[aliromman]

This construction certifies conditional κ = 0.00308595, up from 0.00308520 in PR #5565. The raw crossing rises from (0.00308521055201, 0.00308521055202) to (0.00308595175070, 0.00308595175071): a strict gain of 7.4119868e-7 to 7.4119870e-7. The complete caller uses 66,708 paid jobs, 18 fewer, with the same 12,814 independent productive fields and rank surplus 760. The selected frontier is unchanged.

Proof · Four declarations · Complete receipt · Source pins · Constructor · Validation.

Three ADDs change chart. The new three-plane is the intersection of source frames 728 and 235. This permits helper 307 to finish at rank four instead of five. Each local call has paid delta -2H2 + 2H3 - 2H4 + H5 and target delta H4 - H5. Majorization proves a positive complete-moment change for every 0 < κ < 1. All scalar instructions, coefficients, scalar order, 208 main endpoints and eight owned lifetimes stay fixed. Both stages of the source cascade remain intact.

This is a scoped improvement to the pinned PR #5565 word. The concurrent PR #5599 reports a larger endpoint from a different independent-helper inventory. No combined bound or largest-open-bound claim is made here. The composition handoff identifies the affected fields and the split-cut compatibility checks still required.

Base: canonical main 5e0052ca0aa3036a3afa8b0438927377c8d97d53, priority revision 7. Consumed word and price source: PR #5565 at 9af814164b9dfc21f19ec737959d67cb71488c95. The unchanged executable source capsule is pinned to PR #5545 at 18968423711fd902aaee1099979497d55603e1dc. Discussion #5575 records the live scope and overlap checks.

Python 3.12 and the standard library suffice; no solver is required:

python3.12 -B scripts/research_package.py --package research/p104-coupled-frame-step

Normal and optimized modes both passed with warnings treated as errors. Each prints PASS_P104_COUPLED_FRAME_KAPPA_00308595; the launcher prints PASS_REGISTERED_RESEARCH_PACKAGE. Checks cover all original-input forward rows, 552,049 transpose coefficients, 2,915 exact signed native maps, the physical caller, two rational moment engines, compiler conditions and all 54 strict plus four functional outer predicates. Six new mutation controls and retained native/price controls are rejected. Package metadata, source-object equality, immediate-base ancestry and committed-byte checks pass. Full-history preflight was not run in this shallow checkout; no standalone read-only Git-free replay or unrelated historical suite was run.

The claim is tested at 0.0030859505. The fixed-invoice moment is strictly decreasing on [0,0.0034], so the stated crossing is its raw ceiling on that band. The five framework assumptions remain: native all-column implementation, owned erasure, uniform compiler closure, precision/fixed-tape costs and analytic recovery. The source helper-endpoint review status remains. The uniform word and complete rounded multiplier are not materialized. Independent scientific review and hosted CI remain separate from these author-side checks.

Credit Pierre-Loic Doulcet, @hexapode, for the consumed cascade; @DreamingOfClouds for the PR #5568 event-lattice search and PR #5561 free endpoints; Joel Pulikkan, @GamingPuzzled, for the PR #5569 handoff; @thu-nmrc for PR #5551; and Ali Romman for PR #5580, PR #5544 and PR #5545. The retained notices and credit include Gareth Davidson, David Arias, Cinna Davis, Jacob Alan Sussman, zxv, Cao Yifan and the earlier geometry, BIT, compiler, precision and analytic sources.

New construction, proof and verification by Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. The same assistant performed construction and checks; no independent reviewer or subagent was used.