Lean-Verified Chronos Navier-Stokes Certificates: Unified Clock System for OpenAI's Periodic Candidate - Formal Validation Milestone 2
Year: 2026
Type: preprint
Abstract: This deposit contains a set of Lean-verified mathematical certificates developed as part of the ongoing Chronos formal research program and its application to the three-dimensional incompressible Navier–Stokes equations. The certificates establish a connected formal progression from the Change Clock framework into the unforced Navier–Stokes setting. The current milestone includes formal results for unforced change/dissipation balance, localized balance and pressure-return isolation, componentwise and vector weak-momentum identities, and the construction and use of smooth compactly supported annular cutoff tests for directional and angular analysis. The included Lean developments build on the formally specified Navier–Stokes framework in OpenAI’s NavierStokesAndEuler project and use pinned Lean and Mathlib dependencies for reproducibility. The certificate packages include source files, dependency information, build records, and cryptographic hashes linking the archived files to the exact verified versions. The formal development is cumulative: these results are intended to serve as reusable foundations for subsequent certificates involving pressure return, angular traction, limiting arguments, Liouville-type gates, and related regularity analysis. This is part of a continuing working series. Additional Lean-certified stages may extend or consolidate the present formal dependency chain as the research develops.
Author: Hall, Matthew
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212131356
Cites:
Cited by:
Related to: