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, kB, T and a single length scale LT. 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 ΠD=Υₙ=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 GD = (c³/)LT(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 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 Schwarzschild black hole) in Appendix B Arbitrary spacetime dimension $D=n+1$ throughout