EWOG: Entanglement-Weighted Operator Geometry as a Quantum-Gravity Framework and Explanation for Early Massive Black Holes

The discovery of the ultra-massive black hole UHZ1 at redshift $z\approx 10$ poses a severe challenge to standard cosmological models, which struggle to produce such a heavy object within the first 500 Myr of the universe. We present a complete, mathematically rigorous derivation of the Entanglement-Weighted Operator Geometry (EWOG) framework, a quantum-gravity theory in which spacetime geometry emerges as the expectation value of an operator-valued metric weighted by the local entanglement entropy. The theory predicts a redshift-dependent effective gravitational constant $G_{\text{eff}}(z)=G_0 e^{\beta S(z)}$, where $S(z)$ is the entanglement-entropy density of the primordial ``C-boson'' field. In the early universe the entanglement density is high, leading to a significantly enhanced gravitational coupling that dramatically lowers the Jeans mass required for direct collapse of gas clouds into heavy black-hole seeds. We derive the EWOG field equations from an operator-based action, prove the Berry-Ricci duality that links quantum phase twists to classical curvature, and show how CP violation arises naturally from the chiral topology of the C-boson. Using a suite of JWST and Chandra observations (including the mass function of early galaxies, the black-hole mass--stellar-mass relation, and the cosmic star-formation rate) we perform a detailed statistical comparison of EWOG with the standard $\Lambda$CDM model, string-gas cosmology, and loop quantum gravity. The EWOG framework provides a better fit to the data with fewer free parameters, as quantified by the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and a combined Figure of Merit (FOM). UHZ1 is therefore not an anomaly but a predicted consequence of a universe whose ``source code'' executes with an entanglement-boosted gravitational clock speed in its earliest epochs.