The Spectral Realization of Arithmetic: A Physical Proof Pathway for the Riemann Hypothesis via the SABO Framework and Adelic Quantum Mechanics

Abstract The Riemann Hypothesis (RH) remains the central unsolved problem in mathematics. This paper proposes a structural resolution through the lens of Computational Ontology & Creation (COC), bridging Layer 1 (Mathematical Substrate) and Layer 0 (Physical Substrate). By mapping the arithmetic components of the RH to the SABO Algebra (State, Action, Boundary, Observer), we identify prime numbers not as static integers, but as the periodic orbits of a chaotic quantum dynamical system. We formalize the Berry-Keating Hamiltonian (H=xp) on the Adèle Space as the fundamental Action operator, and establish Hermiticity as the physical Boundary condition. This work suggests that the Riemann Hypothesis is the spectral manifestation of a quantization condition in non-commutative geometry, confirming that the mathematical universe is topologically isomorphic to a specific quantum physical system. Key Contributions: Application of the SABO Framework to Number Theory. Formal definition of the Adelic State Space as the substrate for arithmetic dynamics. Identification of the "Ghost Operator" corresponding to Riemann zeros. Philosophical unification of "The Void" (Layer 0) and "The Code" (Layer 1).