Abstract

We study the complete retained XIV Einstein–scalar contraction on the space of actual reconstructed internal kernels. An explicit mixed-vertex formula and finite branch–vertex inventory define its smooth-cross-line regularization on arbitrary joint tests. Every regularized member respects every reconstruction identity.

The internal retarded-frequency estimates are extended from nonzero pole charts to compact frequency sets containing the origin. Localized microlocal approximation proves convergence to ordinary products on their product-admissible domains. A separate estimate controls the complete regularized contraction, including tests meeting the characteristic locus: its distributional order is at most five and its smoothing growth is polynomial, with an explicit exponent in terms of the crossed distribution's local order. This is a moderate-growth estimate, not a smoothing-uniform bound or a characteristic-limit theorem.

A degree-four null coefficient array excludes a specified highest-degree reconstruction rule, while preserving its associated-graded class. Fixed-kernel and continuous-map limit criteria distinguish convergence of the named sum from a construction on the whole reconstructed space. Auxiliary cutoff locality, regularization comparisons, characteristic-conormal projection, and extension ambiguity are treated separately.

No characteristic limit, normalized quantum coefficient, or quantum admission for the complete frozen graph is asserted. The submission consists of the stated partial construction and estimates.