OpenAI's Ten Mathematical Advances Fail the Reality Test

Abstract

Twelve closed SFT disproofs, twelve first-principles replacements, and the cumulative cross-domain evidence that decides between them. This evidence-led successor directly rejects all ten mathematical and theoretical-computer-science advances advertised by OpenAI on 1 August 2026. It freezes the twelve principal Lean declarations behind those claims, preserves their exact statements and quantifiers, translates them into the pre-existing Smithian Fold Theory (SFT) admission law, and proves twelve source-validity negations. Each source artifact requires an imported three-axiom foundation where SFT permits zero and a theorem-specific carrier excluded by the already admitted SFT object grammar. The same frozen engine separately proves twelve materially and functionally different SFT replacements. No replacement confirms or transfers validity to an OpenAI source claim, and no chain remains open. The paper grounds that verdict in SFT's cumulative evidentiary record rather than compatibility alone: 2,777 admitted results across seventeen branches; first-principles derivation of the complete registered constants and force structure; 2,378 external-validation packages; immutable engine receipts; implementation-distinct replay; and whole-model Lean 4 verification. The release includes the 37-page paper, its Markdown source, a standalone evidence map, a deterministic evidence-and-source archive, executable validators, Lean modules and reports, proof-chain receipts, checksums, and Maria Smith's companion essay on human authorship, the intelligence enclosure and human-machine symbiosis. Captured OpenAI manuscript PDFs are not redistributed. The custody record binds their identities and the exact upstream source version used in the analysis.