# Verification report: OPG-369 four-class theorem

The six-page English preprint proves the Schrijver-Seymour stabilizer inequality for at most four nonloop weight classes modulo the full basis-sum stabilizer, with a componentwise direct-sum extension. The unrestricted source problem remains unresolved.

The originating researcher completed a written self-audit of quotienting, loop deletion, empty-class padding, tight normalization, integer subtraction on minimal faces, all atomic models, the Vamos difference-set identity, exact Rado profile transfer, and iterated aperiodic Kneser. No gap is known in this stated scope after that audit. This is not independent peer review or proof-assistant verification.

Two exact cone-enumeration implementations and multiple inequality orders give the classical 37 primitive rays in ten orbits. Their 888 elemental slacks are binary. The published polynomial table normalizes to the same orbits. The atom checker verifies basis exchange, color-union ranks, and all integer profiles, plus 275,280 ordered label assignments over seven finite abelian groups. A separate bounded search checks 28,560 tight functions of rank at most six. Normal and optimized runs agree. The periodic Vamos example is retained as a negative control. These tests supplement the general proof rather than replace it.

The desktop compiler and Tectonic compile the final source successfully. All six PDF pages were visually inspected; the final build has no overfull/underfull boxes, undefined references, missing characters, or LaTeX errors. The author name appears at the top, affiliation and contact are in a footnote, and AI assistance is disclosed in ordinary prose.

The source manifest binds the manuscript, proof, audit, and portable exact checks. Extracted-archive replays are required by the packaging script before readiness is registered. Third-party source PDFs are not redistributed. Novelty and absolute priority are not certified; classical inputs are expressly credited.