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 Etot=mc2+ℏc/Δx E ₓ₎ₓ = mc² + c / x Etot=mc2+ℏc/Δx (Δx≤Θlocal (x) x ₋₎₂₀₋ (x) Δx≤Θlocal (x) ). 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 ϕ (x) =2c2/Θlocal (x) (x) = 2c² / ₋₎₂₀₋ (x) ϕ (x) =2c2/Θlocal (x) and modified inertia f (aloc, ϕ) =aloc/ (aloc+ϕ/6) f (a ₋₎₂, ) = a ₋₎₂/ (a ₋₎₂ + /6) f (aloc, ϕ) =aloc/ (aloc+ϕ/6). The framework derives, from first principles, the observed baryon asymmetry η≈6. 1×10−10 6. 1 10^-10 η≈6. 1×10−10, true spatial curvature Ωktrue≈+0. 0098 ₖ^ true +0. 0098 Ωktrue≈+0. 0098, QCD string tension σ≈0. 18 0. 18 σ≈0. 18 GeV², and αEM (MZ) ₄₌ (MZ) αEM (MZ) consistent with CODATA, using the observed CMB temperature T0=2. 725 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 (forward₄dₑvolution), 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, observer-centric cosmology