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Rule out role-specific phase deletion in the selected P104 word (no new κ) - #6331
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Mister-Meeseeks merged 1 commit intoOct 31, 2026
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Prepared for @CubeJerry with substantial OpenAI Codex assistance. No new kappa; all selected framework assumptions remain.
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Resolve the role/history-specific gauge question left by #6298 for the selected #6030 word. Even arbitrary input-independent phases at every role and event cannot delete all literal MOVE phase tags while preserving scalar coefficients, unless 4 divides the column multiplicity. Fourteen reached events suffice: eight ADDs with exact rank-two operand certificates and six rank-one MOVEs. Free endpoints and omitted dependent-ADD constraints do not remove the contradiction.
Base: a7638a4.
Selected WORD SHA256: 7834725d9e34ee846a9ccc615221ea81e0201613938afa185d2eda0c9a6c232f.
Exact native/interpreter and predecessor pins: SOURCES.json and TASK.json.
Reproduce (Python 3.12, stdlib):
Expected:
PASS_ROLE_PHASE_COMPATIBILITY,PASS_INDEPENDENT_ROLE_PHASEandPASS_REGISTERED_RESEARCH_PACKAGE.Executed: 9,998-event rational-row replay, eight nonzero minors, all 512 columns of six native edges and both relative paths. Separate integer-dyadic column replay and relaxed event-gauge graphs confirm the certificate. Controls challenge missing independence, hidden writes, wrong phases, omitted compensation and actual source/result corruption; opening the cycle restores consistency. Normal/-O, committed-byte/mode, export and read-only Git-free replay pass. Full-history preflight was not run in the shallow checkout.
No new κ. This is a gatewise fixed-coefficient obstruction, not a defect in the phase-preserving implementation or a lower bound for all resyntheses. Changed coefficients, endpoint-only equivalence and a fully priced replacement remain open. All five selected assumptions remain.
By @CubeJerry with substantial OpenAI Codex assistance and separate row/column verification. Credit Nick Petalas (#6298/#6025), unpaidmoon (#6293), DreamingOfClouds (#6030), Ali Romman and retained native lineage. No human/proof-kernel acceptance.
Proof, exact pins and limits: https://github.com/CubeJerry/integer-mult-bounds/tree/080e8366d98be7e9dc97d5f57f64f60017a474e7/research/role-phase-compatibility
Complete remote Git tree matches the tested contribution.