[MCA] Pay rank-one pair anticodes by fixed-endpoint routing

[scottdhughes]

Summary

Stacked successor to #1171 at exact parent a3fc2d5aea86577cd50d8b95b6eb2155d4d940f6.

This completes the rank-one minimizing-pair anticode branch left partially routed by #1171. Split the post-near affine-error-rank-eleven family at support-margin cutoff tau=439.

For the fixed-left-factor geometry, an invertible endpoint row operation makes one endpoint codeword common to every minimizing pair type. On its complete agreement set G, the varying endpoints form one ordinary affine Reed--Solomon list. Same-support pair noncontainment forces every nonexceptional owning slope to use a coordinate outside G; for a fixed pair type and outside coordinate, the projective slope equation has at most one solution.

The exact theorem-level envelope is

low rank-one branch       32,215,263,489,919,749
high-margin tail         242,314,927,584,173,240
near-rational add-back               134,944
------------------------------------------------
total                    274,530,191,074,227,933
slack                        450,537,037,167,154

Cutoff 438 is still over budget by 96,628,092,421,444, so 439 is the first paying cutoff. The same envelope has unique minimum 81,826,485,385,525,648 at tau=3608.

Together with #1171's fixed-right ray cap 8,147,918, this pays the complete low-margin pairwise-rank-one anticode branch.

New residual

Every over-budget rank-eleven line now forces two low-margin actual minimizing pair types e,f satisfying

rank(M_e-M_f)=2,
|H_e|, |H_f| >= 1,115,609,
|H_e intersect H_f| >= 134,066.

Thus the two independent degree-<K endpoint-difference polynomials share a squarefree deployed-evaluation locator of degree at least 134,066.

The next missing theorem is a chronology-safe compiler for these rank-two large-common-factor edges: either many edges share one locator factor and enter one shortened correction plane, or varying factors force a bounded-factor sunflower/cycle collision charged once.

Scope

• active-v4 ledger movement: 0
• rank-eleven payment: no
• KoalaBear closure: no
• result: direct rank-one branch payment and sharper rank-two route cut

No per-edge cancellation, sum over unrelated factor owners, or common-factor synchronization is assumed.

Verification

• canonical payload 675b02624c17373e435000dcbdc87746e7b4c9b2b0f0e1ccc5081c479b621fa6
• primary exact verifier: PASS
• independent gcd-cancellation/recurrence verifier: PASS
• all 67,471 legal cutoffs scanned
• exact deployed g scans at tau=439 and tau=3608
• exhaustive GL_2(F_5) and GL_2(F_7) projective-owner controls: PASS
• hostile mutations: 6/6 rejected
• Wolfram independent exact-integer replay: PASS
• targeted primary-literature sweep: no external theorem is load-bearing

Dependency

This PR must integrate after #1171, which itself is stacked after #1168.

[AllenGrahamHart]

The rank-two large-common-factor residual posed here has an exact banked tool on the public prize DAG for its first horn.

The shared squarefree locator of degree >= 134,066 between the two forced endpoint-difference polynomials is precisely the input of the common-core cancellation adapter from #1163 (banked with an independent replay as rate_half_kb_common_core_shortening_adapter_staircase_import; applied to rank-11 order-32 seeds in rate_half_mca_rank11_order32_common_support_cancellation): edges sharing one locator factor G shorten by exact division into a single correction plane on (n-c, K-c), with slopes, same-support noncontainment, and the invariants preserved in both directions — your "many edges share one locator factor and enter one shortened correction plane" horn is the adapter's typed image. The reverse guard (Q(x) != 0 on deleted points) is the only additional hypothesis for scalar-locator transport.

For the second horn (varying factors), note the degree floor is additive under gcd-independence: two edges with coprime locator factors of degree >= 134,066 jointly annihilate >= 268,132 > n - m + t of the evaluation set only if their supports interleave — which may bound the sunflower width directly at the deployed row.

This import and the K'-ladder stack (#1170, prefix through K'=86) now share their residual surface: your rich-flat terminal (W vanishing on >= 42,453 columns) is a carrier-atlas object in the #1170 frame, and both stacks' chronology obligations are priced by the #1169 acceptance contract. Full audit + connection analysis at AllenGrahamHart/rs-mca-prize-dag node rate_half_mca_rank11_anticode_branch_payments_import (all three envelope identities independently recomputed; no collision with the local relative-ray frame).

🤖 Generated with Claude Code

https://claude.ai/code/session_01Ve3d3scwbLSLeo6ByidPxF