An SPT-Filtered Euclidean TT Model and Its Conditional Perturbative Properties

This paper isolates the mathematically valid part of a proposed spectral proper-time modification of a transverse-traceless graviton propagator. A positive lower endpoint in an explicitly assumed proper-time measure gives Gaussian Euclidean decay, but it does not follow from a positive internal spectral gap. For a fixed graph, filtered lines control every ultraviolet loop direction exactly when their momentum map has full rank on loop space, equivalently when the unfiltered subgraph is a forest. A nonzero positive Kallen-Lehmann or Stieltjes propagator cannot also have permanent Gaussian decay in the same Euclidean spectral variable. The earlier claims of automatic reflection positivity, causal support, all-loop finiteness, BRST consistency, unitarity, and an MTT-selected ultraviolet completion are withdrawn. The construction remains a conditional Euclidean filter or regulator model.