[ToikY]

Change and mathematical scope

NO VERIFIED GAIN. The comparator is #7334 at aaeec8c0acf01e99a5f331ef363a698d9c084ace with signed #7113 at 07a76c5e2738882c0cb322278e56f6cae3c9885d.

For any nonempty matching of up to four edits, each edit removes one even idle and adds its disjoint body mask to one signed odd idle at its original clock. Both exact engines compared all 18,443 eligible equal-cardinality projector sums across 17 stages. There are 4,527 subset pairs with a complete mask-compatible bijection. None has equal projector sums. Every one of the 60 even clocks has a missing-stage certificate, so no matching survives. The nested two-edit check independently excludes 11,728 unequal-mask placements by their exclusive variables and all 210 equal-mask placements by summed derivatives. Both highest-priced cases have exact derivative entry +16 at [36,36].

The full signed matching price grants at most 3.076075380146476 raw across four edits, before ancillary costs. At its optimistic price witness paid positions would fall to 110,487 with 22,461 productive positions and rank surplus 1,424. The exact support obstruction leaves zero realized saving.

Task and overlap

This is the joint fixed-clock extension of the single-edit #7357 scope under p104-side-correction. #7144 treats diagonal Laurent gauges, #7356 keeps the paid jobs in its sign-transfer model, and #7360 concerns same-role even/even edits. The research commit adds only research/p104-type-b-simultaneous-idle-bound/. The existing #7257 commits address the canonical navigation mismatch documented in #7371.

Validation

Run from a clean checkout with CPython 3.12.

python3.12 -I -B research/p104-type-b-simultaneous-idle-bound/replay.py

The Git-free replay authenticates the exact #7357 predecessor bytes and #7113 caller, reproduces both signed prices, both exact paired checks and the two independent stagewise certificates. All eight receipts match byte for byte and seven changed-input controls reject. Registered-package, source-history, navigation and official export checks passed. The first derivative already excludes every key in scope, so no full-body candidate was built.

Credit and open next questions

#7334 and #7113 supply the benchmark and signed caller. #7357, #7315 and #7323 supply idle stock and one-edit projector methods, #7296 supplies a separate canonical provider check, and #7298 supplies directed arithmetic. OpenAI Codex and subagents materially assisted. A different clock or changed provider needs a new complete invoice and exact signed endpoint check. Review and merge are left to the maintainers.