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Conditional κ = 0.003635479112372 (+(708203588/145412082459)% over #7108 ≈ +0.004870321476%): rank-eight helper split - #7109

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ToikY:codex/signed-rank9-rank8-split
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CrocSwap:mainfrom
ToikY:codex/signed-rank9-rank8-split

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@ToikY

@ToikY ToikY commented Nov 10, 2026

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Change and mathematical scope

Transfer #7107’s retimed rank-eight split to the exact #7108 signed rank-nine certificate. At source cut 37412, retime role 533 through chart 745 and split helper 1468 into two independent rank-three and rank-five returns. The signed caller is byte-identical.

The new complete conditional claim is κ = 0.003635479112372, up exactly 177050897/10^15 = 0.000000177050897 over #7108. The independent raw crossing is (0.00363547911237276261060913791895826, 0.00363547911237276261060913791895827), strictly above the old raw upper endpoint.

Task and overlap

Canonical base f16923d. Changed scope for the p104-side-correction card. #7107 at 5b59588 supplies the split. #7108 at d1ad3c1 supplies the stronger replayed native/caller pair. The independent cut proof checks the shared role 843 and reproduces the emitted word. The diff adds one package under research/signed-rank9-rank8-split.

Validation

python3.12 -B scripts/research_package.py --package research/signed-rank9-rank8-split

The clean replay reproduces the new word, full result, grid and route receipts byte for byte. It covers 71,253 events and 1,482 public outputs, all 512 columns and absolute phase of each of three changed chart pairs, all signed caller routes, two directed price engines, full precision and the compiler and outer gates. The old invoice rejects the new claim, as do the corrupted scalar and wrong-phase controls. Expected output includes PASS_SIGNED_RANK9_RANK8_SPLIT_REPLAY 0.003635479112372 0.000000177050897.

The full invoice has 117,148 paid and 23,428 productive requests, rank surplus 1,520, zero empty-root credits and modeled ordinary charge 847,308,544/10^9. The paired BIT cap is .00376669.

Credit

Credit #7107’s authors, the helper-split method of Ali Romman and CubeJerry, and CrocSwap’s coupled-native, signed Clifford and interval predecessors. OpenAI Codex assisted the transfer, independent emitter and verification.

Open next questions

Full physical fixed-tape realization, rounded provider admission and the #6998 physical tariff bridge remain open. Next bind the retimed helper normalizers and signed routes to the same exact tape tariff.

@ToikY ToikY changed the title Conditional κ = 0.003635479112372 with rank-eight helper split Conditional κ = 0.003635479112372 (+(708203588/145412082459)% over #7108 ≈ +0.004870321476%): rank-eight helper split Nov 10, 2026
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