Research: exact mixed COPY62 retained-hit obstruction

[adamgall]

Result

Scoped negative result; no new supplier, κ, or selected-frontier change.

This independently sampled instance finds a concrete P112 COPY62 support proposal with nine rank-six star slices and one coordinate rank-eight rectangle. It passes every one of the 1,260 full-frame rank demands and covers all112 diagonals, unlike the homogeneous COPY60 witness in #1347.

Its complete source-bound retained-hit family is nevertheless excluded:

• Complete census: 7,616 tagged rank-seven parents, 967,232 maximal row slices.
• Each of the nine new hit patterns has two support representatives; all eight coordinate choices give 4,096 quotient cases.
• 4,093 fail diagonal coverage.
• The remaining three have exact two-root separators: (2,22), (4,22), (2,23). In each case only the coordinate rectangle can contribute, so a rank-one term cannot produce 4 I_2.
• A separate saturated-frame square-duality certificate also rejects the displayed support proposal.

The written domination argument covers arbitrary joint rank-at-most-six descendants retaining their assigned hits, independent transposition, arbitrary complex coefficients under ordinary transpose, arbitrary subtrimming of the coordinate rectangle, and extra cost-zero terms. Other COPY62 supports remain open. Broader solver timeouts are recorded as failures to finish, not impossibility proofs.

Why this question matters

The fully optimistic mixed profile retains the selected non-centre counts and replaces COPY64 with COPY62. Exact rational intervals give a ceiling [0.001783866218920,0.001783866218921], over 5.55% above the selected-word ceiling. This is a rejection screen only: frame changes, restoration, hosting and precision have not been realized or declared free in a supplier.

This changes #1347's homogeneous rank alphabet and its original ten patterns; it is not the existing 99-diagonal representative result with a larger seed. Credit #1347/#1323 and #1402 (Cinna Davis), the retained p112-rank6-cover-representatives package (@woklerx), and the PR1226/1236/1242/717/968 geometry and decoder lineage. The ceiling engine is PR1240's. Prior-round #1909 concerns a different tetrad-local alphabet and is not resubmitted here.

Verification

Only research/p112-rank6-hall-obstruction/ changes. Standard-library CPython 3.12.12, all exercised locally:

uv run --python 3.12 --no-project python -I -B research/p112-rank6-hall-obstruction/verify.py --write
uv run --python 3.12 --no-project python -I -O -B research/p112-rank6-hall-obstruction/verify.py
uv run --python 3.12 --no-project python scripts/research_package.py --package research/p112-rank6-hall-obstruction

All returned:

PASS_P112_MIXED62_QUOTIENT parents=7616 slices=967232 families=4096 diagonal_survivors=3 rank2_rejections=3 controls=9

The registered replay also returned PASS_REGISTERED_RESEARCH_PACKAGE ... outcome=negative-result. The combined three-command phase took12.30s on the recorded host. Positive evidence includes12,544 exact coordinate-decoder entries,10,080 term traces,48 rational square-dual fixtures and an ordinary-transpose complex fixture. The exact scan covers all262,928 orthogonal cliques, including those without live eight-frame extensions.

No full selected-frontier cold replay, native compiler/admission, hosted CI, Lean proof or independent human review is claimed. See VALIDATION.json, CERTIFICATE.json, SOURCES.json, OVERLAP.json and the README's precise theorem and open next question.

Independent selection and coordination

• Seed: 5130d276c01dfff62d214a1fd73e9011
• Track/card: complex-mechanisms / complex-rank-shape-decoder
• Exact baseline: 0b1cccf86e2f5132ed286a26ef0a681a495740ea
• Full chooser provenance: SELECTION.json
• Round2 claim

Prepared by Adam Gall with substantial OpenAI Codex GPT-6 Astra assistance in research, proof reasoning, experiments, implementation and documentation. Apache-2.0; predecessor sources/notices remain unchanged.

[Mister-Meeseeks]

Batch review at 5dba7ccd60b2abe16f5931b3754cf02a92e1f511.

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

Reviewed scope: Complete967232 maximal slices reduce the fixed mixedCOPY62 retained-hit family to4096 choices:4093miss a diagonal and3fail explicit orthogonal-pair rank cuts. Independent rank elimination,262928cliques,positive coordinate decoder and9 controls pass. Joint-trim domination proof reviewed; otherCOPY62patterns and heuristic solver outcomes remain outside the exclusion.

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.