Yang–Mills Mass Gap and Local Quadratic Variation of Phase-Rate

We propose a new mathematical and physical framework to approach the Yang-Mills existence and mass gap problem by shifting the focus from abstract spectral difficulties to local phase fluctuations. Key Concepts & Contributions: Phase-Rate & Holonomy: We reinterpret the time component of the non-Abelian gauge field as a genuine phase degree of freedom, rigorously constructed through gauge-invariant Wilson lines. Local Quadratic Variation (LQV): We introduce the concept of LQV to quantify microscopic field noise, analogous to stochastic quadratic variation in Brownian motion but tailored for gauge fields. The Triple Equivalence: Under standard constructive QFT axioms, we establish a profound equivalence linking a positive mass gap (m > 0), finite positive local phase fluctuations (0 < Lambda < infinity), and vacuum stability. This work provides a unified, intuitive roadmap connecting kinematics, Hamiltonian dynamics, and spectral decay. It bridges the gap between functional analysis and quantum field theory, offering fresh insight into one of the Millennium Prize Problems. (Note: This preprint acts as a working paper detailing the conceptual framework and analytic roadmap. Full quantization and rigorous functional estimates are left for future investigations.)