Induced Gauge Fields from Topological Phase Defects on a Timelike Manifold: The Mass-Gap Mechanism at Fixed Longitudinal Correlation

We propose a phenomenological framework in which gauge fields and rest masses emerge on a four-dimensional manifold M4(x, y, z, w) with an internal timelike coordinate w. The Minkowski signature is not postulated but motivated by kinematic results in piecewise-flat quantum gravity. The macroscopic non-abelian gauge field Ai is induced by the statistical correlator of a foam of topological phase defects (vortex lines in the (i, w) planes), and the internal dynamics along w is isomorphic to Parisi–Wu stochastic quantization, with the stochastic time identified with the observable time.We formulate a conjecture on the generation of a mass gap: at a fixed finite longitudinal correlation length ℓw, the spectrum of internal modes is discrete and bounded from below by ∆ ∼ ℏc/ℓw. We state explicitly that ℓw is an input parameter of the model and is not derived from first principles; consequently, the result is formulated as “a gap at finite ℓw” rather than as a strict solution of the Yang–Mills problem. The boundaries of applicability and open problems are discussed.