Remove two staged544 scalar ADDs with an A2 graph identity

[Clear1nsight]

This changes the literal scalar graph using an A2/Steinberg transvection identity. The three ADDs at A1858 contract to two, removing one forward and one inverse-cleanup ADD on both PR3734 providers and on both current PR3945 terminal-gap-filled words. The complete recursive histogram is unchanged in each source family. All other top-level fields, including the actual native operators and normalization, remain byte-identical for the PR3945 construction. No new supplier or κ is claimed.

The same focused package exhausts the complementary consecutive two-to-three graph rewrite on the older PR3734 words only. Each provider has 168 directed two-ADD motifs and 460 legal common-frame flags across all three central-gate positions.396 flags tie the original recursive moment;64 strictly lose for every 0<a<1, by four explicit subadditivity inequalities. The dimension-only relaxation has 2714 triples including 1014 uncertified nominees; exact subspace geometry prevents a favorable realization. These results cover A after the prelude, B between native warp cuts and restore, with all other boundaries fixed. They do not cover separated events or changed interfaces.

The literal contraction has exactly one legal frame assignment per source word. A bounded rescan after contraction finds no further consecutive inverse A2 motif. The source-bound words, replacement gates, canonical word/cleanup digests, every expansion flag, complete recursive invoice, finite coefficient heights, primitive counts and unresolved costs are retained. This pairs framed rational circuit optimization with algebraic-group/root-system identities and exact dirty-state linear algebra; it changes the event graph rather than extending the retiming radius.

Validation checks exact rational dirty block matrices and the full chronological invoice/hygiene for every legal flag. All four baselines and all four contracted words receive full 723-input ordinary/dual/reverse and cleanup-boundary replay. Expanded whole-word interpreter coverage is six deterministic samples per PR3734 provider; universal coverage uses the exact local composition and projected inverse-cleanup proof. Independent controls enumerate 494 frame intervals and 922 local invoices, reproduce complete flag sets, prove 36 symbolic polynomial identities, reject 108 sign/product/omission mutants, and reject an actual production sign mutation and a missing cleanup operation. Normal and optimized controls pass. Exact registered replay and export/publication evidence are recorded in the final handoff below and VALIDATION.json.

Reproduce with python3 -B scripts/research_package.py --package research/staged544-a2-graph-rewrite. The standalone verifier is Git-free and read-only by default. An optional explicit export writes the contracted PR3734 word outside the package, refusing existing outputs. Physical allocation/owner scheduling, native phase admission, uniform precision/stock/tape, all-size compiler and outer/analytic/BIT obligations remain inherited or unknown, never zero.

Exact sources: PR3734 fa041037a3374eaa08feeca0b26a5d6893194147; PR3945 91f81d131252db704f945891da1ea54e29d46b8b; canonical base 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6. Current main was rechecked unchanged at 08:07:33UTC. Overlap includes 698 fully paginated open PR bodies at 08:17:28UTC and partial signed-in Discussion coverage, not an exhaustive novelty certificate. PR3975's selected-provider rank-two macro-fusion screen and PR3982's R437 parabolic COPY construction concern different objects and contracts.

Credit dataisfire's literal providers; Dugongue's PR3945 construction and PR3863 paid-overhead target; Jeremy Kothe's retained rank-profile rewrites; PR3886's trace/subspace routines; and the Sagar Thakrar, roger-sato and Arham Tahir auditor lineage. Original source and native-lineage notices are preserved. Prepared by Chris R / Clear1nsight with substantial OpenAI Codex assistance; Apache-2.0. Author-checked finite construction/certificate, no independent human or formal-kernel review. Only the new scoped research package is added; no merge, closure or selected-frontier change.

Final prepublication verification: the complete registered replay passed (base180.154s, extra156.274s, optimized controls4.351s), including the PR3945 single-block applicability. Normal controls5.439s, optimized controls4.417s and isolated optimized read-only Git-free controls5.796s also passed. Git-free execution covers the complete controls, not a second complete census. All six Python source hashes match the scientific freeze.

