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A Machine-Verified Conditional Proof of Navier-Stokes Regularity via Dynamical Coupling | Synapse

March 30, 2026Open Access

A Machine-Verified Conditional Proof of Navier-Stokes Regularity via Dynamical Coupling

Key Points

To provide a machine-verified proof of the regularity of 3D Navier-Stokes equations using a conditional approach.
Utilized Lean 4 for formal proofs
Demonstrated proofs via 175+ theorems
Reduced Millennium Prize problem to a single axiom
Confirmed regularity with zero errors in the proofs
Linked barrier growth with high enstrophy levels
Provided independent arguments supported by direct numerical simulation evidence

Abstract

Machine-verified conditional proof of 3D Navier-Stokes regularity in Lean 4 with 175+ theorems and zero sorry. Reduces the Millennium Prize problem to a single axiom: barrier growth with enstrophy. Three independent arguments for the remaining axiom supported by DNS evidence (P(β>0)=97.8%).

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Cite This Study

Anthony W. Eckert (Sat,) studied this question.

synapsesocial.com/papers/69c9c57ff8fdd13afe0bd6ff https://doi.org/https://doi.org/10.5281/zenodo.19272159

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