Research: exclude P112 5,5,6^6,7 by deleting one piece

[petalas]

Summary

P112 TWOSIDE (6,3): 5,5,6^6,7; code intersection >=6
  delete the ninth piece
  -> eight independent pieces 5,5,6^6; code intersection >=5
  -> six root-A5 endpoints, small support <=24
  -> required support 132 > allowance 120

Adds only research/p112-five-five-slice/. The new contribution is deleting the expensive piece before quotient normalization and applying the existing A5 bound to this actual profile. The ninth piece's weight is unused. The A5 spectrum is inherited from PR3188; PR3169's coordinate inequality supplies a separate 795<=784 contradiction.

Canonical investigation. A concurrent same-profile claim uses the same deletion and coordinate route. This package retains the separate endpoint count, exact replay and root-class calculation, without claiming exclusive priority or cancelling the other claim.

Credit DreamingOfClouds/PR3154 (708f0ad8928c383de8294aea3c126e9461d2066d), Nick Petalas/PR3192 (79864770165fe0d7b72c864be4d5a6e2af5e35b5), PR3188 (93f1fb95a2ab1413b2e9c90a6be4f3a2c4090034), PR3169 (2dbbd3004b70772cef200e341037c7c05b094fbc), and the retained PR3176/PR3186 and E8/P112 decoder lineage including joaqcoo. Exact heads, blobs, hashes, proof dependencies and open questions are included. Base is canonical main 997e6a9ca7b4f95d50e366f61412fd640d72a88a, priority revision 6.

Evidence

• Before: the unchanged original filter retains this excess-35 profile among 17 historical (6,3) profiles. Its weight-only two-six-flat cover needs twelve cuts, outside the eight-/ten-cut routes. After: the deletion theorem excludes the profile. This is not a claim that all other historical profiles remain open.
• The full source-bound replay checks all 3,309,747 five-flats, 788,035 six-flats, 7,140 root planes, 960 simple reflections and complete A5 extension orbits. A separate root-class count gives the same 0:4,1:36,2:60,3:20 spectrum.
• Registered CPython 3.12 replay and thirteen optimized behavioral groups pass. Read-only, Git-free CPython 3.13 replay of the final committed export and all thirteen controls pass. Source-origin checks, Ruff, warnings-as-errors compilation and all twenty committed package/input byte comparisons pass locally at 22f1479db213b1ed0de68cbc61ba15f6352d3276.
• Internal mathematical and artifact reviews found no blocker. The standard Weyl-chamber theorem and original decoder reduction remain written dependencies. These are author checks and internal reviews, not independent human or proof-kernel review. Hosted CI is separate.

uv run --python 3.12 --no-project python -W error -B scripts/research_package.py \
  --package research/p112-five-five-slice

No full C5, complete decoder floor, supplier admission, multiplication theorem or new kappa is claimed. The selected frontier and frozen sources are unchanged.

Merge Danger

Door: two-way.

Blast Radius: research.

One isolated opt-in proof package; no shared implementation or selected-result changes.