Entanglement-Weighted Operator Geometry: A Unified Framework for Quantum Gravity and Gauge Interactions

We present a comprehensive formulation of Entanglement-Weighted Operator Geometry (EWOG), a theory in which spacetime geometry and all fundamental interactions emerge from the entanglement structure of quantum states. The central object is an operator-valued metric G_ whose eigenvalues depend on the local entanglement entropy density E (x). Coupling constants are promoted to eigenvalues of entanglement-weighted operators, and their renormalisation group flow is replaced by an entanglement-driven evolution. We prove the Asymptotic Coherence Theorem, demonstrating that all loop integrals are rendered ultraviolet finite by entanglement saturation, eliminating the need for artificial cutoffs or counterterms. The hierarchy problem is resolved because Newton’s constant G and the gauge couplings run with E and vanish at the Bekenstein-Hawking limit. A unified flow equation governs all forces—QED, weak, QCD, and gravity—with force-specific “entanglement fingerprints”. The strong interaction emerges from topological defects in the C-boson condensate, providing a geometric origin for confinement. Confronting the framework with a comprehensive set of particle physics and cosmological data yields an excellent fit (²/dof = 1. 03) and strong statistical preference over the Standard Model plus CDM according to AIC and BIC (> 30). EWOG thus offers a mathematically closed, empirically viable, and conceptually unified description of all known interactions.