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Millennium & Smale Problems

Attacks on six open problems

Formal attempts at problems from the Clay Millennium Prize list and Smale's 1998 list. Each paper has a Lean-verified proof skeleton. These are ongoing research — the papers present proof strategies and verified components, not always closed proofs.

5 papers

Formal Verification Working Paper Lean DOI Flagship
Grade Decomposition and Gevrey Regularity for Navier-Stokes: A Machine-Checked Conditional Framework
We introduce a grade decomposition of the Gevrey energy balance for the incompressible Navier-Stokes equations. The physically correct model uses $\mathbb{C}$-valued Fourier coefficients with a factor of $i$ in the advection; the real-coefficient model trivializes all grade-3 terms.
9,473 words 7 claims
Formal Verification Working Paper DOI Flagship
Toward Dimension-Independent Finiteness of Central Configurations for Positive Masses: A Scope-Audited Reduction with Named Open Bridges
A proposed route toward finiteness of central configurations for positive masses, with formalized components and explicit assumptions.
35,806 words 6 claims
Mathematics Draft Lean DOI Flagship
Toward the Riemann Hypothesis: A Superquadratic-Growth Framework for Zeta Moments and its Limits
We present an algebraic framework relating the growth of the zeta moments to Hankel-determinant structure, together with an honest account of where the framework does and does not reach the Riemann Hypothesis.
21,863 words 23 claims
Mathematics Draft DOI
The Euler Product Smoothness Theorem: Multiplicative Structure Forces Latent Existence
We prove that the distribution of values of random Euler products on the critical line possesses a stable Latent — a finite rational approximation with exponential convergence — and provide a **complete structural proof** of the Euler Product Smoothn
45,536 words 84 claims
Physics Draft DOI Flagship
Toward an Exact Latent Encoding of the Gravitational Three-Body Problem
A proposed finite Latent encoding for gravitational three-body trajectories, with convergence and formalization status separated from the main claim.
12,550 words 3 claims