Constructive MTT Quantum Gravity II: A Conditional BRST/BV Compatibility and Physical-State Reconstruction Contract for SPT-Filtered Models

This paper gives a typed compatibility contract for BRST lifting, gauge independence, Borel summation, and reflection positivity in the Modal Triplet Theory quantum-gravity program. First, a common bounded functional calculus preserves a linear BRST complex when the kinetic Laplacians, spectral projections, domains, and boundary conditions intertwine the differential; independently chosen filters do not ensure this. Second, an exact finite-cutoff quantum BRST measure gives Ward identities and gauge-fixing independence by super-Stokes, while Borel summation preserves a linear Ward identity only under a common analytic domain and uniform Gevrey-one remainder bounds. Third, BRST cohomology yields a physical pre-Hilbert space only when reflection positivity is proved on the full BRST-closed positive-time observable algebra and exact classes lie in the reflection null radical. Positivity on the TT subspace alone is insufficient. We also prove that a nonzero positive Kallen–Lehmann measure cannot have permanent Gaussian decay in the same Euclidean spectral variable, so the old SPT positivity argument cannot be used. The result is a rigorous conditional theorem and an explicit exit certificate. Current MTT data provide useful finite classical and free-field inputs, but not yet the selected gravitational quantum measure, quantum master equation, constructive Borel theorem, or physical reflection-positivity theorem required by that certificate.