[ToikY]

Change and mathematical scope

NO VERIFIED GAIN. Extend the fixed-paid endpoint exchange in #7391 by granting exactly role 1454 where it is already cocharted, preserving its paid path and dirty return. Of 20,455 inherited cuts, 3,961 lack a third coframe. The other 16,494 cuts give 15 contact-separated segments. Role 1454 defeats the old two-row separator at every eligible cut.

Eight exact prefix tests reach their cap and exclude all eight. A separate forward pass exhausts all 478 cuts in the remaining seven segments. The exact input x1251 = 1, x1481 = 4 gives zero on all three live rows and −4 on the required helper difference. An independent backward replay reconstructs all 15 coframe segments and confirms all exclusions. Zero unresolved in the three-role scope.

The single compatible optimistic edit keeps all 110,519 paid positions and exchanges productive ranks 5,9 for 6,8. The whole directed gross upper is 0.026750025281436337 raw units. The verified saving is zero.

Task and overlap

Use #7334 at aaeec8c0acf01e99a5f331ef363a698d9c084ace and signed #7113 at 07a76c5e2738882c0cb322278e56f6cae3c9885d. The third role changes the admissible prefix bank, so the exact two-role obstruction alone does not settle this scope. The package is the only new commit, stacked on two existing #7257 CI commits.

Validation

python3.12 -I -B research/p104-three-role-endpoint-exchange-bound/replay.py

Clean replay authenticates exact inputs and reproduces six receipts, including the independently derived coframe and reverse checks. A changed public dependency manifest rejects. Registered replay, committed bytes and modes, source history, navigation and Git-free export passed locally. Suffix, determinant, physical and full multiplier checks were not reached after prefix exclusion.

Credit

#7391 supplies the exact inherited range and price receipts, #7370 the original endpoint catalogue, #7362 the signed stock, #7363 and #7341 the third-role endpoint and readback, #7355 and #7382 the reverse methods, and #7298 the directed tariff. #7334 and #7113 supply the literal inputs. OpenAI Codex and subagents materially assisted.

Open next questions

Larger banks and changed donor itineraries remain outside this scope. Any such proposal needs its own complete price, exact prefix and suffix, and dirty-return verification.