Modal Triplet Theory: From MTT to Standard Model

We derive the full Standard Model from the coherent fixed-point sector of Modal Triplet Theory (MTT). Three parallel internal bundles over four-dimensional spacetime, with base-only warping, yield commuting vertical Laplacians and a joint harmonic projector that is bounded on the relevant Sobolev scales. The Fundamental Contractivity Condition then guarantees a unique coherent fixed point, and the four-dimensional effective field theory is obtained by restricting the MTT energy to the coherent sector. We show that the Standard Model gauge group emerges geometrically, with the identifications B1 → U(1)_Y, B2 → SU(2)_L, and B3 → SU(3)_C. Chiral matter in three families arises from a gauge-preserving Z3 flavor holonomy, and anomaly cancellation is proven constructively using an integer-lattice basis. The Higgs sector and electroweak symmetry breaking follow with the correct curvature-dependent mass shift and renormalization-group evolution. Yukawa hierarchies and mixings originate from internal overlap integrals. A numerical one-loop renormalization-group analysis with modest high-scale thresholds reproduces observed low-energy couplings. We include a detailed particle dictionary, verify standard consistency conditions, and clarify the geometric origin of high-scale gauge normalization. The result is a self-contained and rigorous derivation of the complete Standard Model from MTT.