TEORÍA DE LA DISTINCIÓN. REALIZABILIDAD FÍSICA ELEMENTAL Everything is Distinction: How Information ≡ Area ≡ Existence Derives Exact Black Hole Entropy, Gravity as Saturation, and Maxwell's Equations as Theorems

Abstract

Theory of Distinction: Elementary Physical Realizability What minimal condition must something satisfy to be considered physically real? This work shows that all of physics can be derived from a single answer: that which admits a finite operational procedure distinguishing it from its absence. From this single definition of scope, with no postulates about space, time, matter, fields, or dimensions, the following are proven as theorems: existence of a minimal quantum of reality \Delta_0, identity Information \equiv Area \equiv Distinction, quantization M=N\Delta_0, exclusion principle, operative immanence (no physical exterior), confinement to a single connected relational network, time as irreversible accumulation and necessary expansion, emergence of 3D space via pure algebraic topology, fundamental correlation \exp(-|i-j|) with S^1 phase, gravity as network saturation (RSGM) with a unique f(R) action recovering GR+$\Lambda$CDM in weak regime and replacing singularities with regular saturation boundaries in strong regime, electromagnetism as U(1) holonomy with Maxwell equations derived, matter as topological protection Q\in\mathbb{Z}, exact entropy S=N\ln2 with no logarithmic corrections, and quantum mechanics as a distinguishability limit. Everything is distinction. Space is the sum of distinctions. Time is the order of their effectuation. The only empirical, falsifiable hypothesis is the numerical identification \Delta_0 = 4\ln2\,\ell_P^2. The structure is fully falsifiable by R>R_{max}, \ln A corrections, M_{NS}>M_{max}, exact w=-1, or a true singularity.

Keywords