Horizon-Quantized Informational Vacuum (HQIV): A Unified Framework from Causal Horizon Monogamy and Discrete Null-Lattice Combinatorics

Horizon-Quantized Informational Vacuum (HQIV) is a relativistic completion of Jacobson's thermodynamic gravity that enforces entanglement monogamy on overlapping causal horizons together with the informational-energy conservation axiom. Two independent constructions — (i) a geometric route from phase-horizon corrected Maxwell equations satisfying Schüller's hyperbolicity criterion and (ii) a combinatorial route from integer mode counting on the discrete Planck-scale null lattice extended to octonions — converge on the identical auxiliary field and modified inertia. Lean 4 verified The framework derives, from first principles, the observed baryon asymmetry, true spatial curvature, QCD string tension, using the observed CMB temperature to select the current "now" hypersurface. It also embeds the Standard Model inside Spin(8) with triality generations, provides a geometric resolution of the black-hole information paradox via a soft dynamical firewall, and predicts a 51.2 Gyr wall-clock cosmic age whose apparent 13.8 Gyr appearance follows from observer-centric ADM lapse compression. All results are fully reproducible: the complete Python lattice evolution, CLASS patch, octonion Lie-algebra calculator, interactive browser tool, and N-body simulation code are provided in the repository. The multi-observer consistency and locality of the observer-centric manifold are explicitly demonstrated. This work presents a minimal, testable candidate for a unified description of gravity, the Standard Model, Yang-Mills mass gap, and cosmology emerging from a single principle. Keywords: HQIV, horizon-quantized vacuum, entanglement monogamy, discrete null lattice, octonions, Spin(8) grand unification, modified gravity, baryogenesis, black-hole information paradox