Unified Theory of Horizon Coherence (UTHC): Mathematics and Observational Tests – Informational Realization (v1)

This work is the second part of the Unified Theory of Horizon Coherence (UTHC) series, extending the conceptual framework introduced in the earlier preprint by developing its mathematical structure and confronting it with observational data. UTHC is an exploratory informational approach in which quantum mechanics, gravity, cosmology, and particle physics emerge from the entropic microstructure of the horizon. Here we derive the informational entropy functional, the flux‑geometry equations, and the infrared RG flow, and we extract the IR exponent ε=0.50±0.02 directly from SPARC RAR data. Through the holographic relation Δ=4+4ε, this yields a data‑driven scaling dimension Δ=6.0±0.08, linking galactic dynamics to horizon microphysics without free parameters. The framework reproduces MOND‑like scaling, flat rotation curves, and the empirical relation a0∼cH0. This preprint should be regarded as exploratory theory rather than established physics.