From Phase Differences to Spacetime: A First-Principles Derivation in G-MaTT

Abstract We derive the origin of spacetime from first principles in Generalized Mass as Twisted Time (G-MaTT). Starting with a set of phase differences $\Delta\phi_{kl} = \phi_k - \phi_l$, we construct the Gelfand spectrum $\chi = \text{Spec}(\mathcal{A})$ — the configuration space of all possible phase histories. We then define a spectral triple $(\mathcal{A}, \mathcal{H}, D)$, where $D = \slashed{\nabla}_\chi \times \mathcal{M}$ encodes the geometry of the primordial mass-time torsional potential $\mathcal{M}_\mu$. Finally, we show that spacetime emerges via spontaneous symmetry breaking $U(1) \times SU(2) \to SO(3,1)$ — the minimal stable representation of the symmetry group after initiation. This process generates 3+1 dimensions, time, and mass — all from phase relations. No extra dimensions, no strings, no fine-tuning — just phase, algebra, and topology.