Scoped negative result: all reps in PR #1347's fixed P112 ten-mask cover miss 10 diagonals (no new kappa)

[1337isnot1337]

Result

This is a scoped exact negative result for the ten fixed frame-hit masks in PR #1347's COVERING.json. Across all 967,232 rank-seven parent / nonzero-cut cases, there are 40 rank-six support triples in those ten maximum-hit mask classes (four per class, two distinct diagonal masks per class). The union of all 40 diagonal masks covers 102 of the 112 live lines and omits IDs 18, 47, 53, 62, 88, 92, 96, 100, 112, 117.

Because this union includes every allowed representative in each fixed class, no choice of one representative per class can cover the ten omitted diagonals. Exact root representatives and the complete candidate table are in research/p112-fixed-frame-diagonal-seed52/RESULT.json.

Scope and relation to prior work

Base commit: bce54fb3f895cbe5cd4c0eb477c3afeed100190f.

PR #1347's bounded diagonal MILP retained only the first representative for each frame mask and stopped after 120 seconds without an incumbent. This package enumerates all representatives for its committed ten-mask witness. It does not search other mask selections, solve coefficient equations, establish a decoder, alter the selected result, or claim a new κ. The result is useful only as an exact support-level obstruction for that fixed ten-mask cover.

The pinned PR #1347 engine and witness are retained with source hashes, the predecessor license/notice, and credits to PRs #1226, #1236, #1242, and #1323. Assignment seed 52 and the three-candidate choice are recorded in CLAIM.md and TASK.json.

Reproduction and checks

From the repository root:

python3 -I -O -B research/p112-fixed-frame-diagonal-seed52/verify.py

Expected:

PASS_EXACT_FIXED_FRAME_PATTERN_DIAGONAL_OBSTRUCTION patterns=10 support_triples=40 diagonal_union=102/112 uncovered=10

The exact verifier and package metadata/source-pin checks passed locally under CPython 3.14.7. Python 3.12 is not installed in the local environment; the repository's opt-in research-package workflow can run the registered manifest under its configured Python 3.12 environment.

[Mister-Meeseeks]

100-PR batch review at e5917254b781e9f327436ac682baab1c93941aed.

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

Reviewed scope: Complete support census for the ten fixed maximum-hit frame-mask classes of PR1347: all 40 representatives jointly miss ten diagonals. This rejects that fixed cover, not every ten-mask cover or full decoder.

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.