Coordinate refinement of aligned composition: conditional κ = 5.2790906739644e-5

[rohanarun]

Full verification passed on research c420393: 92 isolated modules, 20 patch checks, complete regeneration and six controls; all 51 research-head CI checks passed. Validation receipt added with documentation-only status changes.

Final-coordinate refinement of #91 gives the conditional bound κ = 13197726684911/250000000000000000 = 5.2790906739644×10⁻⁵, approximately 0.002443% above #91 at 264f202b52edc04d0c72ca9cb3138282ca68b9ad. The exact bit saving is 52793693766767/10¹⁸.

Swap coordinate labels 5/6 at h23 and 22/23 at h25 in the complete physical words. The role counts (26,387 / 34,772), XOR sequence, width (130,417,912) and total recursive rank (74,988,452,500) stay unchanged. Fresh fixed-basis residual profiles improve the moment. Every frame, source, output and scatter label is transported together; the full Cartesian data family is preserved. All endpoint, cleanup, copied-center and growth charges remain paid.

python3 research/aligned-coordinate-refinement/verify.py --regenerate
python3 research/aligned-coordinate-refinement/test_controls.py
make verify

The scan tested 48 identity/adjacent coordinate choices. It is a finite search, not a global optimum. The result retains #91's analytic, ordered-residual compiler, all-size recursion, scalar overhead, routing, prime selection, exact recovery and fixed-tape hypotheses. The inherited Lean companion applies to #91's arithmetic; this new exponent is checked by exact rational Python certificates, not a new Lean proof.

Credit Chafik Boukhalfa's #91 composition, Thomas DiFiore's #74 coordinate construction, Rohan Arun's #78/#85 refinements, eumemic, Rohan Garg, Avi Eisenberg, Dominik Scholz, Alejandro Zarzuelo Urdiales, and all earlier contributors and OpenAI. All inherited notices and licenses remain preserved. Prepared by Rohan Arun with OpenAI Codex assistance.

[Mister-Meeseeks]

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

Contribution: Adjacent coordinate flags and complete profile reassembly.

Review and limits: Exact-head CI evidence; historical variant retained independently of the selected record.

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: f5f5ebdfc92fa6001d209aafba432a36ff9d86f5. Publication: b84ba67156a01f9c2cb34fe1e3cb1dcdeab00d9c.