[ToikY]

CLAIM — bounded separated-A2 follow-up to #3998 at 389268a, on the two frozen PR3734 providers only. Seven strict separated three-ADD motifs per provider have intervening events disjoint from their three registers and cross no native warp. The preliminary complete bill removes seven forward and five inverse-cleanup ADDs beyond the credited consecutive A1858 contraction, while retaining the complete recursive histogram {1:2440,2:725,3:224,4:102,5:20,8:8}. Scope is now frozen witness certification and the unchanged-paid-profile result, not more search or native expansion. Next: exact whole-word/dual/cleanup checks and a separate rational/composition checker; stop if these fail. No measured speedup, new supplier or kappa claim. #1865 is credited as earlier nonconsecutive commuting fanout work, with a different C3 identity/source. #3886/#3941/#3942/#3957 retime the fixed graph; these contractions change it. Canonical main20ecf289/priority6 refreshed; 711 fully paginated open PR bodies including drafts plus live1166/active-board/source checks, broader Discussion/closed/code coverage partial. Handoff-first refined scalar-to-moment, changed from historical R439 to an explicit fresh PR3734 graph witness. Science cutoff09:41:56UTC; claim expires09:56:56UTC on2026-10-19. Credit Chris R/Clear1nsight3998, dataisfire3734, Dugongue3945/3863, Jeremy Kothe and retained trace/subspace/native/auditor lineage. ToikY with substantial OpenAI Codex assistance and separate AI check context. No merge or frontier change.

[Clear1nsight]

FINDING / HANDOFF — bounded graph-Gaussian screen stopped; no new PR or κ.

On both frozen PR3945 providers at 91f81d131252db704f945891da1ea54e29d46b8b, we tested length3–8 ADD windows on3 or4 registers, using every unit-pivot column order and ascending/descending Gaussian row-elimination order, with replacements at most two instructions longer and fixed external/native/caller boundaries. Per provider:3164 windows,6573 distinct changed factorizations;5710 compatible and863 incompatible. Exact frame/profile-set optimization priced6141 replacement/profile cases:5682 ties and459 strict losses. The51 reduced signed types are non-improving for every0<a<1 by exact Abel-prefix inequalities. These are reduced profile cases, not all possible circuits/Gaussian words.

Local matrix identities for all13146 replacements were recalculated. Separate RREF/brute-force controls cover18 stratified replacements,96 intervals and132 flags, with102 signed rows and66 wrong-coefficient controls. The optimistic direct-climb allowance favored1009 windows, but full geometry/successor charges remove those opportunities.

Evidence is LOCAL-ONLY and provisional for external review: no new hosted package, whole-word replay, registry, optimized/Git-free replay or supplier acceptance is asserted. The mathematical class and counts above delimit the finding; a larger-window campaign is not justified by it. Reopen with an actual changed native/caller boundary or a positive complete allowance. Main20ecf289 and the selected frontier remain unchanged. No continuing reservation; no advance claim was posted.

Credit PR3998, PR3886/3941/3942/3957/3964/3970, dataisfire, Dugongue, Jeremy Kothe and the retained compiler/packing lineage. Chris R / Clear1nsight with substantial OpenAI Codex assistance.

This differs from ToikY’s active separated-A2 witness claim above on PR3734. Our bounded PR3945 Gaussian result imposes no restriction on that different class/source.

[ToikY]

DONE / claim released — PR4019, exact head f408e09, certifies the seven fixed separated A2 contractions on both frozen PR3734 providers. Beyond your credited A1858 contraction: seven forward plus five projected-cleanup ADD records removed; full paid histogram, helper widths and native descriptors/order unchanged. No recursive/κ/runtime gain, later-PR3945 applicability or native admission is claimed.

Full723-input source/credited/final ordinary/dual/reverse/cleanup checks, separate rational/composition/point-set frame checker (149 complete boundary states/provider),40 production controls and14 independent semantic cases pass. Exact19-file byte/history and official export checks pass; all four commands normal/-O pass in a fully read-only20-file Git-free empty-PATH export with unchanged bytes/modes/inodes. Hosted CI39229105796 passes on exact head and CPython3.12.15.

Full Discussion handoff and remaining obligations. Your separate PR3945 Gaussian-window result is acknowledged as a different class/source. Credit remains with Chris R/Clear1nsight3998, dataisfire3734, Sagar Thakrar/roger-sato/Arham Tahir, Jeremy Kothe, Dugongue and the retained native/owner/compiler lineage, with1865 credited as the earlier different nonconsecutive C3 precedent. New fixed witness/checks by ToikY with substantial OpenAI Codex assistance and separate AI contexts. No continuing reservation, merge, closure or frontier change; maintainer edits disabled.