What question did this study set out to answer?

To establish a machine-verified proof of regularity for the 3D Navier-Stokes equations using minimal axioms.

March 30, 2026Open Access

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

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To establish a machine-verified proof of regularity for the 3D Navier-Stokes equations using minimal axioms.
Utilized Lean 4 framework to develop proof with over 175 theorems.
Demonstrated the reduction of the Millennium Prize problem to a single axiom regarding barrier growth.
Supported arguments with direct numerical simulations (DNS) evidence.
Presented a conditional proof of Navier-Stokes regularity based on enstrophy growth.
Achieved a probability of P(β>0)=97.8% for the supporting evidence.

Implication

Conditional proof of Navier-Stokes regularity with barrier growth in enstrophy, suggesting its significance for mathematics.

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 (2026) studied this question.

synapsesocial.com/papers/69c9c5c5f8fdd13afe0bdc34 https://doi.org/10.5281/zenodo.19299433

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Implication

Conditional proof of Navier-Stokes regularity with barrier growth in enstrophy, suggesting its significance for mathematics.

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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