[ToikY]

Change and mathematical scope

NO VERIFIED GAIN. Δκ = 0 on exact #7334 aaeec8c, conditional κ = 0.00364665195644, with signed #7113 at 07a76c5. This checks fixed-paid productive 2+3 and 3+2 splits through existing nested charts.

Two exact catalogue methods verify that none of the 336 rank-six or rank-seven labels is an intermediate for the nine 1090→127 helpers. The broader literal catalogue covers all 80 unprotected rank-five helpers in 28 endpoint cohorts and records 68 occupied representatives across five cohorts. In the selected 3→241 cohort, two primes verify 11 full prefix minors and independent chronology verifies eight transfers through invertible ADDs on identical public banks. All 19 selected-group banks are excluded. The other 49 representatives are outside the support scope and remain unresolved.

One productive split retains all 110,519 paid positions and gives ΔT2 +17, ΔT3 +17, ΔT5 −17 across 17 copies. One directed optimistic credit is 0.207666506667591 raw. Across 80 distinct roles the compatible upper is 16.61332053340722 raw with ancillary costs relaxed. One extra paid rank-one defeats any single edit. No verified savings and no literal candidate.

Task and overlap

This refines #7111 on canonical main e545235. #7367 closes a separate rank-seven cohort. #7363 supplies an earlier exact exterior method on a different rank-eight cohort. #5994 and #6040 use older cochart words. #7314 and #7319 supply the exact inherited helper census.

Validation

From a clean checkout with CPython 3.12:

python3.12 -I -B research/p104-rank-five-catalogue-bound/replay.py
python3.12 -B scripts/research_package.py --package research/p104-rank-five-catalogue-bound

The Git-free replay regenerates nine exact receipts and rejects altered inputs. Local registered replay, committed source and mode checks, six navigation tests, and official Git-free export and replay passed. The branch reuses exact #7257 planner repair d2e54af. Suffix and rational pairing were skipped because no tested bank passed prefix support.

Credit and open question

#7334 supplies the exact word, #7113 the signed caller, #7298 the directed tariff, and #7143/#7161/#7274 provide chart and productive endpoint lineage for other groups. OpenAI Codex and subagents materially assisted proof, implementation, independent replay and packaging. The four untested occupied cohorts remain open to separately capped support tests.