Conditional kappa = 0.001274032592088050: sharper bit bad-class charge on #458

[Srikrishnabalaji]

Summary

• Reprices the binding bit moment of Conditional κ = 0.001274032589159993: complex kernel with paid residual adapters #458. The bit histogram, the complex root, and the six-level balanced assembly stay as published there.
• The source theorem charges each bad edge at most (2 m^3 / 2^80) * (6 N (N - 1) + 3 N + 6 (N - 1)) rank-one children, with N = 2 m. At m = 78 that is strictly below the round 10^-16 * 32 m^2 envelope.
• Replaying the inherited envelope reproduces Conditional κ = 0.001274032589159993: complex kernel with paid residual adapters #458's kappa 1274032589159993/10^18. The sharp charge gives kappa 25480651841761/20000000000000000 (0.001274032592088050), a gain of 2928057/10^18. The assembly remains bit-bound. Both moment engines certify the new root, all 47 outer inequalities hold, and the next 10^-18 grid point is rejected.
• No residual is split across families.

Test plan

• python research/sharp-bit-bad-fraction/prove.py prints PASS and the kappa above
• The cited complex root from Conditional κ = 0.001274032589159993: complex kernel with paid residual adapters #458 stays strictly above the new bit root
• The diff does not import the 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: Sharper proposed bad-class charge on the hosted bit moment. Arithmetic is distinct from applicability of the proposed 2m^3/q probability law to the retained orthogonal cover. The later count-only correction explicitly withdraws that probability transfer.

Keeping this PR open: The claimed sharper 2*m^3/2^80 exceptional fraction is a GL-cover estimate, while the supplier retains the orthogonal-cover invoice. PR491 explicitly withdraws this probability transfer. Supply a valid bound for the actual cover or revert to the retained bad fraction and reprice; arithmetic alone does not discharge this obligation.

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: dc297912ad446779f983818816617c03dfc76e16.