[pinterbanget]

Summary

This adds research/free-controller-replay/. It is an independent free-algebra replay of the noncommuting-stage theorem in Dugongue's #4534: #4470's p16 controller stays exactly diagonalizable with pairwise noncommuting D_s that commute with the central Q. It extends my commutative replay #4516 to ordered words.

Claim type: an independent exact replay. No new κ.

Results

• The identity. L·W·R = diag(q^{ε_i} d_{w_i}) holds in all 1,024 entries, coefficient by coefficient over ordered words in ℚ⟨d_s⟩[q, q^{−1}], using Frame-aware native construction lemmas and exact p16 certificates (no new κ) #4534's certificate (vendored, SHA256-pinned).
• Chronology. Reversing the idle words breaks 212 entries, so the check is sensitive to chronology.
• Structure. Exponents are 16 of each sign. G = (32, 31, 29, …, 1, 0), and the other 15 words are contiguous prefixes or suffixes of G.
• Boundaries. L and R are invertible, and they and their inverses are dyadic.

Evidence

python3.12 -B scripts/research_package.py --package research/free-controller-replay --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/free-controller-replay
  PASS_REGISTERED_RESEARCH_PACKAGE research/free-controller-replay outcome=completed   (~1 s, stdlib only)

Head: 84c19218bca3b2c963e98a545481f32d78e77b17. Base: canonical main f9f85c1e.

Not covered

• Frame-aware native construction lemmas and exact p16 certificates (no new κ) #4534's adapter, retiming and lazy-response tools.
• Any physical noncommuting D_s.

Credit: Dugongue (#4534) and Cinna Davis (#4470). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code