Lean-Verified Chronos Navier-Stokes Certificates: Unified Clock System for OpenAI's Periodic Candidate - Formal Validation Milestone 2

This record contains the publication-facing verification report and the complete reproducible Lean 4 certificate package for Formal Validation Milestone 2 of the Chronos Navier-Stokes program. The formal adapter was compiled against OpenAI's public NavierStokesAndEuler repository at the pinned upstream commit using Lean 4.34.0-rc2. It connects OpenAI's actual selected periodic candidate to the Chronos change, arrow, action, and aim clock framework. The verified results include the instantaneous clock balance throughout the positive presingular time domain, nonnegativity of the arrow rate, exact equivalence between ordinary action and aimed action, zero initial change, arrow, and aimed-action rates, and the accumulated history identity for every oriented interval within the candidate's full presingular domain. The PDF explains the mathematical definitions, formal connection, principal Lean theorem, proof structure, pinned environment, and axiom-audit results in a readable format. The ZIP archive contains the Lean source modules, reproduction script, checksums, complete build logs, and static audit results. The pinned reproduction completed successfully with 9,308 build jobs. All 20 audited declarations reported only the standard Lean and Mathlib logical foundations, with no sorry, admit, or sorryAx dependencies. Together, the two files provide both a human-readable account of the result and the complete machine-checkable certificate needed for independent reproduction.