A Persistence Equivalence for the Riemann Hypothesis (Working Draft)

We aim to prove that the Riemann Hypothesis is equivalent to a topological statement: all nontrivial zeta zeros lie on the critical line if and only if the maximum persistence lifetime of the prime gravitational manifold satisfies Lₘax (N) = O (√N polylog (N) ). The forward direction chains the von Koch estimate, a Riemann-Stieltjes convolution bound, and the Bottleneck Stability Theorem. The reverse direction uses the Ingham omega theorems, Fourier attenuation analysis, polynomial orthogonality, and the Elder Rule of 1D persistent homology. Working draft v1. 0; formally typeset manuscript in preparation. Fifth paper in the Prime Gravity series.