Prove dirty-private identity for PR2979's isolated cleanup

[petalas]

Summary

For PR #2979's original 5,207-gate cleanup, prove this exact block identity for arbitrary live and dirty private entrance arrays:

                 live input   private input
live output           A             0
private output        0            I_91

All 91 private arrays return unchanged at their literal last touches, with no private-to-live leakage, in both providers and orientations. The 72 warp maps are arbitrary noncommuting linear maps; no inverse or native phase identity is assumed.

Adds only research/rank7-cleanup-dirty-identity/, with a written proof, source pins, exact forward and backward checkers, receipts and controls. Answers PR #3238's explicitly unrun arbitrary-cleanup-entrance question and strengthens clean zero-return to dirty-private preservation. PR #3208 checks different R2 words and native obligations; it is credited, not repeated.

Base 463113d675af7410ac91d53a4fed51ec6494eb9a, priority revision 6. Contribution 171c95e2940341e56377d655a162635fa3caedfa. Both inputs match PR #2979 head be191346391661f4d35fc0d1508d0a6029572576. Canonical investigation.

Evidence

• Before: PR Research: audit all PR #2979 private frees and their expanded native dependencies #3238's original-word proof depends on the preceding computation and clean private allocation. It explicitly leaves arbitrary cleanup entrance unrun.
  After: all 723 entrances are independent, including private dirt; the exact block identity passes. A separately implemented backward interpreter checks all 728 private rows/columns across providers and orientations without importing the forward checker or predecessor code.
• Before: doubling literal gate 4844 is invisible when private entrances are zero.
  After: the dirty checker rejects its exact errors live302 -= d1003/4, private930 += d1003/8, private934 += d1003/8.
• Eleven behavioral groups, optimized registered replay, source metadata/pins, Ruff and all 11 publication-byte comparisons pass. A Git-free committed export passes all tests under a second Python version. Environments: CPython 3.12.15 and 3.13.5, Linux x86_64, standard library only.

python3.12 -B scripts/research_package.py --package research/rank7-cleanup-dirty-identity

Canonical main and live overlap were refreshed before submission; no relevant upstream delta or overlapping dirty-cleanup result was found. Credit Marius-Paul Dumitrean, Jeremy Kothe, Mason Hale, Jeremy Diviney, commdata2338/PR #3238, 24kHandsome1201/PR #3208, ToikY and the retained construction lineage. Full source credit and open next questions are in the README.

Merge Danger

Door: two-way

Blast Radius: isolated

No frozen source, shared checker or selected-frontier change. This is a finite algebraic cleanup certificate, not native/physical supplier admission. The unchanged schedule still needs 91 distinct arrays; borrowing, ownership, movement and finite precision are unpriced. No stock, paid-profile or kappa improvement is claimed. The live block is not identity. Hosted CI, independent human review and full supplier/outer replay remain separate.