The Galactic Acceleration Anomaly as an Algorithmic Noise Floor: Deriving the MOND Scale from Entropic Thermodynamics

Astrophysical observations consistently indicate that Newtonian dynamics appears to break down in galactic outskirts, producing a mass discrepancy strictly correlated with a universal acceleration threshold of a0 ≈ 1.2 × 10−10 m/s2 (the MOND acceleration scale). Standard particle dark matter models treat this correlation as a coincidence of halo structure. This paper resolves the galactic acceleration anomaly by applying the Algorithmic Theory of Reality (ATR) and its thermodynamic formulation of the cosmological constant. By treating emergent gravity as an entropic force subject to the thermodynamic limits of information processing, we demonstrate that dark matter is a thermodynamic artifact of the universe's finite-bandwidth architecture. Key Results: The Algorithmic Noise Floor: We prove that when the local gravitational Unruh temperature drops below the ambient Gibbons-Hawking temperature of the cosmological event horizon, the local gravitational signal becomes informationally irresolvable. Derivation of the MOND Scale: Equating these temperature scales derives the MOND scaling law a0 = c2/RE = cH∞ from first principles, successfully reproducing the cosmological order of magnitude of the observed scale without ad hoc dark matter halos. Unification of Dark Matter and Dark Energy: The derivation reveals an exact algebraic proportionality between the MOND scale and the dark energy density: a02 = (8πG / 3)ρΛ. Both phenomena are shown to be manifestations of the same holographic boundary. Deep-MOND and BTFR: The framework naturally recovers the deep-MOND effective acceleration scaling and the Baryonic Tully-Fisher Relation (BTFR) as thermodynamic identities, alongside falsifiable predictions for the redshift evolution of a0. The galactic acceleration anomaly is thereby demystified: it is not the gravitational pull of invisible matter, but the entropic noise floor of the cosmological event horizon taking over the gravitational dynamics when the local signal fades below it. Supplementary Material: All algebraic steps, temperature equivalencies, dimensional uniqueness proofs, and the ℏ cancellation are independently reproducible via the companion computational verification script (using CODATA 2018 parameters), available at: https://github.com/srdrymn/atr-verifiy-mond-scale