Nikul Solanki Protocol: A Complete Rigorous Analytic Framework for Yang-Mills Existence and the Mass Gap

This document outlines a unified mathematical framework for proving the global existence and smoothness of 4D non-Abelian Yang-Mills theories and the derivation of a strictly positive mass gap \Delta > 0. By integrating Twistor Geometry, Geometric Heat Flows, Stochastic Quantization via Regularity Structures, Logarithmic Sobolev Inequalities, and Topological Bounds, this paper provides a complete analytical proof strategy that bypasses the limitations of perturbative methods and singular discrete lattice limits.