Abstract: This monograph presents a complete causal chain deriving fundamental physical parameters, including the fine-structure constant (α), from the statistical and geometric properties of prime numbers. Using the Sieve of Eratosthenes as a foundational variational framework, we demonstrate that the distribution of prime gaps under specific boundary conditions (Theorem T0: Forbidden Transitions) leads to an information-theoretic equilibrium. Key mathematical developments include: The Gallagher Fluctuation Theorem (GFT): Reinterpreted through the lens of the Ruelle Variational Principle to model sieve dynamics. Fixed-Point Convergence: Identification of a stability point (μ∗=15) in gap-class fractions, eliminating free parameters. Information Geometry: The derivation of a Lorentzian metric and coupling constants as emergent properties of the "Persistence Potential." This work provides a zero-parameter alternative to the Standard Model, where physical constants are shown to be algebraic identities arising from prime number theory. Includes Python scripts for numerical verification of the 14-step causal chain.
Yan SENEZ (Sat,) studied this question.