Constructive MTT Quantum Gravity III: A Massive Scattering Benchmark and the Massless-Graviton Infrared Contract

This paper separates a massive or infrared-regulated scattering benchmark from the physical massless-graviton problem in Modal Triplet Theory quantum gravity. A positive transverse-traceless mass gap does not describe the physical massless graviton, and finite-volume Gaussian and BRST results do not by themselves construct the local Lorentzian theory required by Haag–Ruelle scattering. The paper proves the operator statement that for isometric incoming and outgoing wave operators, the scattering operator is only a contraction in general and is unitary exactly when their ranges coincide. It also proves that a normalized SPT factor leaves the leading massless soft pole unchanged. Standard massive Haag–Ruelle theory is retained as a conditional benchmark after its full axioms are supplied. The physical gravity route instead requires a selected Lorentzian BRST theory, asymptotic null geometry, soft-charge control, dressed states or inclusive observables, infrared-regulator removal, and an appropriate completeness theorem. Current MTT data do not yet provide that packet. The paper therefore supplies a precise infrared dependency theorem and executable exit contract, not a unitary MTT gravity S-matrix.