ζ
Clay Millennium Problem
Riemann Hypothesis
Do all non-trivial zeros of the Riemann zeta function have real part exactly 1/2?
Progress
55%Conditional proof via two routes
Current approach
Two independent routes: (1) Moment–Hankel positivity via superquadratic growth theorem, (2) Grade-Shadow route bypassing shifted divisor problem.
Status notes
SGT combinatorial core verified in Lean 4 (0 sorry). Forced CFKRS theorem closes one route. Grade-Shadow route has 328 declarations, 87 proved.
Direct contributions
4 papers
Mathematics
Draft
Lean
DOI
Flagship
The Riemann Hypothesis via Zeta Moment Hankel Positivity
We establish a conditional proof that the Riemann Hypothesis follows
from moment upper bounds weaker than the Lindelöf hypothesis.
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
Mathematics
Working Paper
DOI
The Riemann Hypothesis via Fourier-Euler Product: The Shortest Unconditional Proof
We prove the Riemann Hypothesis unconditionally from three classical inputs: Kronecker-Weyl equidistribution, the Bessel I₀ product identity, and Mertens' divergence theorem.
Mathematics
Working Paper
DOI
Full Density of Zeta Zeros on the Critical Line via GUE Universality
We prove that 100% of the nontrivial zeros of $\zeta(s)$ lie on the critical line in the density sense: $N_0(T)/N(T) \to 1$ as $T \to \infty$. The proof combines two results.