Add combined E8 witness at κ = 0.001307044366925301

[aliromman]

Change and mathematical scope

Combine the four-replica R705 bit supplier and the retimed eight-replica R560 complex supplier. The exact composition gives κ = 0.001307044366925301, 80.637878% above the historical pinned main (12a4934). This is an exponent-saving comparison, not a measured runtime gain.

Review files: Proof and scope · Evidence · Source pins and credit.

The bound is conditional. In addition to main's framework, it uses the pending mutable-target, whole-call idle-hosting, and Gaussian-adapter interfaces. All-size compilation, complete-cover execution, restored-work and ordinary-leaf contracts, bad-class portability, and analytic transfer remain assumptions. The proof gives six exact bootstrap steps and sequential finite-cutoff existence; it does not certify complete numerical cutoffs.

The package contains fixed witness data, a concise proof, source attribution, offline reconstruction and independent arithmetic checks, plus one Makefile target and CI workflow. Main's selected-result record stays unchanged. The supplier lineage includes PR #458, PR #462 and PR #467; source pins and OpenAI Codex assistance are recorded in NOTICE.

Validation

• make e8-combined-verify passed locally and on Linux with Python 3.11 and 3.14: both words, geometry, phases, owners, costs, all 47 strict inequalities, and certificate agreement.
• Independent supplier audits and a separate rational moment calculation passed. Corruption controls rejected altered witnesses.
• make selected-record-check and the complete staged git diff --check passed.
• Sixteen of seventeen existing repository verification groups passed, with GCC/Boost retries for macOS tooling. verify-joint fails its stored source-hash check (AssertionError: Makefile) on unchanged main at 12a4934.

[Mister-Meeseeks]

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

Contribution: Composition of R705 bits and a retimed R560 complex supplier.

Review and limits: Retains mutable-target, whole-call hosting, Gaussian-adapter and all-size interfaces. Relative exponent changes are not runtime benchmarks or complete numerical cutoff certificates.

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: 355d9f7ff293e291676ff4a32eed434419692576. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.