Proof-Heavy

We define the **Latent** of a smooth system as the basis-free element of a graded Hilbert tensor algebra that completely characterizes the system's distributional, dynamic, and functional properties.

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.

This paper studies **harvestability** as a horizon object for portfolio allocation within a CRRA investor model facing Ornstein-Uhlenbeck eigenmodes.

The CDF of a weighted sum of correlated lognormal random variables has lacked a tractable characterization since Fenton (1960). We show that eigenvalue conditioning of the correlation matrix, followed by Fourier-cosine inversion, yields an analytic, grid-free $N$-term spectral representation of that CDF: the **Spectral Lognormal Distribution**.

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.