Replace the P112 A5 frame census with a Parseval proof

[petalas]

Summary

Replace the orthogonal-frame census step in PR3205 with a short analytic Parseval proof.

A5 simplex, orthogonal eight-root frame
  variance sum = 10
  8c0 + 3c1 >= 4, hence 2c0 + c1 >= 2
  remaining cost after thirty cuts >= 120 + 2c0 + c1 >= 122

The proof removes the 2,025-frame census as a mathematical dependency of this root branch. PR3205 retains priority for support-thirty shortening; no new shortening range or historical profile is claimed. The new inequality, sharp frame/cut witness, exact receipts, source pins and reproduction instructions are in research/p112-orthogonal-shortening/.

Credit Nick Petalas/PR3205 for the concurrent theorem, PR3203 for its predecessor, PR3188/3176 for the inherited mixed-edge and A5 geometry, and DreamingOfClouds/PR3154 with the retained E8/P112 decoder lineage. Publication commit: d4bf10f9b8c61d1d2b05bad59c86f0b08076a616.

Evidence

• Before: a complete 2,025-frame computation supplied the lower bound 122; allowing arbitrary punctures gave only 120.
  After: the analytic variance bound gives 122 for every orthogonal frame. Scalar, Gram/Parseval and literal witness checks pass without a frame search.
• Registered CPython 3.12.15 replay passes both inherited implementations, the new checks and twelve optimized behavioral groups.
• The exact committed, read-only, Git-free export passes all four commands under optimized CPython 3.13.16. All 24 committed package/input byte comparisons and archive integrity checks pass.
• Ruff E,F,I,B,UP,PLE,PLW,RUF, formatting and warnings-as-errors compilation pass. Internal mathematical and artifact reviews found no substantiated blocker; independent human and proof-kernel review remain separate.

python3.12 scripts/research_package.py --package research/p112-orthogonal-shortening

Merge Danger

Door: two-way. Blast radius: isolated.

One new opt-in research package. The inherited A5 spectrum, root/D7 classification and mixed-edge bound remain dependencies for the known shortening corollary. At thirty-one cuts the root witness reaches equality 120, so this proof stops there. Full C5, the decoder floor, supplier admission and kappa remain unresolved or unchanged. Hosted CI is separate from the local checks above.