[pinterbanget]

Summary

This adds research/pr4544-cancellation-check/, an independent check of Clear1nsight's #4544 (head 0898b3a8). #4544 audits the cancellation step (10) ⇒ (11) in zxv's #4483 and states that it is sharp. Every #4483-compiler κ claim depends on this step, including #4535's. All of #4544's claims are confirmed. No new κ.

Checks

The verifier is separately written, uses exact rationals and imports nothing from #4544.

1. Slack identity. (1−β)(ηI−B−F) = (η−β)A − (1−η)F + (1−η)(βI−B) holds as a polynomial identity in ℚ[β, η, B, F, A] with I = B+F+A. A rejection control is included.
2. Extremiser. At B* = β(A+F)/(1−β) the exit fraction is (βA+F)/(A+F), as a polynomial identity. The fraction is monotone in B (derivative numerator A). An exact grid of 11,968 cases confirms that the uniform guarantee holds iff (η−β)A ≥ (1−η)F.
3. Necessity of Remove tensor padding (199.32× smaller uniform-rank exponent) #4483's (10). From only F ≤ X and A ≥ D·X, the adversary A = D·X, F = X with a saturated mirror gives (D+1)(η − exit) = (η−β)D − (1−η) identically. So (10) is exactly the uniform condition.
4. Controls. Dropping the root debit gives an exit fraction of 11/20 > 1/2 while the gross test passes with equality. Dropping the leaf mass gives an exit fraction of 1.
5. Binding. The pinned research/rank-convergence/PROOF.md (blob 75f45183, SHA256-checked) states (2), (3), A_t = (T−P)H_t − R_t, (9), (10), (11) and the premises verbatim.

#4544's own registered package also replays at its head (PASS_REGISTERED_RESEARCH_PACKAGE, 1.3 s).

python3.12 -B scripts/research_package.py --package research/pr4544-cancellation-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4544-cancellation-check outcome=completed   (<1 s, stdlib only)

Limitations:

• This covers the scalar lemma and its binding only, not the Chernoff bound behind D, the mirror certificate, funding or realisation.
• Audit PR4483's sharp cancellation threshold with exact extremisers (no new kappa) #4544's shared CI and navigation repairs are not reviewed here.

Head: 3c5f6a8ba707371ff2def3d102592e932c560679. Base: canonical main f626db5c.

Credit: zxv (#4483) and Clear1nsight (#4544). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code