Formal Verification Is Not Foundational Derivation

Abstract

Twelve Closed SFT Source-Validity Disproofs of OpenAI's 2026 Mathematical Artifacts. This paper freezes twelve principal Lean declarations associated with OpenAI's ten advertised advances and asks whether each exact submitted artifact is a valid derivation inside the already admitted Smithian Fold Theory (SFT) model. Under the pre-existing SFT admission law, all twelve exact source-artifact validity propositions are disproved; all ten advertised bundles are invalid as submitted SFT results; twelve SFT-native reconstructions remain separately proved; and no native-to-source validity transfer exists. The release includes the paper, a companion essay on human credit in machine-assisted discovery, complete proof-chain evidence, corrected compatibility and completeness audits, implementation-distinct verification, Lean 4 source and reports, model-admission receipts, and checksums. The closed audit records 3,072 enumerated routes and decisions, 120 proof steps, 60 executable checks, 48 controls, zero open chains, and a whole-model Lean PASS over 2,777 admitted claims across seventeen branches. The result distinguishes conditional formal verification under imported foundations from foundational derivation under SFT's registered zero-axiom and zero-free-parameter constraints. It does not assert redistribution rights over OpenAI's captured manuscript PDFs, which are excluded from this deposit.