Compose endpoint bit and semantic bulk interfaces for conditional κ = 1.19720853e-5

[DominikScholz]

Composing icekylinx's #24 bit interface with Zhihao Chen's #23 semantic/bulk assembly, while retaining #21's complex circuit, gives

$$T(n)=O(n(\log n)^{1-\kappa}),\qquad \kappa=\frac{119720853}{10^{13}}=1.19720853\times10^{-5}.$$

This is 8.93617% above #23's witness in asymptotic exponent saving. Later contributions now give stronger bounds; this completed composition and its source pins remain available for work building on it. It is not a practical runtime claim.

Compatible assembly

The contribution imports 17 unchanged #24 source files, pinned at ed90fd940279c336ebc45968631bdebfb087b505, and uses its bit saving 2993093/250000000000 at dimensions (32,30,40). The arbitrary-width interchange contract feeds #23's routing and complex adapters.

The complex saving stays 18e-6, with #21's circuit, literal scalar charge and #23's semantic guard C1=1. The mixed-dimension product row stock is recomputed: bit/complex halving depths 444/544, wire exponents 44/41, coefficient 41840 and sufficient degree 86000.

Headroom is 1e-12. All 47 strict constraints and seven margins pass; the final absorption gap exceeds 3e-14. The package includes the compatibility proof, exact certificate and proof patch against pinned #23. Its parameterized assembly reproduces the original at the original parameters.

Review and validation

• Both pinned predecessor certificates reproduce exactly.
• All six selected endpoint scalar producers were freshly reconstructed.
• The complete composition and three rejecting controls pass.
• The proof patch applies to the pinned source; source manifests and generated artifacts reproduce.
• Independent final Standards and Spec reviews found no actionable findings. They independently checked all source imports, the product stock, semantic compatibility, exact certificate, negative controls and patch.
• Full repository rerun passed: make verify exited 0 with 178 tests and all inherited arithmetic and patch checks. Regenerated artifacts remained unchanged.

This PR is ready for review. It starts at #23 commit 661ebabc1076c9f525d7ce4967c876b203fa9827; the main-branch diff includes pending predecessors. The result retains the written finite, analytic, basis, routing and fixed-tape hypotheses. Exact checks and agent reviews do not formally verify the complete theorem. No PDF was created.

Attribution

Dominik Scholz, with substantial OpenAI Codex and GPT-6 Astra assistance, contributes this composition, compatibility accounting and exact witness.

Credit icekylinx for #24's finite network and basis; Zhihao Chen (jacklightChen) for #21/#23, semantic compatibility and product-stock arguments; and RaD/hipotures for semantic precision, routing, phase-cell inverse and bulk mechanisms, with its recorded assistance disclosures. All earlier authors retain their notices. Original Apache-2.0 and CC0 licenses remain unchanged.

[Mister-Meeseeks]

Thank you @DominikScholz. This contribution is now recorded on main in the scoped reconciliation review and contributor credits.

Contribution: Compose the endpoint bit supplier with the semantic bulk reduction.

Review and limits: Fresh own certificate and negative controls; compatible bit/complex/row stocks are charged together.

The complete original source, proof/research notes, notices and relevant replay/CI evidence are retained through the pinned source archive. The review distinguishes fresh runs, exact-head historical CI and prior integration evidence. Closing this historical PR as reconciled; its obsolete headline does not replace the current selected bound, and draft/retracted claims retain their explicit qualifications.

Reviewed head: c297233e788a23e9833ad1ee07fc8517accd0f42. Publication: b84ba67156a01f9c2cb34fe1e3cb1dcdeab00d9c.