Arithmetic Information Entropy and the Hubble Tension: A Deterministic Derivation of the α-Drift from Riemann Zeta Zeros

This paper proposes the Arithmetic Theory of Everything (AToE), a novel theoretical framework that derives fundamental physical constants from the spectral density of the non-trivial zeros of the Riemann Zeta function The study adresses the "Hubble Tension"—the 5.6 km/s/Mpc discrepancy between early-universe (CMB) and late-universe (Local) measurements—by demonstrating that the fine-structure constant 𝛼 is not a static parameter. Instead, it follows a non-linear, deterministic drift driven by the Prime Number Theorem. This work suggests that the expansion of the universe is an emergent phenomenon of "Arithmetic Cooling" within a quantized Prim-Fock space. Notes:This research was developed within the AToE Theoretical Framework. All mathematical proofs rely on the GUE statistics of the Riemann spectrum