Planck-Scale Discreteness as Rendering Resolution: A Directional Anisotropy Prediction for Lorentz Invariance Violation (Paper IV)

This paper proposes a novel framework for interpreting Planck-scale discreteness as a fundamental rendering resolution, predicting a specific directional anisotropy in Lorentz Invariance Violation (LIV). We argue that a lattice-like gravitational substrate must manifest not only as energy-dependent delays but also as a statistical bias in the arrival times of high-energy photons from gamma-ray bursts (GRBs) relative to their celestial coordinates. By introducing directional anisotropy as a critical observable, this work provides a new methodological pathway to empirically test the granular nature of the universe beyond current isotropic constraints.