Unified Theory of Horizon Coherence (UTHC): Unity from GEC to Quantum Mechanics, Gravity, and the Standard Model

Unified Theory of Horizon Coherence (UTHC) is an informational framework in which gravity, quantum coherence, and galactic dynamics emerge from a single organizing principle: Global Entropic Consistency (GEC). In this view, horizons act as finite‑capacity information reservoirs, and any local change in informational content must be balanced by horizon‑mediated entropy flux. This requirement leads to a universal infrared relation a² = aₙ a₀, where aₙ is the Newtonian acceleration and a₀ = cH₀ / (2π) is the information‑flux scale set by the cosmological horizon. Applied to circular motion, this immediately yields the observed Baryonic Tully–Fisher relation v⁴ = G M a₀, providing a purely informational explanation of galactic rotation curves without invoking dark matter halos. In this formulation, galactic phenomenology, the Unruh effect, and Bekenstein–Hawking entropy arise within a unified entropic framework describing the infrared sector of horizon thermodynamics. Gravity appears not as a fundamental force or geometry, but as horizon‑mediated information flow constrained by GEC. The empirical infrared exponent ε ≈ 1/2 suggests that the leading irrelevant deformation of the horizon entropy functional has scaling dimension Δ ≈ 6, providing a concrete constraint on possible ultraviolet completions. The present work develops the infrared theory, derives its observational consequences, and outlines the requirements for a future microscopic pixel Hamiltonian and renormalization-group flow. In this view, gravity emerges as the macroscopic manifestation of information redistribution in a system with finite horizon information capacity.