Entanglement-Weighted Operator Geometry: A Quantum-Information Theoretic Framework for Gravity and Cosmology

We present a complete mathematical formulation of Entanglement-Weighted Operator Geometry (EWOG), a novel framework that recasts spacetime geometry as an emergent phenomenon from quantum information processing. By postulating that the metric tensor is fundamentally an unbounded self-adjoint operator on a bipartite Hilbert space, weighted by the entanglement content of the quantum state, we derive a unified action principle that naturally yields modified Einstein field equations. The theory predicts an effective gravitational constant \ (G₄₅₅\) that evolves with cosmic time, explaining recent JWST observations of unexpectedly massive galaxies at redshift \ (z 14\). Furthermore, we demonstrate that galactic rotation curves can be reproduced without dark matter particles through entanglement gradient effects. We provide rigorous statistical validation using AIC/BIC model comparison and Figure of Merit analyses against observational datasets spanning early-universe galaxy formation to local galactic dynamics. The framework satisfies all known conservation laws while offering testable predictions for laboratory quantum-gravity experiments.