Research: sharp k8 factory register bound and target frame barriers (no new kappa)

[aliromman]

The retained k8 source-factory interface needs at least 224 helpers in addition to its 112 sources. This proof permits arbitrary rational scalar gates, cancellation, undo and redo, gate reordering, and operations between blocks. It does not fix the operation multiset. The 192 required values have 168 incomparable support frames; first formation requires two distinct registers at each frame. All 14 packet programs are executed to check the matching 224-helper upper witness, and all 192 values are bound to the actual final seven-slot word.

Review files: Proof and scope · Evidence · Source pins and credit.

The package also proves that none of the 112 target end frames can contain any of the eight complete cold-block frames or any of the eight complete center frames. Exact replay shows why scalar restoration is insufficient: all 32 cold helpers can be restored after A on all 704 arbitrary input columns, but their frames still prevent whole-block target borrowing. A complete two-cap split calculation requires six or eight carriers. A four-cap, four-carrier algebraic witness shows the limit of that split result. A separate cost screen covers only descent between local formation jobs with the remaining invoice fixed.

This is a scoped negative result. It does not prove the full 480-helper word optimal, does not bound a fixed-count paid profile, and does not supply a new kappa. Target dirt, formation and restoration of mixed-cap carriers, new private queries, and changed interfaces remain open. No source guard was weakened.

Reproduce offline with Python 3.10+ and the standard library:

python3 -I -O -B research/k8-frame-antichain/verify.py
python3 -I -O -B research/k8-frame-antichain/independent.py

Both pass. The independent checker imports no primary code; it checks 112 scalar columns, all 192 value witnesses, 168 antichain frames, 112 split ranks by integer determinants, and 1,792 cap pairs. Five mathematical controls, normal and optimized relocation, an actual word corruption, a missing-certificate-value control, and whitespace checks pass. The separate unchanged seven-slot native rebuild passed all 2,896 exact phase edges. Its commands, pins, and limits are recorded. The seven-slot-specific 34 controls and old owner-map replay were not repeated by this lane; the concurrent owner lane owns its new complete invoice. No hosted CI, new full supplier audit, or formal multiplication theorem proof is claimed.

Exact experiment base: abdc6a7002abdbcd9e21bfc5e1a795784deacfdf. Main advanced to ba82555c64e1879e4b7decce28186f208fcb8262 and selected PR #1042 during the work; the package keeps its source pins. PR #1074 source: 052afc128954f7b6a2b3c409eb4d72248e4020f2. Rebuilt raw word content: c2b294300760e1fd6eeab8c22c4d13e4633dca40e52cac8da0d68163a76e3ca8. Only research/k8-frame-antichain/ is added; selected records and upstream/ are unchanged.

The overlap refresh reached PR #1128. PR #899 is the prior fixed-operation-multiset helper result. PR #1126 studies a positive-lift ADD minimum for the cell cores, with a different alphabet and objective. PR #1103 and PR #1105 concern distinct target-borrowing interfaces. PR #1107 and PR #1124 change the local endpoints or word and are not excluded by this result. Source and predecessor credit are in NOTICE.md and SOURCES.json.

Prepared for Ali Romman (@aliromman), with substantial OpenAI Codex assistance in research, proof, implementation, and review. Apache-2.0. All inherited realization and analytic assumptions remain.

[Mister-Meeseeks]

100-PR batch review at 8e2e18b93d8c6b302e540ad5edc767cb98cf1514.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Antichain first-formation argument gives 224 extra registers for the specified k8 value/frame interface; target caps and limited descent invoice, not full-word optimality.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.