κ = 7.92580093369946e-4: w3 cube layer on #325's p10b word with a stronger p = 10 complex supplier

[LJH-217]

Conditional κ = 396290046684973/(5·10¹⁷) ≈ 7.92580093369946e-4 (+3.71 % over #315, +1.97 % over #332/#333). The complex supplier binds; the bit root is 1.07 % above its leaf cap.

What this adds

• Bit side: PR Conditional κ = 0.000752893499605334868002344: source-bound w3 word and complete finite admission (+0.1855% over #309) #310's w3 Design T and twin condensation, ported to h = 20 and applied to PR Conditional κ = 7.696840393833340e-4: a stronger p = 10 bit word — re-annealed pair module, p = 10 local design, balanced cube orientation, tiered reuse matching (+0.71% over #315's word) #325's p10b word (exported unchanged from Conditional κ = 7.696840393833340e-4: a stronger p = 10 bit word — re-annealed pair module, p = 10 local design, balanced cube orientation, tiered reuse matching (+0.71% over #315's word) #325's own pipeline; the export reproduces Conditional κ = 7.696840393833340e-4: a stronger p = 10 bit word — re-annealed pair module, p = 10 local design, balanced cube orientation, tiered reuse matching (+0.71% over #315's word) #325's bit root exactly). Design T frees 480 helpers and needs no new frames; twin condensation adds 320 line frames. Bit root 7.70277e-4 → 8.01726e-4.
• Complex side: a p = 10 gcert/1 program built with A stronger complex supplier: compile-cost-annealed complex modules, five-stage complex saving 7635/10⁷ (+1.17% over #233; no new κ) #304's recipe on Conditional κ = 7.696840393833340e-4: a stronger p = 10 bit word — re-annealed pair module, p = 10 local design, balanced cube orientation, tiered reuse matching (+0.71% over #315's word) #325's re-annealed pair module, A p = 10 complex supplier: five-stage complex saving 7795/10⁷ (centre-sharing) and 7737/10⁷ (#304 recipe), both kernel-checked in Lean (no new κ; raises the complex cap above 7727) #327's p = 10 triple module and Conditional κ = 7.64230861320245e-4: the paired-cube bit word at cube size p = 10 (h = 20, m = 100), with a new centre-sharing complex supplier (+1.21% over #314) #315's all-but-one module (flow R 6,265). b = 396604388013523/(5·10¹⁷), against 7795/10⁷ for A p = 10 complex supplier: five-stage complex saving 7795/10⁷ (centre-sharing) and 7737/10⁷ (#304 recipe), both kernel-checked in Lean (no new κ; raises the complex cap above 7727) #327's p = 10 program.
• Conditional κ = 7.64230861320245e-4: the paired-cube bit word at cube size p = 10 (h = 20, m = 100), with a new centre-sharing complex supplier (+1.21% over #314) #315's complex checks ported to p = 10, with the five p = 11 pins derived from the certificate or re-pinned.

Checks (bash research/w3-p10b-complex-p10/verify.sh <fresh dir>, ~5 min)

Manifest; rebuild of the final word from the vendored base (both hashes); ported Design T verifier (legality, all F₂ columns, nondegeneracy); #266's official legality and five-stage columns checkers (11,940 columns, bridge controls); exact nondegeneracy and #315's prime-witness rule on the new frames; exact width-100 bank tiling; Sussman's gx.check1 + gxcore, labels, scalar words, splice controls and precision guard on the complex program; both rational moment engines with the 10⁻¹⁶ fallback; #315's outer assembly on the complex-bound path (47 strict constraints, cap rejected, adjacent κ rejected). PR #200's complete complex checker and PR #194's contract were also run on the complex program (receipts in receipts/).

Open obligations

#310's native downstream chain (bank review with charts, changed projector charts, geometry admission, finite invoice) is not ported to p = 10; only bank feasibility is shown. #315's own scalar/prime/finite stages cannot take an edited word. The complex guard keeps #315's p = 11 additive row constants. All inherited interfaces remain assumptions; this is a conditional finite construction, not a formal verification.

Credits and AI disclosure

Builds on #325/#315 (DreamingOfClouds), #310 (utcorvusvolat-dotcom's w3 work), #266's checkers, #327's triple module and the #304/#256/#233/#202/#200/#194/#184 complex lineage with Sussman's checker; see NOTICE.md. Prepared with substantial Anthropic Claude assistance.

Submitted by Louis Harrison (@LJH-217)

[Mister-Meeseeks]

Thank you @LJH-217. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: w3 cube layer on p10b with a stronger complex word.

Review and limits: Historical partial-interface construction. Its shipped checks do not establish all native p10 downstream obligations; PR351 supplies a separate native completion. Preserve that distinction.

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: 11b4de5ff8ed5fccf55d4af1043358d257308e8e. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.