Prime Gaps as Dynamical Regulators of Ramanujan-Type Infinite Radicals Esse título:

This preprint introduces a rigorous arithmetic–dynamical framework in which Ramanujan-type infinite radicals are interpreted as fixed points of nonlinear discrete dynamical systems. Prime-dependent perturbations governed by prime gaps are introduced, leading to a precise notion of dynamical stability. The main result establishes that Legendre-type bounds on prime gaps arise as necessary conditions for stability, without asserting the truth of Legendre’s conjecture itself. The work is conceptual, modular, and intended as a structural bridge between infinite radicals, prime gap theory, and arithmetic dynamics.