Prove A5 shortening and exclude P112 2,5^2,6^6,7

[petalas]

Summary

Prove a characteristic-zero P112 shortening lemma with common small support at most 29, then exclude the actual TWOSIDE (6,4) profile 2,5^2,6^6,7.

10 independent pieces, code dimension >=6
    delete the unrestricted last piece
9 independent pieces, code dimension >=5
    common small support <=26, six endpoint supports <=20
A5 endpoint requirement >=128 > allowance 120

The A5 spectrum is inherited from Nick Petalas/PR3188 and the deletion method from PR3195. PR3197's support 24 application is credited. DreamingOfClouds/PR3154 supplies TWOSIDE and the original filter; retained geometry preserves the E8/P112 lineage, including joaqcoo. Exact heads, blobs, hashes, proof, evidence, reproduction and open questions are in the package. Canonical investigation.

Evidence

• Before: the coordinate inequality gives only 795<=800 at support 26 and cannot exclude this caller.
• After: the full A5 spectrum requires 128>120; the general support 29 lemma still gives 122>120. At support 30 both the strict count and root-only premise cease to certify a contradiction.
• Registered CPython 3.12.15 replay and all 18 optimized behavioral controls pass, including complete historical-table validation, source/receipt corruption and ambient-module collisions. The exact committed read-only Git-free export passes replay and all 18 controls on CPython 3.13.16. All 19 publication-byte comparisons pass. Ruff, formatting and compilation checks pass.
• Finite coverage includes all 4,097,782 five-/six-flats, 7,140 root planes, 960 reflections and complete A5 extension orbits. Internal mathematical and fresh artifact reviews found no remaining substantive objection. Evidence is author-checked; independent human and proof-kernel review remain separate.

Reproduce from the repository root:

RUN="$HOME/.cache/integer-mult-bounds-runs/a5-shortening-review"
mkdir -p "$RUN"
TMPDIR="$RUN" uv run --python 3.12 --no-project python -W error -B \
  scripts/research_package.py --package research/p112-a5-shortening

Merge Danger

Door: two-way

Blast Radius: isolated

Only the new research package changes. This closes one actual profile, not full C5, the complete decoder floor, a supplier or a new kappa. The standard Weyl-chamber theorem and original decoder reduction remain dependencies. The selected frontier and frozen inputs are unchanged; no full supplier cold replay, Lean or Docker build is claimed. Development used substantial automated drafting and finite checks.