On the Lattice-Theoretic Mechanics of Beta Decay, Nuclear Stability, and Unified Topological Transformations

Abstract We present a rigorous mathematical framework for nuclear transformations and fundamental particle interactions, moving away from the probabilistic assumptions and continuous-space anomalies of the Standard Model. By modeling space and nuclear architecture as a discrete hexagonal lattice regulated by a Mod 9 invariant, a 5184 frequency threshold, and a 7-cycle periodic break governed by the 3I pulse sequence (8\text{-}13\text{-}8\text{-}5\text{-}13\text{-}8), we resolve longstanding physical crises—including the beta decay continuous energy spectrum, the necessity of the neutrino hypothesis, and the mechanical divergence between quantum field theory and general relativity.