Eliminate duplicate fixed-PAIR ancestors in physical coefficient evaluation

[Clear1nsight]

The retained physical coefficient evaluator computes an identical ancestor twice when a prepared PAIR permutation fixes the requested head field. This PR adds a source-guarded package-local CSE adapter that evaluates it once while retaining ancestor validation, the unit inverse check and both multiplications.

On the stated all-fixed-head-PAIR subclass, preparation count improves from 2^d-1 to d. The actual serialized coefficient fixture at d=3 uses 7→3 preparations, 2,840,912→2,228,010 record actions (21.57% fewer) and 90,711,429→39,007,018 numerical word actions (57.00% fewer), including both admissions, program extension, stacks, erasure and restoration. No record tapes or numerical backing are added. A finite bounded row comparison is additional control work and is explicitly charged separately.

The proof is uniform over accepted stable inputs and arbitrary prime-power high lifts because the guard checks the actual prepared permutation. Ordinary nonfixed PAIR, GOOD, reverse tail, UNIT/half-unit and negative inverse remain covered. General nonfixed trees may still branch exponentially; no global DAG or linear-total-cost claim is made.

The full component bill remains K_CSE=A_parent+E+A_leaf+W_CSE+N+D; each physical leaf atom/prefix still performs four positive and two negative-inverse coefficient calls. Source production, complete payload transport, original-width stock and remaining physical tariffs are open. The selected conditional kappa is unchanged.

Validation: 11 original/adapted serialized-path pairs against an independent matrix oracle with runtime Word.inspect disabled; high-digit/root rejection and cleanup, false-fixed-guard mutant, AST/source authentication; normal/optimized/Git-free replay with corruption controls. Separate same-session AI review tested six extra mixed histories/nonzero coordinates/mod27 lifts. This is not human or formal-kernel acceptance.

Package fixtures are admitted rank-seven definitions in the exact physical runtime, not a reconstructed complete R437 catalogue. A separately labelled local-only check on PR4008’s frozen actual IDLE27776/rank26→COPY1603/rank7 fixture confirms 3→2 preparations with the same value/bytes/heads/arena audits; that pending-source witness is not part of this PR’s canonical-only CI claim.

Predecessor credit: PR4008 (70c5ed674c7dc1c339254bae3818dd52a0015ac1) identified the duplicate ancestor and six-call bill; PR4011 (fc1426353de3389409a27e5b9bc146a95edf811c) independently optimizes admission, which remains unchanged here. Runtime/normal forms retain Jose Manuel, David Arias and source527/PR2160/2159/2234/2310/2332/2405/2697/2753 credit; current-source work retains zxv/PR3690, PR3950/3967 and the correspondence/stock chain attribution in README.

Authored under Chris R / Clear1nsight with substantial OpenAI Codex assistance. All changes stay inside research/r437-fixed-pair-cse/; frozen sources and selected frontier are unchanged.

Published head 5127d57d3ca6768969c7194343db373fe4c6c8df passes exact21-file package/input byte and canonical-source-history preflight. The11 new package files have unchanged science after the final combined registered replay. Canonical20ec/priority6 refreshed unchanged after the publication delay at12:15UTC; science frozen11:12. Claim. Hosted CI pending at creation. Reproduce with python3 -B scripts/research_package.py --package research/r437-fixed-pair-cse.