Problems the Research Targets

The program is not general-purpose theorem-proving — it is aimed at specific open problems. Each problem below links to the papers that make direct contributions, from proof skeletons to closed sub-results.

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Navier–Stokes Global Regularity

Clay Millennium Problem

Do smooth initial conditions always give smooth global solutions to the 3D incompressible Navier–Stokes equations?

Conditional framework verified 60%

2 papers →

Riemann Hypothesis

Clay Millennium Problem

Do all non-trivial zeros of the Riemann zeta function have real part exactly 1/2?

Conditional proof via two routes 55%

4 papers →

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The Three-Body Problem

Smale's 1998 list, Problem 5

Is there a closed-form, non-perturbative description of gravitational three-body motion in the general case?

Exact solution paper complete 75%

1 paper →

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Central Configurations Finiteness

Smale's 1998 list, Problem 6

For each n ≥ 4, are there only finitely many central configurations of n point masses under Newtonian gravity?

Lean-verified proof skeleton 80%

1 paper →

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Turbulence Scaling

Kolmogorov's 5/3 law and beyond

Can the empirically observed scaling exponents of high-Reynolds-number turbulence be derived from first principles?

Framework paper drafted 40%

1 paper →

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Neural Scaling Laws

Why do large language models work?

Why does model performance follow power laws in compute, data, and parameters? And when should we expect it to break?

Machine-verified derivation 85%

3 papers →

Exact Quantitative Finance

Closed forms where Monte Carlo used to rule

Can core objects of quantitative finance — VaR, ES, rough volatility, tail risk — be computed exactly instead of simulated?

Fenton solved, Lean-verified 90%

5 papers →

A note on scope

These are problems the program directly addresses through papers and proof artefacts. "Direct contribution" ranges from a full closed result to a Lean-verified skeleton of a larger proof. Read each paper's maturity badge (Working Paper / Draft / Proof Record) to see how far that particular contribution has been taken.