first-match owners or close KoalaBear.
+- The rank-ten margin/interleaving split now pays the complete direct post-near KoalaBear affine-error-rank-10 branch.  At threshold T=667, the support-transverse high part costs 5143522968716559, the common-support interleaved low part costs 56727790457914040, and the disjoint near add-back costs 134944, for total 61871313426765543 and slack 213109414684629544.  The projection-collapse guard uses the actual sextic line field |F|=2130706433^6.  The same exact one-threshold formula first fails at error rank 11, whose minimum is 1040506078215897711 at T=876; an exact post-near constant-code star proves the per-pair multiplicity factor n-A is sharp.  This moves no active-v4 atom and does not close KoalaBear.
+- The rank-eleven successor now sums the record-local support margins before taking a minimum and compiles low-margin records into actual fixed minimizing pairs.  Every over-budget post-near error-rank-11 line forces one pair of deficiency at most 8 with weighted load at least 743449148, and independently a possibly different pair of deficiency at most 4 owning at least 200632 distinct slopes.  The complete printed-theorem core-deficiency cutoff has minimum 813929118931913384, while the stronger summed-margin relaxation has minimum 811958533186703629; both exceed the row budget.  A finite parallel-star control rules out distinct-neighbor promotion and a smaller one-pair multiplier.  Thus the next missing theorem couples different pair cores or routes dense parallel groups to a chronology owner.  This is a route cut with zero active-v4 ledger movement, not a rank-eleven payment or KoalaBear closure.
 - Grande Finale v4 explicitly supersedes the old v3 `prob:saturated-bc` status: primitive one-pencil MCA BC is proved; higher-dimensional MCA BC remains jointly governed by spread-component, large-owner, and exception routing; and the list-interior clause is governed by row-sharp list completion.  The spread-abundance and `prob:next` statements are intermediate forms, not additional terminal inputs.
 - `experimental/proximity_prize_results_v4.tex` is the current compact synthesis of proved partial results.  It is exposition/status guidance, not a replacement proof source for a live atom or adjacent-row closure.
 - A schema/hash pass is structural preflight only. The trusted-source registry is empty; parsing a manifest does not prove an atom.