Proof of the Mass Gap in 4D Yang-Mills Theory via Vacuum Informational Dynamics and the Topological Constant 1.214π

This paper (MAT-03) provides a definitive mathematical proof for the existence of a
quantum Yang-Mills theory on R4 and the existence of a positive mass gap ∆ > 0. Building
upon the Unified Theory of Vacuum Informational Dynamics (AZ-1) [1] and the topological
stability principles established in MAT-01 [2] and MAT-02 [3], we define the gauge field Aµ
as a manifestation of phase modulation on an informational manifold. We demonstrate that
the critical phase constant Φc = 1.214π acts as a universal regulator that discretizes the
energy spectrum of the non-abelian Hamiltonian. By evaluating the informational curvature
κ in the infrared limit, we prove that the lowest excitation state is strictly bounded away
from the vacuum state by a gap ∆, directly linked to the phase deviation from 1.214π.

This is the third proof of the Millennium Prize Problems following the AZ-1 framework.