[petalas]

Summary

- The literal 2,5,6^8 caller has an open small-piece support obligation.
+ Pieces of support ranks 2,5,6,6 span no nonzero P112 root-code word.
+ The caller must have eight distinct projective quotient endpoints.

Prove sharp full-root near-normal section rigidity at thresholds eleven and seventeen. Reflection closure and the four missing-frame partners contradict the four-piece support budget's slack one. The theorem holds over every characteristic-zero field under the standard E8 Weyl-chamber premise, with arbitrary coefficients, overlaps and cancellations.

This is a partial answer to PR3295's caller handoff. Full 2,5,6^8 exclusion remains open. No full C5, decoder floor, physical supplier, new kappa or selected-frontier change is claimed. Only research/p112-root-support-rigidity/ is added.

Evidence

• Before: the retained handoff did not supply the four-piece representation exclusion. After: the written proof, exact section receipts and precise quotient implication are in PROOF.md and RESULT.json.
• Complete annihilator enumeration covers 4,097,782 binary spaces. A separate affine-coset enumeration covers 3,989,832 sections and accounts for the leading-zero spaces. Complete histograms and critical support-set hashes agree. All 112 literal frame-partner inventories and the 120-normal transport pass.
• Registered CPython 3.12.15, optimized CPython 3.15, two sharp boundary controls, four actual false-receipt CLI controls, duplicate-key and changed/linked-source controls, Ruff and formatting pass. Exact committed-byte/source-history checks and all three actual optimized read-only Git-free committed-export commands pass; all sixteen exported hashes remain unchanged.

python3.12 -W error -B scripts/research_package.py \
  --package research/p112-root-support-rigidity

Canonical base and submission refresh are 6f100d4bb5083f8c35d96fd95a539811c62f245c, priority revision 6. Final bounded overlap covered 307 open PRs and 2,234 Discussion records with complete pagination; arbitrary diffs and unpublished work remain outside coverage. Canonical claim and scope.

Both enumeration engines share authenticated geometry and digest encoding. The standard Weyl theorem, full caller exclusion, human/proof-kernel review, historical heavy caller suites, selected cold replay, Lean and Docker remain outside the executed checks. Credit Nick Petalas/PR3295 and PR3289, PR3161/3162 and the root-simplex geometry, DreamingOfClouds/PR3154, joaqcoo and the retained E8/P112 lineage. Exact source pins and open next questions are included.

Merge Danger

Door: two-way.

Blast Radius: isolated.

One new opt-in research package. Archival retention does not admit a supplier or select a frontier.