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

Abstract We derive the Planck frequency Ω₀ = c⁵/ℏG from first principles in Generalized Mass as Twisted Time (G-MaTT), demonstrating that it is not a dimensional coincidence but the natural clock rate of the primordial mass-time torsional potential ℳ_μ. In G-MaTT, reality begins with ℳ_μ—a pre-geometric, dimensionless potential identical to the source of mass and time—defined over a configuration space χ with no prior spacetime. Time emerges as t = (1/Ω₀) ∫ ℳ_μ dχ^μ, making Ω₀ the conversion factor between torsional phase and physical time. We show that Ω₀ arises from the unification scale of quantum mechanics (ℏ), relativity (c), and gravity (G) within the mass–torsion correspondence. This derivation implies that: Time is emergent and discrete at the Planck scale, Spacetime is not fundamental but a low-energy condensate, UV divergences are avoided because no continuum exists above Ω₀, Quantum gravity is testable via torsion-amplified interference (e.g., neutron phase shifts). This work proves that G-MaTT is not merely interpretive—it is a predictive, falsifiable framework that resolves the measurement problem, explains the Standard Model, and redefines unification as torsion-first emergence.