The Theory of Persistence : A Complete Monograph

Persistence Theory (PT) starts from a simple question: when a system passes through constraints, what disappears, and what persists? Its fundamental principle is the information identity log2 (m) = DKL (P || Uₘ) + H (P), which splits the total capacity of a constrained system into persistent structure and residual entropy. The Eratosthenes sieve is not assumed to be “the world”. It is used as the minimal arithmetic laboratory where persistence under constraint can be made exact. In this setting, the stationary structure of the mod-3 gap transition matrix yields s = 1/2 as a theorem. Combined with CRT decomposition, maximum entropy, Fisher–Rao geometry, and the unique fixed point mu* = 15 = 3 + 5 + 7, this produces a chain of derived identities for dimensionless Standard Model observables. The monograph derives 43 Standard Model observables with no continuously adjustable fitted parameter: coupling constants, particle masses, and mixing angles. The headline comparison gives a mean deviation of 0. 30% from experimental values, with median deviation 0. 06%. The electromagnetic coupling is reproduced at 0. 004 ppb; the Weinberg angle at 0. 01%; the strong coupling at 0. 05%. The same zero-parameter constraint is then tested beyond the Standard Model sector, including chemistry, nuclear and condensed-matter quantities, and cosmological observables such as the Hubble constant and the dark-energy equation of state. The English monograph is a preprint of 883 pages; a French version is also available. The work is accompanied by 51 primary open-source Python verification scripts and structured JSON reports intended to reproduce the numerical claims and support independent auditing. Preprint. Not yet peer reviewed.