The Unified Horizon Principle: Information-Gravity Duality at Causal Horizons

DCT/QG - PART V: The Unified Horizon Principle: Information-Gravity Duality at Causal Horizons Release Tag: v1.0-part-V This paper formulates the Unified Horizon Principle (UHP) - a consistency condition asserting that horizon thermodynamics and Newtonian gravity are two faces of the same information-geometry, controlled by the fundamental quartet ${c, ℏ, k_B, \mathcal{T}}$ and a single length scale $L_{\mathcal{T}}$. Background: DCT treats gravitational collapse as $D →D-2$ dimensional reduction, with degrees of freedom recorded on ledger surfaces. Key Contributions Master Identity: Derives the relation $\Pi_D=\Upsilon_n=1$, linking the thermo-geometric invariant (built from Unruh temperature, Landauer erasure, and the area law) to the pure-geometry invariant (built from Newton's constant and Gauss-law normalization). Field Equations Without G: Reproduces the Einstein equations in arbitrary dimension $D$ using only horizon thermodynamics and the Clausius relation, with Newton's constant emerging as $G_D = (c³/\hbar)L_\mathcal{T}^{(D−2)}$. Information-Gravity Duality: Interprets UHP as asserting that the gravitational coupling and the horizon's information density are conjugate variables - fixing one determines the other. DCT Embedding: Connects UHP to the Null-Pair Removal (NPR) mechanism, ledger-core geometry, and the transdimensional constant $\mathcal{T}=1/(4 \ln 2)$. Falsifiability: Identifies observational channels (black-hole thermodynamics, analog horizons, cosmological tests) where deviations from UHP would manifest. Technical Notes Self-contained derivations with explicit algebra in Appendix A Worked numerical example ($10 M\odot$ Schwarzschild black hole) in Appendix B Arbitrary spacetime dimension $D=n+1$ throughout