[ToikY]

Change and mathematical scope

NO VERIFIED GAIN. A fixed-paid productive endpoint exchange between helper 1481 and any of the 615 eligible 3→127 helpers fails at the two-role prefix gate. The 76,466-event census finds six cocharted partners, 20 exact ranges and 20,455 raw cuts. On the exact input x1454 = 1, x1481 = −2, both live rows evaluate to zero while the required helper difference evaluates to +2. The forward continuation checks all 5,080 cuts in the remaining 12 ranges. Independent reverse replay reconstructs every range and confirms all 20 exclusions. Zero unresolved in this scope.

The optimistic productive ranks change from 5,9 to 6,8 with all 110,519 paid positions fixed. All pairs share role 1481, so at most one is compatible. The whole directed gross upper is 0.026750025281436337 raw units. The verified saving is zero.

Task and overlap

The literal input is #7334 at aaeec8c0acf01e99a5f331ef363a698d9c084ace with signed #7113 at 07a76c5e2738882c0cb322278e56f6cae3c9885d. The scope refines #7370 by exchanging two retained suffixes, rather than splitting an individual helper. #7386 studies paid terminal retargets. The package is the only new commit, stacked on the two existing #7257 CI commits.

Validation

python3.12 -I -B research/p104-fixed-paid-endpoint-exchange-bound/replay.py

The clean replay authenticates the word and dependencies and regenerates seven deterministic receipts. Three altered-input controls reject. Registered replay, committed bytes and modes, source history, six navigation tests and Git-free export replay passed locally. A replacement construction and its complete multiplier checks were not run because the necessary prefix condition fails.

Credit

#7370 supplies the rank-five endpoint catalogue, #7362 the complete rank stock and rank-nine cohort, #7130 the cocharted basis precedent, #7124 the output rechart precedent, #7355 the reverse engine, #7382 the bank trace, #7338 the benchmark admission, and #7298 the directed tariff. #7334 and #7113 supply the literal inputs. OpenAI Codex and subagents materially assisted.

Open next questions

Grant exactly role 1454 where it is already cocharted, keep its paid itinerary, and test the resulting three-row prefix bank. Any survivor must restore role 1454 and preserve all future COPY guards. Other endpoint pairs and paid-itinerary changes are outside this exclusion.