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_{\rm tot} = mc^2 + \hbar c / \Delta x Etot=mc2+ℏc/Δx (Δx≤Θlocal(x) \Delta x \le \Theta_{\rm local}(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) \phi(x) = 2c^2 / \Theta_{\rm local}(x) ϕ(x)=2c2/Θlocal(x) and modified inertia f(aloc,ϕ)=aloc/(aloc+ϕ/6) f(a_{\rm loc},\phi) = a_{\rm loc}/(a_{\rm loc} + \phi/6) f(aloc,ϕ)=aloc/(aloc+ϕ/6).

The framework derives, from first principles, the observed baryon asymmetry η≈6.1×10−10 \eta \approx 6.1 \times 10^{-10} η≈6.1×10−10, true spatial curvature Ωktrue≈+0.0098 \Omega_k^{\rm true} \approx +0.0098 Ωktrue≈+0.0098, QCD string tension σ≈0.18 \sigma \approx 0.18 σ≈0.18 GeV², and αEM(MZ) \alpha_{\rm EM}(M_Z) 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 (forward_4d_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, observer-centric cosmology