Research: exclude the final two P112 (5,4) beta shapes

[petalas]

Summary

Exclude the two remaining TWOSIDE (b,t)=(5,4) beta weight shapes reported by #3162, over every characteristic-zero field.

 Pinned fifteen-shape residue after the preceding thirteen exclusions:
-3,4^2,6^6
-2,5^3,6^5
+Both excluded by the root-simplex inequality 15*53 - 9s <= 5U

Three small pieces leave six pieces in a one-dimensional quotient. Their fundamental codewords form a root A5 simplex, whose fifteen edges meet any coordinate at most nine times. Counting outside the small supports gives 615 <= 600 and 561 <= 560, both impossible. The second margin is exactly one.

The new package contains the full proof, exact source pins, bounded standard-library replay, receipt, controls and open next questions. Credit DreamingOfClouds/#3154 for TWOSIDE and the handoff, Nick Petalas/#3161/#3162 for the preceding exclusions and geometry convention, and the retained E8/P112 decoder lineage.

Evidence

• Before: Research: prove a ten-deletion P112 span bound #3162 leaves the two named shapes. After: the new theorem excludes both under its explicit nine-piece/code-intersection hypotheses. Combining with the earlier thirteen exclusions inherits that predecessor's finite theorem and TWOSIDE filters.
• The registered Python 3.12 replay passes all 4,097,782 five/six-flat kernels, 7,140 root-plane pairs, 960 simple reflections and 17 behavioral groups. Optimized Python 3.13 and a read-only Git-free source export give the same receipt.
• All 14 publication-byte comparisons pass for commit 857384079ab640a949fb7618b7909664d3e737e5. Internal mathematical and implementation reviews found no substantiated objection. Hosted CI and independent human/proof-kernel review are separate.

python3.12 scripts/research_package.py --package research/p112-root-simplex-exclusion

The README gives interpreter selection and external scratch-directory commands. The proof uses the standard Weyl-chamber theorem. Full C5, other cells, C(P112)>=64, supplier admission and kappa remain unclaimed.

Merge Danger

Door: two-way.

Blast Radius: research.

Adds one isolated registered package. No selected-frontier, shared-runner or frozen-source changes.