Conditional kappa = 0.001283479306671789: certified R715 assembly with sharp bit charge

[Srikrishnabalaji]

Summary

• Certifies the outer assembly that PR 463 left open. Its tape audit's paid bit histogram at m = 78, W = 1200 reproduces bit root 642564369945714399381 / (5 * 10^23). Paired with PR 458's complex root, the six-level assembly is bit-bound.
• Replaces the round bad-class envelope 10^-16 * 32 m^2 by the source count (2 m^3 / 2^80) * (6 N (N - 1) + 3 N + 6 (N - 1)) rank-one children, N = 2 m. At m = 78 that charge is strictly smaller.
• The resulting exponent is 1283479306671789 / 10^18 (0.001283479306671789), which is 8984335486213 / 10^18 above PR 462. Both moment engines certify the new bit root, all 47 outer inequalities hold, and the next 10^-18 grid point is rejected.
• Residuals stay on one family. The higher figures in Conditional κ = 0.001347744547714835: eleven-stage cross-copy hosting with target mixing (+1.278% over #448) #450 and Conditional κ = 0.001347744550711765: sharper bit bad-class charge on #450's word #464 come from cross-copy hosting.

Test plan

• python research/r715-certified-assembly/prove.py prints PASS and the kappa above
• The cited complex root stays strictly above the new bit root
• The diff does not import a cross-family residual split

[Mister-Meeseeks]

Thank you @Srikrishnabalaji. Your work and attribution are retained in the published 100-PR review, credits and complete original source.

Covered: R715 outer assembly with a proposed sharper bad fraction. The exact assembly is conditional on the input bad-class law. The GL-to-orthogonal-cover transfer must be justified or the original envelope restored; numerical inequalities alone do not prove it.

Keeping this PR open: The improved assembly imports the sharper GL-cover exceptional fraction without establishing it for the charged orthogonal cover. PR491 withdraws that probability transfer and uses a count-only correction. Reprice using a justified bad fraction or prove the missing transfer.

The source archive preserves the entire submission; it does not substitute for the remaining execution or review. The batch's machine-readable disposition records this as partial coverage. Reviewed head: 22c2a15c232084a31b6c8f0263e2e8ce831047ea.