Discrete Holographic Trigonometry, Metric Scale Projections, and the Effective Waveguide Confinement of Spatial Boundaries: An Exact Framework for Metric Refraction

This work formalizes Discrete Holographic Trigonometry, demonstrating that continuous Euclidean geometry emerges as an effective boundary projection of an informationally discrete space. It resolves the diagonal paradox to simultaneously derive quantum entanglement correlation limits and the observable cosmological horizon, establishes the effective optical phase angle of the universe, and analytically resolves the Cosmic Microwave Background Axis of Evil alignment anomaly via topological refraction with zero free parameters.