Arithmetic Genesis: A Dynamical Extension of the AToE for the Derivation of Classical Observables

This paper introduces a formal dynamical extension to the Arithmetic Theory of Everything (AToE), transitioning the framework from a static description of particle masses to a functional model of physical interactions. By conceptualizing the vacuum as an active information-processing medium governed by the Nyquist-Shannon sampling theorem, this work derives fundamental physical phenomena directly from number theory. Key contributions include: Redefining Motion and Gravity: Motion is modeled as a sequential phase-update within a 12-dimensional Prime-Fock space, while gravity emerges as a latency gradient resulting from informational bottlenecks in the arithmetic substrate (pp. 1, 4). Cosmological Derivations: The framework provides deterministic derivations for the CMB temperature (2.725 K) as vacuum Nyquist noise and explains the 5.3:1 Dark Matter to baryonic matter ratio as a geometric consequence of D12 → D3 projection (pp. 1, 6). Unification: By treating the Einstein Field Equations as balance equations of informational flux, the paper provides a bridge between General Relativity and Quantum Mechanics, reinterpreting the Heisenberg Uncertainty Principle through the lens of spectral aliasing (pp. 4-5). The work concludes with a "Call for Computation," proposing experimental tests via LIGO residuals and atomic clock drifts to verify these arithmetic signatures (pp. 7-8).