Technical Defense: Topological Phase-Lock and Nodal Criticality: A Discrete 4D Lattice Boltzmann Formalism for the Resolution of Cosmological Singularities

This document formalizes the mechanical defense of the PNI Equation (PNI). We demonstrate that the update limit Vn = 0.7314 and the refractive index nΥ ≈ 1.0822 are emergent properties of self-organized criticality in a 7,200-state discrete 4D manifold. By applying the Lattice Boltzmann Method (LBM) to vacuum jitter (ˆγp), we resolve the Big Bang singularity as a topological "Bounce" driven by Shannon capacity saturation.