Work in progress: A Lean 4 Formalization of the Classical Continuation Chain for Periodic Navier-Stokes on T^3: Energy Identity, H^3 Commutator Reduction and the BKM Route

Work in progress (draft). Companion paper to the Lean 4/Mathlib repository. Proved unconditionally: H^3 BKM control and the periodic BKM criterion. Clay Statement (B) is proven only conditionally on the open named Prop PeriodicBKMIntegrability. Does NOT solve the Clay problem or prove Navier-Stokes regularity. Source: https://github.com/BenFrohman/periodic-ns-classical-continuation at commit 0cd3551. Sibling reduction paper: 10.5281/zenodo.23842296. © 2026 Benjamin Stanley Frohman (ORCID 0009-0006-7068-3718). Licensed under Apache-2.0. New version: corrected PDF (banner/DOI wording, updated status). Work in progress; does not solve the Clay problem.