Mathematics

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.

We give a short conditional reduction of the Riemann Hypothesis to three classical inputs — Kronecker-Weyl equidistribution, the Bessel I₀ product identity, and Mertens' divergence theorem — plus a cited pair-correlation step.

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.

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

We propose a conditional moment-based diagnostic for the Riemann Hypothesis based on stable finite rational approximations — *Latents* — for the distribution of $|\zeta(1/2+it)|$ on the critical line.