The Riemann Hypothesis as a Computational Phase Transition: Indistinguishability of Arithmetic and Geometric Spaces at the Planck Scale and the Genesis of the Mathematical Universe

In this paper, we reformulate the non-trivial zero distribution of the Riemann zeta function (the Riemann Hypothesis) as a "phase transition phenomenon" arising from physical computational limits. We demonstrate that the observational limit imposed by the universe's minimum time unit (Planck time) results in distinct behaviors depending on the real part of the zeta function's domain. Specifically, in the classical region, arithmetic and geometric structures are clearly distinguished. In contrast, in the quantum region (the critical strip), the quantum fluctuations of both structures become indistinguishable, resulting in the restoration of Hamiltonian symmetry. Furthermore, we redefine this region as the "Realm of Creation of the Mathematical Universe" and propose that the zeta function serves as the "Primordial Blueprint" encoding all mathematical operations.