Research: exclude P112 3,4,6^8 with a weighted A6 cover

[petalas]

Summary

P112 profile 3,4,6^8, code-intersection dimension >= 6
  -> seven weight-six endpoints, allowance 140
  -> mixed root/D7 branch >= 142
  -> weighted root-A6 branch >= 141
  -> one actual TWOSIDE (6,4) profile excluded

Adds only research/p112-a6-weighted-cover/, with the characteristic-zero proof, exact receipt, pinned sources, separate finite checks and replay instructions. This answers one part of the C5 handoff. Canonical claim and its scope correction.

The new lemma retains a binary six-flat and four-flat plus the orthogonal puncture frame, while relaxing the rank-three support to four arbitrary coordinates. The initial 2,4,6^8 candidate was discarded because #3162 already excludes it. The present profile needs twelve certified cuts and has no rank-four nonbasis anchor, so the pinned ten-cut and twelve-cut-anchor results do not close it by that route.

Credit DreamingOfClouds/#3154 at 708f0ad8928c383de8294aea3c126e9461d2066d for TWOSIDE, Nick Petalas/#3176 at 1111a074414c4d2be8b4e230133d873432780814 for the retained support-72 alphabet and geometry, and the credited E8/P112 lineage in SOURCES.json, including #3164/#3175 and joaqcoo's model. Frame traversal is adapted from #3180. Canonical main remains 997e6a9ca7b4f95d50e366f61412fd640d72a88a, priority revision 6.

Evidence

• Before, forty arbitrary deletions give only 137 incidences; retaining the frame and six-flat but allowing twelve arbitrary small coordinates gives only 139. Neither exceeds 140. After, the actual four-flat restriction gives at least 141.
• Complete primary coverage includes 788,035 six-flats, 2,025 frames and 963,900 relevant four-flat tests. A separate forward-echelon census covers all 3,309,747 four-flats and reconstructs frames by Weyl orbit. Exact masks and weighted counts agree.
• A separate Gram-intersection, two-plus-three clique and integer-rank implementation agrees on all 7,350 mixed five-cliques, including 3,360 independent cases.
• Registered Python 3.12 replay and sixteen optimized controls pass. Python 3.13 agrees, including all four programs from the read-only Git-free export of the exact commit. Ruff, warning-as-error compilation, replay planning and all 22 publication-byte comparisons pass locally.
• Published commit: 92675b36a8e0ea41b40f0bcda2a3dd9f313abb0e. Remote branch head matches it.

python3.12 -B scripts/research_package.py --package research/p112-a6-weighted-cover

The standard Weyl-chamber theorem, inherited root-plane argument and original decoder reduction remain explicit dependencies. These are author checks with separately implemented finite algorithms, not independent human or proof-kernel review. Hosted CI is separate. No full C5, decoder-floor, supplier or new kappa claim; the selected frontier is unchanged.

Merge danger

Door: two-way.

Blast radius: research.

One isolated opt-in package. No shared-code, priority, selected-result or canonical frozen-input changes.