Derivation of the de Broglie Matter Wave from Generalized Mass as Twisted Time (G-MaTT)

Abstract We derive the de Broglie matter wave—including the relation λ = h/p and the complex wave function ψ(x)—from first principles in Generalized Mass as Twisted Time (G-MaTT). In G-MaTT, mass is not a property of matter but arises from the primordial mass-time torsional potential ℳ_μ, defined over a pre-geometric configuration space χ. Particles are stable topological knots in the emergent mass torsional field M̂_μ, and their propagation accumulates a physical phase θ(x) = ∫ ℳ_μ dχ^μ. We show that: The spatial gradient of this phase is proportional to momentum: |∇θ| = p / ℏ, The wavelength of interference is λ = 2π / |∇θ| = h/p, The wave function arises from superposition of phase-coherent M̂_μ-branches. No quantum postulates are assumed—only the geometry of ℳ_μ. This derivation confirms that the matter wave is not a physical wave in space, but the observable interference of torsional field histories.