Abstract

We study a fixed two-component retarded distribution model with a compact product smoothing profile, a nonconstant advanced scalar root, and an ambient first-order source jet. The localization includes aligned crossed cones, internal coincidence, and separated internal endpoints.

The response rows and two-line adjoints are assembled in one distributional convention. For the negative placement $5z$, we integrate the internal cones exactly before taking smoothing asymptotics. This replaces a radius–angle absolute-value estimate by a boundary/interior decomposition. A derivative-controlled first correction to the weighted master convolution determines the previously missing third temporal derivative of the integrated vertex.

The complete seven-row family has an inverse-cubic leading distribution on arbitrary localized tests, with a compact-uniform $O({\delta }^{-2})$ remainder and an independently controlled logarithmic-scale derivative. The nominal inverse-quartic contribution of $5z$ vanishes. The advanced cone fundamental solution identity also gives a genuine cancellation between the inner-tip part of the positive placement $5a$ and the response leading coefficient.

The collected inverse-cubic distribution nevertheless survives: a separated support-isolated test detects it. The raw family therefore does not converge, and corrections supported on $z=a$ cannot restore convergence. The available remainder estimate does not establish convergence after leading subtraction. No complete lower-order expansion, finite part, profile universality, or physical quantum admission is claimed.