Conditional κ = 0.001591968902833346: subspace16 complex with full R420 replay

[chafreaky]

Conditional κ = 0.001591968902833346, +0.06189551% over PR547 at eecca20a24258cb6d9f698b1984a95029bac0a1c (κ = 0.001590984155135328). Complex b = 0.001594507308884431019637 binds; unchanged PR543 R420 bit c = 0.001653826988146798944268 remains slack.

Concurrent #550 claims κ = 0.001591045666134196; this candidate is 0.05802704% higher. Its rank-five scalar expansion is not used in this package.

The new contribution is a frozen assignment of 63 complex delivery-gate frames, after exact zero-response pruning. It changes the local profile by 16(e1 − e2 − e3 + e4) while preserving scalar operations of the sliced word, starts, central cut, helper widths and PR548's physical owners. Strict concavity proves a lower moment for every 0 < b < 1; both rational engines verify the actual global endpoint. Global gain is computed from the complete profile, not added to an earlier κ.

Package: research/subspace16-r420. Cold verification reconstructs both suppliers, including the complete original PR543 driver and interleaved-interface audit; all 2,929 complex Clifford phase edges and 224 endpoints; local/native/wrapper controls; all literal owners and seven corruptions; fresh finite invoice; two exact moment engines, six bootstrap steps, 47 strict outer inequalities and four rejection controls.

python -B research/subspace16-r420/verify.py --work /absolute/new/subspace16 --boost-include /usr/include

Final immutable package passed cold on macOS/Python3.14.8 (179.7s) and Linux aarch64/Python3.12.3 (229.5s). Receipts are in research/subspace16-r420-validation. All semantic results and complex word/program/phase/template hashes agree. R420 raw template hashes differ only through geometry timing metadata; expanded bit-operator hashes agree. GitHub CI is monitored separately and is not claimed green.

Attribution: PR548's complex construction, PR534 frame lifts and owner assignment; PR541/544 static44; PR535/531 and PR484 compiler lineage; eumemic's PR543 R420 bit supplier and original upstream authors. All names, licenses and assistance notices are preserved; 245 vendored files were compared byte-for-byte with their source Git blobs.

This finite witness retains the all-size compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic-transfer premises. The unchanged complex data controller remains a pinned dependency. No unconditional multiplication theorem, new Lean certification, measured speedup or κ = 1 result is claimed.

[Mister-Meeseeks]

Thank you @chafreaky. This contribution at e7faafc4fec401d24080e5b2df12f964f1cfe123 is incorporated in the reviewed family through #588, published in 9594b61.

Subspace16 is a specific construction and owner assignment; it remains a parallel witness, not combined arithmetically with later gains. Fresh complete replay passed.

Preserved implementation and research:

• research/subspace16-r420
• research/subspace16-r420-validation

The family review and individual disposition record the scope, evidence and attribution. Parallel and intermediate contributions remain credited even where a later composition has a stronger bound. The published multiplication bound remains conditional on the documented compiler, realization, hosting and analytic assumptions; these finite checks are not a full Lean multiplication proof.