Diagnose and resolve R5 affine remainder inflation - #59
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August 17, 2026 22:49
Record the non-theorem R5-B1c affine-correlated first-leaf feasibility diagnostic. The leaf-centered candidate reduces the midpoint residual to a strict Arb bound near 2.06e-27, and the first-order cancellation defect is bounded near 1.55e-39. However, the reported pure-alpha second-order remainder remains near 1.27e-9, so none of the predeclared eta radii satisfies the candidate self-map inequality. The status is AFFINE_CORRELATED_REMAINDER_TOO_WIDE. This does not justify freezing an R5 v1.1 protocol or imply nonexistence of the response-preserving graph. It does not modify the frozen protocol, run other leaves or R6, or perform normal K=1 residual recovery.
Audit the provenance of the wide pure-alpha remainder reported by the R5-B1c affine first-leaf diagnostic. The B1c implementation subtracts interval-enclosed center and first-order terms from an already interval-enclosed whole-leaf expression, so it does not constitute a correlated Taylor remainder. An explicit 192-bit Arb directional-Hessian enclosure bounds the true second-order Lagrange remainder near 2.20e-28, approximately 5.78e18 times smaller than the B1c reported bound. A high-precision three-point center difference is consistent with the strict Hessian scale. The result is B1C_REMAINDER_DEPENDENCY_ARTIFACT. This is a diagnostic, not an R5 certificate. It does not modify the frozen protocol, run other leaves or R6, or perform normal K=1 residual recovery.
Remove the accidental .git worktree-pointer entry from SHA256SUMS.txt. The .git path is a regular pointer file in the local linked worktree but a directory in GitHub Actions, causing tools/verify_release.py to report .git_exists=false and .git_sha256=false. Keep repository metadata outside the release checksum boundary. No R5 scientific result, Arb bound, protocol, certificate, or diagnostic classification is changed.
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Summary
Add the R5-B1c affine-correlated first-leaf feasibility diagnostic and
the subsequent R5-B1d audit of its reported second-order remainder.
B1c successfully constructs a leaf-centered candidate with:
1.3543e-14;2.0646e-27;1.5501e-39.However, B1c initially reports a pure-alpha remainder near
1.2687e-9and therefore records: