[ToikY]

Change and mathematical scope

Splits independent helper 1285 at its existing chart-117 cut on the exact #7109 word. One rank-nine productive child becomes rank-five and rank-four children. The paid MOVE profile and signed caller are unchanged.

• Previous conditional κ (Conditional κ = 0.003635479112372 (+(708203588/145412082459)% over #7108 ≈ +0.004870321476%): rank-eight helper split #7109) is 0.003635479112372. New conditional κ is 0.003636447857731.
• Exact absolute gain is 0.000000968745359. Exact relative gain is (24218633975/908869778093)%, approximately 0.026646979093%.
• The independent raw interval is (0.00363644785773120955770150093800963, 0.00363644785773120955770150093800964). The predecessor rejects the new claim. The paired BIT pin remains 0.00376669.
• The complete invoice changes productive requests by {4: +18, 5: +18, 9: -18}. The paid counts are unchanged. The rank surplus is 1,520, with zero empty root credits. The modeled ordinary total is 847,350,304 of 10⁹.

Task and overlap

Base is e54523517d0f03e58352e647c403a5af3e525a57. The source is #7109 at ae3f9d6a944ade32267fe5a94af853914a99d6aa. This is a changed source-bound instance of p104-side-correction. #7107 and #7109 use retimed rank-eight helper splits. This witness splits a distinct rank-nine helper at an existing cut and adds no paid moves.

Validation

Replay with python3.12 -B scripts/research_package.py --package research/cocharted-rank9-helper-split. The hash-bound archive rebuilds the exact #7109 word and emits the candidate from the dyadic witness. It checks all normalized endpoints, physical endpoints, both changed chart maps on all 512 columns, phase and scalar negative controls, signed caller routes, grid and precision bounds, and both directed price engines. A clean extraction reproduced the canonical word and both result receipts.

Credit

Credit to the #7109 and #7107 lineages, Ali Romman and CubeJerry for the split construction, and the signed-caller and P104 contributors. OpenAI Codex assisted discovery, construction and verification.

Open next questions

The same conditional premises apply as in #7109. The physical fixed-tape realization, total rounded provider and #6998 tariff bridge remain open. The next source-bound check is to reconcile the #6998 conversion and A6 trace under one tape width model.