research: exclude two P112 profiles with unequal endpoints

[petalas]

Summary

TWOSIDE (6,4): 3,5^3,6^5,7 or 4^2,5^2,6^5,7
  delete the unrestricted last piece
  retain five code dimensions on nine independent pieces
  small support <= 28; endpoint capacities = 12,20,20,20,20,20
  PR3169 coordinate inequality forces 795 <= 784

Proves both profiles impossible over every characteristic-zero field. The new contribution is the unequal-endpoint application, not a new A5 inequality. Source, proof, exact receipt and registered reproduction are in research/p112-unequal-endpoint-deletion/.

Credit DreamingOfClouds/#3154 for TWOSIDE and the original reduction; Nick Petalas/#3169 for the coordinate inequality, #3197 for the distinct uniform-endpoint deletion application, #3195 for the shorter adjacent caller, and the retained E8/P112 geometry and decoder lineage.

Evidence

• Before: both profiles pass the 69-profile historical filter. Their best weight-certified two-flat covers need sixteen cuts, beyond the fourteen-cut rule. The old incidence upper bound is 812; a uniform endpoint charge gives 816.
• After: both exact invoices give upper bound 784 against required 795. All 4,097,782 inherited five/six-flats and 117,649 endpoint assignments replay. Twelve behavioral groups, the separate cover oracle and four semantic mutant rejections pass.
• Registered Python 3.12 replay passes. The exact committed, read-only, Git-free export passes replay and all tests under optimized Python 3.13. All 15 package/input Git-byte comparisons and archive-integrity checks pass at c9926e2f4adf2c6adfc2a6dba358b2eff581ab87.
• Reproduce: python3.12 -B scripts/research_package.py --package research/p112-unequal-endpoint-deletion.

Canonical main remained 463113d675af7410ac91d53a4fed51ec6494eb9a at submission. The 17:13 UTC overlap refresh covered 246 open PRs and 1,988 Discussion records with complete pagination and no warnings; exact-profile hits were this package and its claim. This is not a novelty guarantee. Canonical investigation and claim.

Evidence is author-checked. The geometry engine is re-executed, not independently reimplemented. Standard Weyl theory and the original decoder reduction remain dependencies. No full C5, decoder floor, supplier admission or new kappa is claimed; no native/full supplier or proof-kernel replay was run. Development and local checks used substantial automated assistance.

Merge Danger

Door: two-way

Blast Radius: isolated

New research package only. Frozen inputs, shared code, priorities and the selected frontier are unchanged.