EWOG: Symmetry conservation laws and its connection to CCC

We present a complete mathematical formulation of Entanglement-Weighted Operator Geometry (EWOG), a theory where spacetime geometry and matter emerge from a fundamental operator algebra weighted by entanglement density. The theory is defined through an action principle incorporating the Entanglement Weight Operator W = e^ C, where C represents the C-boson field encoding quantum coherence. Using variational principles and Noether's procedure, we derive three fundamental conservation laws: (1) Weighted Energy-Momentum, revealing energy exchange between matter and the C-boson field; (2) Coherence Charge Qc, stabilizing spacetime connectivity; (3) Weighted Angular Momentum J, explaining galactic rotation without dark matter particles. We further extend the theory to include CP violation through phase coupling in the C-boson sector, providing a mechanism for matter-antimatter asymmetry, and connect it to Conformal Cyclic Cosmology (CCC) through conformal invariance of the coherence charge. The theory offers unified explanations for JWST anomalies including early massive galaxies, Hubble tension, and supermassive black hole growth, making testable predictions for future observations.