[aliromman]

The common-coframe decoder in Dugongue's PR5687 needs a new recursive invoice. This package proves that every coordinate common-main coframe assignment to the retained full nine-axis centre-free word has paid rank mass minus helper rank mass at least 2464. It also permits paid replacement warps. Eight exact integral flow/cut certificates prove the minimum, and one assignment attains it while leaving every native warp ordinary.

The complete consequence is negative: every p >= 1 and every prefix split in the standard query-thinned caller loses for supplier saving 0 <= C <= .01. Its target-minus-paid moment is at most -(53126/125)(p+2)-112. At p16 the rank surplus is at most -10192. No new kappa, complete supplier or selected-frontier change is claimed. Different native words, non-coordinate Clifford coframes and different callers remain outside the theorem.

The verifier rebuilds both complete source graphs and all 408 helper endpoint debits. It checks capacities, conservation and flow=cut directly, without running the discovery optimizer. The attaining invoice is 796 H1+348 H8+281 H9 paid and 405 H9+3 ordinary identity outputs returned. No original helper is erased or double-counted. The all-p proof grants the ordinary decoder and all extra ordinary work for free, so the rejection does not rely on a new machine implementation.

python3.12 -B scripts/research_package.py --package research/common-coframe-coordinate-cut

Registered normal and optimized checks pass, including six corrupted-certificate controls. The exact 16-file committed-byte check, official export integrity check, Git-free optimized replay with empty PATH, and an actual damaged-source rejection pass. Scientific replay commit: c4cfb6aac99933fb6dd5454f4ad18b89bc9aa377; final documentation records that evidence. No full native/phase, precision, stock, tape, ordinary/outer admission, proof assistant or independent human review was run. Full-history ancestry is unavailable in the shallow checkout. Hosted CI is separate.

Base and canonical refresh: df0137efd35e11b4445734bf612bdd4c7ebc330c, priority revision 7. Scoped coordination separates this full nine-axis source from PR5698's restricted eight-plane optimum and active native/helper searches. Only research/common-coframe-coordinate-cut is added.

Credit Dugongue PR5687 for the ordinary decoder; Cinna Davis, Dugongue and the retained centre-free source; Cao Yifan's native word; DaysSky, Nick Petalas, Ryanson Jonathan, zxv, Jacob Alan Sussman and all source notices. Discovery reused Ali Romman's PR5698 flow routine; the new verifier checks its certificates independently of that optimizer. PR5693 supplies a parallel general cut direction. Flow/cut duality and concavity are classical. New source specialization, witnesses and caller bound: Ali Romman, with substantial OpenAI Codex assistance and no subagents. Apache-2.0.

Hosted CI at final head: run 40286868279 ran 449 shared tests, with 21 skipped. The plan failed the two existing CurrentCiNavigationTests checks for the selected review and source-manifest links in current-status.md. This PR does not edit those files. The package replay job was skipped. The local scientific replay evidence above remains separate; hosted replay and independent review are not claimed.