Research: source-bind R437 ordinary coupling at c=1/576 (no κ claim)

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Change and mathematical scope

The old C0 program fails the complete recurrence at c=1/576. R437's actual paid program passes it, including the full bad-class fallback. This package establishes a source-relative ordinary-rate implication and finite source-adapter audit, with no supported multiplication κ increase.

Two exact engines enclose the new moment at .9999983130605053632871630546…, versus 1.0000087717216952679207496066… for the old source. Conditional on the changed program's uniform physical refinement/cost premises, the ordinary saving is a=575/331776 ≈ .001733097029321. The proof retains the 10^6 power majorant, original-width stock and eventual fit, both padded C0 returns, and complete wrapper coefficient 4283584 C.

The adapter reconstructs 903,456 paid requests from the actual R437 word, owners and residual idles; all 7,814,016 local-call events pass the retained chronology controller. The new rank-34 idle is consumed by the actual numerical callback and controlled CALL/RETURN fixture. A separate reduced physical fixture exercises Profile(1,576) and both padded returns. These are explicitly separate finite experiments, not one complete GL64 production cohort.

The fixed retimed T360 root remains unchanged. The prospective physical synthetic transfer retains both root/router terms and its normalization; its displayed saving .001725225817793 is not a multiplication κ. No selected-frontier or shared-code change is made.

Task and overlap

Explicit user-assigned scope r437-ordinary-t360: R437 into the stronger ordinary coupling, then joint retimed T360. Scope is unchanged; the bounded outcome is enabling LOCAL_PROGRESS. Base: canonical main 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6.

Exact inputs:

• PR3647: 36ff441479ff9c7e70d83f0becccd44da50effb8.
• PR3562: abb93be8b9ceca07a2b17f3a97db7bb6b074271d.
• PR3682: 431e6c6023ef352c41696469de7fb614cd4ded8c; its endpoint matches PR3653 at 607a09ff441c79b215a8127a81f4cc70021d0d9b: .001730418899766071163804 - 10^-46 - 10^-70. These pending public claims remain distinct from selected admission.
• Physical root/support/Fourier source pins and all retained byte hashes are recorded in the package.

The submission refresh covered 394 open PR bodies and 2,469 Discussion records at 2026-10-18 15:24 UTC, with no pagination warnings. PR3668 overlaps the scalar histogram comparison. The active independent word audit concerns the local identity and single-change controls; this package adds the ordinary recurrence/constants and source-bound adapter. Coverage is not a novelty proof.

Validation

Standard library, CPython 3.14.5; reproduction entry point:

python3 -B research/r437-ordinary-t360/verify.py

• Bounded replay passes exact moments/constants, actual catalogue/controller and rank-34 gate, physical wrapper provenance/cleanup/reuse, and the exact Count width predicate. Wrong-parent, foreign-program and wrong-source controls reject.
• The committed Git-free export passes the same checks; 128 retained source mappings match their exact Git blobs.
• The pinned R437 author cold verifier passed all 13 commands in 41.76 seconds with the exclusive replay lock. Raw logs and receipts are retained; replay is not independent supplier admission.
• Fresh clean-context Astra medium review returned CONCLUDE: YES for scientific commit 0c770abd231422a24cc4aecd45509440946b0a3c, independently reran the bounded checks, and checked all 13 cold-log hashes. Review is retained under reviews/; this is AI review, not human or formal approval. Subsequent changes concern publication documentation and evidence only.

REPLAY.json documents the self-contained archive workflow. It needs no runtime network or foreign Git objects and does not opt into the optional catalogue-based VERIFY.json registry. No full GL64 payload, combined production cohort, T360 admission replay, all-size refinement proof, Lean or Docker was run. The interrupted exploratory full Count boundary bisection is disclosed; the final check uses its exact power predicate plus small actual selector calls.

Credit

Retain ai-nanachi's R437 composition, Ali Romman's public1043 helper470, eumemic/DreamingOfClouds and native/owner lineage; Jose Manuel's ordinary/root/support/Fourier work, David Arias, Nick Petalas, Adam Gall, Gareth Davidson; Ross Richardson, roger-sato, Rohan Arun, Pierre-Loic Doulcet, PR3638's T360 work and all original notices. New investigation, code, proof and packaging used substantial OpenAI Codex assistance at human direction. Apache-2.0 and inherited notices are preserved.

Open next questions

See the package README and PROOF. The first unresolved obligation is one authenticated production R437 ordinary/native/router cohort, including its complete GL64 program and uniform changed-source refinement/cost proof. T360 uniform height/online precision/hosting and the complete Gaussian/CRT/product/recovery join remain open. Finite stock or prefix certificates do not discharge those obligations, and unknown costs are not zero.