Conditional kappa 0.001590984155135328: R420 bit plus PR548 complex

[rohanarun]

Conditional kappa = 0.001590984155135328, +0.0171593% over this PR's earlier 0.001590711200057236. Compose #543's verified R420 bit supplier with #548's stronger complex component. The complex supplier binds.

Bit c =0.001653826988146798944268 (#543 at 2065fe4f72a914d907f1046603f5a36f17018535); complex b =0.001593519419282306763502 (#548 at 66dbc2bffc1bfa8d50b3f9a2ac7ccba8fd9f6f36). No source word, owner map or physical invoice is changed. PR548's bit supplier is not used. This recomputes the actual two-supplier minimum and outer assembly rather than adding separate gains.

Fresh exact checks pass: both rational moment engines on both actual profiles, lower acceptance/next-grid rejection, rank deficits and halving bounds, six explicit finite bootstrap cutoffs, 47 strict outer inequalities and four invalid-parameter/grid controls.

Independent physical replay: PR543 native columns, interleaved-interface checks, both stage counts, complete hosting/invoices and baseline controls passed previously on Python3.14. PR548's complete changed-complex component now also passes: static44 reconstruction, 477 frame lifts, cold-dirt source substitution, scalar/frame checks, changed local phase edges, residual wrappers, complete owner/controller controls and finite invoice. Its final canonical-word/global-template hashes and complete profile match the published source. Hash-bound unchanged phase/data dependencies are reused. The unused PR548 bit word was not rebuilt.

Offline arithmetic-only verifier:
python -B research/r420-static44-composition/verify.py /absolute/new/receipt.json

Physical source pins and fresh receipts are retained separately. Earlier PR544-based results and all observed failures/repairs remain in history/ and evidence/. A dedicated Python3.11/3.14 workflow checks arithmetic; GitHub CI is separate and is not claimed passed.

PR543's phase-B source rewrites retain its explicit H1-H5 interleaved scalar-interface argument. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic-transfer assumptions remain conditional. No unconditional theorem, full Lean proof or measured speedup is claimed.

Prepared for rohanarun with OpenAI Codex assistance. This is a composition contribution. Credits: eumemic #543 (Claude-assisted R420), Dugongue #548/#541 (OpenAI-assisted complex improvements/static44), chafreaky #544, rohanarun/Claude #534 frame lifts, icekylinx #535/#531 and phase/compiler ancestry, DreamingOfClouds #484 and all original authors retained in source notices.

[Mister-Meeseeks]

Thank you @rohanarun. This contribution at eecca20a24258cb6d9f698b1984a95029bac0a1c is incorporated in the reviewed family through #588, published in 9594b61.

Pure composition of unchanged #543 bit and #548 complex profiles through two exact moment engines and all outer inequalities. The larger #543 bit rate prevents adding the two parent gains arithmetically; the actual supplier minimum binds. Both underlying changed operators are independently replayed elsewhere in this family. Historical earlier #544 composition and failures remain retained.

Preserved implementation and research:

• research/r420-static44-composition

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.