Certify rank-seven chronological packing bound and cost-neutral repair

[RossRichardson]

PR2979 changes the helper-boundary inventory, so its favorable pattern mix also needs legal chronological placement. This adds an independent source-bound check of that bridge: the naive integer mix is short by 473 width-seven slots on its strongest contiguous interval, while the declared saturated pattern swap preserves every rank tariff. The existing 1,063-swap T74 witness passes the new literal geometry checker.

The proof derives the 13,440-bin / 14,976-role cut from the source event template and exact order, checks all 55,611 contiguous intervals and all 1,064 points of the stipulated pattern family, then independently checks all 271,728 final helper roles, masks, source windows, compact prefixes and physical-family exclusions. Both copies project to identical T37 rows, and the complete conditional paid histogram agrees with a separate pattern derivation. The precise lower bound is k >= 473; k=473 only passes this necessary cut. The pattern family permits at most one width-seven helper per capacity-16 bin, so this is not an unrestricted packing obstruction.

The swap preserves the near-cap integer profile; it does not attain or recertify the fractional cap. Native width derivation, arbitrary-dirty-input/restoration/phase arithmetic, stock, precision/tape, outer release and all-size/compiler implications remain inherited premises. No new supplier, kappa, formal-kernel or independent human proof is claimed.

Validation: registered CPython 3.12, optimized 3.12 and read-only Git-free optimized 3.14 replay agree. Thirteen mathematical rejection controls and one frozen-source-byte control pass. All 33 committed files match tested bytes, and all 19 frozen exports bind to their original Git blobs/SHA256. The patch applies to refreshed canonical main b3f3ee0392b71b118fd086a6eaf6b4cab54ef455 (16:12 UTC); priority 5 and selected record are unchanged. Hosted checks are separate; no rerun or dispatch requested.

Exact predecessor: PR2979 at be191346391661f4d35fc0d1508d0a6029572576. Credit Marius-Paul Dumitrean for the construction, cut and swap; Kothe, Dugongue, Hale, Diviney, Lu, themilkman216, Tekalign, icekylinx and the retained chronology/owner lineage. Ross Richardson with substantial OpenAI Codex assistance and separate AI mathematical checks; Apache-2.0.

Reproduce: python3.12 scripts/research_package.py --package research/rank7-chronological-face. Proofs, exact result, pins, portability scope and open questions are in that package. Canonical investigation claim. Next useful task is full chronological feasibility for the remaining 473 <= k <= 1063 interval, rather than another cap-root calculation.