Temporal-Resonance Multiplicity and the Gravitational Portal in TEBAC 9D/9D+: Interacting Radius and Spatial-Square Bounds — One-Sided Location, Vanishing Radial Error, and Controlled Ultraviolet Tails

This cumulative preprint presents Version 74.0 of ''Temporal-Resonance Multiplicity and the Gravitational Portal in TEBAC 9D/9D+.'' The new contribution develops nonperturbative estimates for the inherited scalar--auxiliary interacting measure on a normalized three-dimensional torus with a finite Fourier cutoff. The action, composite-source subtraction, and nonlocal auxiliary exchange are retained throughout. The results assume a prescribed contact envelope that includes the previously studied logarithmic counterterm trajectory; they do not derive that trajectory from the full primitive TEBAC law. The analysis establishes a second-moment bound for the squared field radius on the scale of the squared Wick variance and proves that the probability of a fixed relative deficit below the Wick variance tends to zero as the cutoff is removed. Retaining the dimension-dependent radial integration entropy improves the mean-square difference between the actual squared radius and its computed conditional radial mode to \(O(M^{-1})\). The same rate holds for the corresponding difference of smoothed composite sources, without replacing the inherited source subtraction by the conditional radius. Exact averaging of Fourier sine--cosine phases in a quadratic angular comparison is combined with the full quartic Gibbs reweighting. This yields moment and tail bounds for the spatial square in the actual interacting angular measure. Together with the radial estimate, these bounds show that source frequencies above \(M^{1/2+\varepsilon}\), for \(0<\varepsilon<1/2\), contribute \(O(M^{-4\varepsilon})\) to the mean squared norm of the smoothed source. In particular, the threshold \(M^{3/4}\) gives an \(O(M^{-1})\) bound. The accompanying materials include the full cumulative LaTeX manuscript and compiled PDF, an extract of the new section and conclusion, verification code, and symbolic, rational, and numerical check results. Exact inequalities and certificates are distinguished from numerical implementation tests and from physical parameter assignments. The scope remains explicit. These results establish relative-scale radial control and suppression of a moving ultraviolet tail within the stated scalar parent. They do not yet establish a cutoff-independent \(O(1)\) radial mismatch, fixed-threshold source localization, control of the remaining low-to-intermediate frequency band, or the physical selection of the primitive contact trajectory. The full scalar--gauge--fermion measure, complex phase, and same-family continuum and physical spectral identification remain separate tasks. Version 74.0 does not claim unconditional physical closure of TEBAC 9D/9D+.