The Global Entropic Consistency Principle (GEC): A Strictly Physical Axiomatic Framework

The Global Entropic Consistency Principle (GEC) is formulated as a strictly physical conservation law governing the informational structure of a closed quantum system identified with the causal horizon. The horizon is defined as the maximal informational boundary of the system, represented by a finite-dimensional Hilbert space composed of elementary subsystems (pixels). The fine-grained entropy of the horizon is invariant under its unitary evolution, expressed as d/dt Sglobal = 0. This invariance is interpreted as a necessary condition for the existence of the horizon as a consistent informational object. Local entropies associated with individual subsystems may vary, but must satisfy a compensation condition ensuring global invariance. In the continuum limit, this yields an informational continuity equation: ∂ₜ s + ∇ · Jₛ = 0. This equation forms the basis for understanding microscopic and macroscopic physical behavior: quantum mechanics is compatible with the microscopic continuity of informational density, while geometric and gravitational phenomena correspond to macroscopic organization of informational fluxes. The GEC provides the informational foundation upon which the Unified Theory of Horizon Coherence (UTHC) is constructed.