Nine-stage low-read E8 composition: conditional kappa 0.000996761861969671

[rohanarun]

Transplant #379's low-read E8 bit schedule into #381's nine-stage unsplit layout, keeping #377's nine-stage complex component unchanged. Exact pricing gives conditional κ = 0.000996761861969671, 0.11097150583734022% above #381 (0.000995656966441037). Bit coarse saving is 0.000997756388440101; complex coarse saving stays 0.000999240641319551. The bit side binds.

Only the local phase-B schedule changes. Its commuting elementary scalar additions are identical. The paid-rank change has a positive weighted second-difference decomposition, proving a strict recursive-moment decrease for every exponent between zero and one. Stock, rank mass, call count, fallback, width, and halving degree remain unchanged.

Verification: full local replay PASS at 26b8600364803eddd66c25a187c7fb8435b7f632, including the complete #381 baseline and #377 component, exact candidate reconstruction, all 1,825 physical columns through nine stages, 18 omitted-bridge controls, six record mutations, frames, geometry, banks, finite accounting, two rational moment engines, all 47 outer inequalities, and adjacent-grid rejection. The initial draft replay exposed one missing nested provenance manifest; it was restored byte-for-byte from the pinned source in the current head. Both GitHub Python 3.11/3.14 replays and all 58 repository checks passed on that head. Dedicated run: https://github.com/CrocSwap/integer-mult-bounds/actions/runs/38118041701.

Comparison update: #382 appeared during submission and reports 0.000998243154231047, above this PR. This remains a reproducible +0.11097% improvement to #381's unchanged bit-word lineage, not a claim to beat #382.

The complete package is research/e8-nine-stage-low-read/; run python -B research/e8-nine-stage-low-read/verify.py /fresh/output. CI covers Python 3.11 and 3.14. Original source manifests, authorship, proof interfaces and dependencies are retained. Credits: #379 (eumemic / OpenAI Codex), #381 (DaysSky / Claude), #377 (Zhihao Chen / OpenAI Codex), and the suppliers credited in their notices. This PR contributes the composition and explicit second-difference certificate.

Scope: conditional on the inherited signed-integer lifting, nine-stage bridge, finite-bill/induction, Clifford/compiler, compressed-window, dirty-bank, common-grid, row, and all-size analytic interfaces. No new Lean proof or unconditional exponent claim. The three joint-dual metadata files reuse #318's source-pin repair without a mathematical change.

[Mister-Meeseeks]

Thank you @rohanarun. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Nine-stage low-read composition.

Review and limits: Full wrapper and exact second-difference pricing certificate. Explicitly distinguish fresh compiled checks from the low-read package's stored baseline receipts.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: 26b8600364803eddd66c25a187c7fb8435b7f632. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.