Mathematical Foundations of G-MaTT: Toward a Full Quantum Field Theory from Pre-Geometric Torsion (Supplementary)

Abstract We provide the rigorous mathematical underpinning of the Generalized Mass as Twisted Time (G-MaTT) framework, completing its transition from a physical hypothesis to a background-independent, UV-finite quantum field theory. Crucially, we resolve the ontological gap in prior work by deriving the configuration space $\chi$ as the Gelfand spectrum of a self-referential phase algebra, eliminating assumed manifolds. The dynamics are governed by a branch-summed path integral over pre-geometric torsional histories, with the Twist–UnTwist (TUT) mechanism encoded geometrically as bundle desynchronization. In the infrared, synchronized branches yield: the Standard Model gauge group $SU(3)\times SU(2)\times U(1)$, Einstein–Cartan gravity as emergent torsion-curvature coupling, the Born rule from Fourier-tower interference. All UV divergences vanish because no smooth manifold exists above the Planck scale—only desynchronized branches. This supplement validates G-MaTT as a mathematically complete, falsifiable theory of pre-geometric torsion, where mass, time, space, and quantum fields condense from a single potential.