Modal Triplet Theory: From MTT to a UV-Finite, Unitary Quantum Gravity

We construct perturbative quantum gravity directly from the coherent fixed-point sector of Modal Triplet Theory (MTT). The projected graviton two-point function admits a Stieltjes/Bernstein (Kallen–Lehmann) representation, ensuring Osterwalder–Schrader positivity and causal retarded support. A Spectral Proper-Time (SPT) factorization of the coherent projector yields a universal Gaussian damping on internal graviton lines, so every one-particle-irreducible amplitude containing at least one graviton propagator is ultraviolet finite. Using the Batalin–Vilkovisky formalism within perturbative algebraic quantum field theory, we prove the Quantum Master Equation to all orders for anomaly-free matter content; background-field BRST identities and Nielsen gauge-parameter independence hold. Independently, in the Calabi–Yau/toroidal corner, one-loop modular invariance ensures finiteness. In the infrared, the Bernstein form factor tends to unity, so general relativity is recovered up to corrections of order (box/Lambda²). The construction is regulator-independent and anchored in the modal fixed-point geometry, providing a first-principles proof that perturbative quantum gravity around MTT fixed points is unitary, causal, and ultraviolet finite.