Quantum Information Permeability — Foundations and Gravity. Paper I: From a Relational Quantum Network to Einstein's Equations

We present Quantum Information Permeability (QIP), a pregeometric framework in which spacetime, gravity, and quantum dynamics emerge from three axioms on a relational network of quantum events. Axiom~A1 defines the universe as a directed graph whose nodes carry tripartite Hilbert spaces with octonionic bath dimension~8. Axiom~A2 introduces purity congestion ₖ=1- (ₖ²) as the sole dynamical field. Axiom~A3 (the Maximum Throughput Principle) selects the physical state by extremising a coherent-throughput functional; this uniquely forces a quantum erasure channel with permeability ₈₉=1/ (1+ (ᵢ+ⱼ) ). From these axioms we derive: the spacetime dimension d=3+1 and Lorentzian signature, via Fano-plane projection of seven octonionic throughput channels; the coupling =2-12, fixed by a holographic unit-throughput identity with zero free parameters; and the full Einstein field equations, obtained by three independent routes---the primary one varying the discrete throughput functional on the E₈ lattice with no continuum assumption. The PPN parameters satisfy ₏₏₍=₏₏₍=1 exactly, and gravitational waves propagate at~c with two tensor polarisations. The source-free Maxwell equations (all 12 components) are derived from the Fano-plane structure of the same octonionic algebra, with gravity using the associative part and electromagnetism the non-associative complement.