Modal Triplet Theory: MTT as a Superset

This paper presents Modal Triplet Theory (MTT) as a “superset” framework that contains General Relativity, Quantum Mechanics, Quantum Field Theory, the Standard Model, Effective Field Theory, Kaluza–Klein models, Noncommutative Geometry, string/M‑theory, the heterotic Hull–Strominger system, and Loop Quantum Gravity as coherent fixed‑point projections. We formalize five standing modules (bounded geometry, spectral gap, projector, smoothing flow, convex energy) and prove a Superset Containment Theorem showing that the axioms and equations of each target theory arise as reductions of the same 10‑dimensional modal dynamics. Two structural results drive the program. First, selection: a Green–Schwarz–corrected functional is strictly convex in the heterotic flux/Strominger slice, so admissible flux backgrounds are unique coherent fixed points rather than members of a landscape. Second, quantum gravity: the transverse‑traceless graviton two‑point function has a Stieltjes/Bernstein representation (reflection positivity and causal support), and the coherent projector admits a spectral proper‑time factorization that inserts a universal Gaussian on internal graviton lines; consequently, any 1PI diagram with at least one graviton line is UV‑finite and the BV quantum master equation holds to all orders for anomaly‑free matter, with GR recovered in the infrared. A small bottleneck vector Θ (spectral gaps, harmonic norms, volumes, curvature and overlap integrals) controls parameters simultaneously across gravity, gauge, Yukawa, EFT, and cosmology, enabling global, falsifiable fits across regimes.