This monograph develops Persistence Theory (PT), a mathematical framework that studies the informational content of prime number gaps through the lens of information geometry, sieve theory, and statistical mechanics. The starting point is elementary: the Eratosthenes sieve, applied to residues modulo successive primes, produces gap distributions with a rich algebraic and geometric structure. The Chinese Remainder Theorem decomposes these distributions into independent components over Z/pZ; a Fisher metric emerges naturally on the resulting statistical manifold; holonomy angles sin²θp = δp (2 − δp) encode the geometry of each sieve step. The central observation - and the one that motivates the 282 pages that follow -is that these purely arithmetic quantities, evaluated at a fixed point μ* = 15 determined by the sieve's own convergence structure, produce numerical values that coincide with Standard Model parameters to unexpected precision. For instance, the product of holonomy angles over the three "active" primes 3, 5, 7 yields 1/α = 137. 035999… ; ratios of anomalous dimensions reproduce sin²θW = 0. 23119; an ODE driven by sieve-derived coefficients reproduces the running of αs. In total, 41 observables — couplings, mixing angles, mass ratios — are computed with a mean deviation of 0. 3% from experimental values, using no fitted parameters. The monograph documents the mathematical chain in detail: 19 unconditional theorems, explicit derivation traces for each observable, a bridge construction via Pontryagin duality and Osterwalder–Schrader reconstruction, and 230 validated Python scripts (100% PASS). It also identifies 15 falsifiable predictions, including Dirac neutrinos, normal mass hierarchy, and a specific value of H0. Whether these numerical coincidences reflect a deep structural connection between prime arithmetic and particle physics, or whether they arise from a more prosaic mechanism, is a question the author believes can only be settled by the predictions. The monograph aims to present the mathematical content with sufficient rigour and transparency for the reader to form their own judgement.
Yan SENEZ (Sat,) studied this question.