DONE: sharp odd-dihedral joint tariffs with dirty workspace

[RossRichardson]

DONE / HANDOFF — PR1966, exact head 691e6eb9417384d1820de4fdc167fc3e9797b75e. Claim released.

For every odd rotation period n=2m+1>=3, arbitrary heterogeneous formal diagonal targets and any finite restored dirty workspace, the reflection-only rank-one-idempotent model has sharp bounds X>=A, Y>=B, X+Y>=A+B+t, where A=sum d_n(k_i+e_i), B=sum d_n(k_i), and t counts the longest reflections. Every pair (A+j,B+t-j) is attained. The exact nonnegative tariff is alphaA+betaB+t*min(alpha,beta).

The new faithful-regular half-cut supplies the joint constraint missing from PR1941's two separate bounds. For two longest D10 reflections it forces ten calls where separate cuts and parity permit eight. It also gives all-count/all-workspace S3 special cases without reusing their finite search certificates. Adam Gall #1941/#1911, commdata2338 #1414, Cinna Davis #1541/#1870/#1953, Ross Richardson #1766, Aaron Wang #1763 and the register-model lineage retain credit. The claim is a written formal-model theorem with finite corroboration; no physical supplier, selected frontier or new kappa is claimed.

Reproduce: python3.12 -I -B scripts/research_package.py --package research/odd-dihedral-joint-tariff. Registered CPython 3.12.12 replay passes: 3,770 complete short words, 392 forward/inverse dirty pair witnesses, all 155 projectors through four roles across five periods, 2,478 rejected omissions, six package tests including actual detector-removal sensitivity and optimized read-only relocation. Separate exact-verification specialist code checks all 5,200 single targets over odd periods 3–101 and 216 full-matrix conjugations; proof/code review found no blocking defect. CPython 3.14.6, source metadata, selected integrity and whitespace checks pass. Hosted snapshot has 61 queued checks; no hosted pass is asserted.

The research base remains 0b1cccf. Main advanced to ecc75c7 with selected record, guidance, scoped inputs and runner unchanged. Final overlap refresh covered 535 open PRs and 592 Discussion records with complete pagination/no warnings. Original task/claim, seed 721bc4f2e2d9f3c304d6dab0f34c1803, exact source heads, evidence and limitations are retained in the PR package.

Remaining useful work must change the paid alphabet or establish a fully priced physical/compiler/hosting/frame/precision/tape and recursive interface. No further finite-register search in this same formal two-reflection model can improve its direct bill. No Lean or independent human review. Prepared for Ross Richardson with substantial OpenAI Codex assistance; Apache-2.0.