We show that asymptotic safety in functional renormalization group approaches to quantum gravity arises as a truncation shadow of a well-defined ultraviolet endpoint functional generated by projection-induced spectral proper-time damping in Modal Triplet Theory (MTT). Working on bounded-geometry time slabs and within an admissible regulator class, we prove Gaussian-damped ultraviolet integrability of the renormalization-group flow and construct a scheme-stable ultraviolet endpoint functional in a Banach space of analytic local and entire form-factor actions. We show that the linearized renormalization-group map at this endpoint has a finite-dimensional unstable subspace, yielding finite predictivity. Fixed points observed in finite truncations are obtained as shadows of the endpoint under truncation and canonical rescaling, rather than as exact fixed points of the full untruncated flow. The results clarify regulator dependence, the appearance of nonlocal form factors, and the robustness of asymptotic-safety calculations as consequences of projecting an underlying ultraviolet endpoint. All statements are slab-local and admissibility-conditioned.
Peter Nero (Thu,) studied this question.