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Audit the relay premise in the P104 carrier-merge bound (no new κ) - #6323
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A common merge frame does not establish the source-normal retention used to apply #6315's merge lemmas when public relays are allowed. Exact receiver-covering walks expose that missing implication; the Lean theorem statements themselves are not refuted. Prove the repaired bound total+(k-1)tau >= 7k+sum(eta_c), recovering 8k under explicit source-normal retention.
Base: 2485805.
Audited #6315: 3667554. Exact source blobs/hashes: PREDECESSOR.json and SOURCES.json.
Reproduce (CPython 3.12, stdlib):
Expected: PASS_REGISTERED_RESEARCH_PACKAGE.
Executed: four normal/optimized primary and independent commands; all 247 carrier subsets, two actual endpoint-chart examples, 2,457 small-lattice instances and 383 independent dimension tuples. Wrong geometry and missing source/coverage hypotheses reject. Sixteen actual source/manifest/receipt corruptions reject; committed bytes/modes, export integrity and read-only Git-free replays pass. Fixed exhaustive domains; no random search. Complete remote tree equals the tested tree.
No new κ. This is an abstract-walk premise audit and scoped dimension proof, not a cheaper dirty-restored physical program or a counterexample to the pair floor 14. Purity/restoration, full-span and no-cover implications remain open; all five framework assumptions remain. No Lean build, hosted CI, selected cold replay or complete-history preflight claimed.
Prepared for @CubeJerry with substantial OpenAI Codex assistance, including separate source/geometry review. Credit Matarener (#6315) and DreamingOfClouds (#6030), with retained lineage. Apache-2.0.
Proof, validation and open questions:
https://github.com/CubeJerry/integer-mult-bounds/tree/f3bebf8236dec18dea8ec6b714a12dda6cf25243/research/carrier-merge-relay-premise