[ToikY]

Change and mathematical scope

NO VERIFIED GAIN. Exact Δκ = 0, or 0% relative to conditional κ = 0.00364665195644 on #7334 at aaeec8c with signed #7113 at 07a76c5. This tests fixed-paid 3+4 and 4+3 splits for the five chart 602→127 rank-seven helpers.

Complete literal geometry finds 65 representative banks on five rank-six charts and no eligible rank-five bank. Two prime computations verify 45 direct prefix exclusions, including all 13 singleton keys left by the earlier cap. Independent chronology engines verify 20 additional transfers of full rank through unchanged banks and invertible scalar operations. The exact closure lists all 65 dispositions and zero unresolved cases. The additive commit preserves the ten predecessor receipts and adds four residual receipts.

One proposed split keeps all 110,519 paid positions and changes the productive histogram by T3 +17, T4 +17 and T7 −17 across 17 copies. The directed optimistic one-edit upper is 0.294636248924991 raw and the compatible five-target upper is 1.473181244624955 raw. One additional paid rank-one position defeats a single edit. No candidate triggered a physical construction or complete κ replay.

Task and overlap

This refines the #7111 investigation on canonical main e545235. #5718 and #6040 concern an older chart-602 entrance split. #7363 gives the rank-eight exterior method on exact #7334 with a different endpoint cohort. This package concerns the productive rank-seven residual and checks transfers through its literal scalar chronology.

Validation

From a clean checkout with CPython 3.12:

python3.12 -I -B research/p104-rank-seven-prefix-bank-bound/replay.py
python3.12 -B scripts/research_package.py --package research/p104-rank-seven-prefix-bank-bound

The Git-free replay regenerates fourteen pinned receipts and rejects altered price, word, and residual selection inputs. Local registered replay, committed source and mode checks, six navigation tests and the official Git-free export and replay passed. The branch reuses the exact #7257 planner repair d2e54af for hosted verification.

Credit and open question

#7334 supplies the exact word, #7113 the signed caller, #7314 and #7319 the helper census, #7338 the admitted price stock and #7298 the directed tariff. OpenAI Codex and subagents materially assisted proof, implementation, independent replay and packaging. No bank reaches suffix or rational pairing. Other endpoint cohorts or changed paid itineraries remain separate questions.