Abstract

We transfer the analytical obstruction of Cheung's X-A–Convolution to the supported I-B/X-A-ST setting without changing its regulator, gauge algebra, Cauchy data, or observation test. All wave operators remain on the declared Minkowski completion; the regular conical host is prescribed rather than reconstructed. The complete convolution data are stated explicitly, so the obstruction is proved rather than hidden in a positivity assumption.

The decisive identity is ${\mathsf{E}}_0\mathsf{C}{T}_{g,\epsilon }(K\xi )=S_{\epsilon }\xi$, not the identity required for coordinate covariance. For the parent compact witness we obtain a strictly positive translation-energy formula for $c_{\epsilon }$ at every allowed fixed width. The same coefficient survives evaluation on the scalar solution of the switched action, despite that action's plateau Noether identity. We retain the second-order defects and the genuine pure-gauge two-jet without promoting either calculation to an all-orders statement.

The supported transfer identifies precisely which compact sets must lie in the inherited developing chart. A change of variables, including its density Jacobian and transported two-point kernel, preserves the positive defect; it does not make convolution diffeomorphism natural. Laboratory field interpretation is conditional on this explicit support certificate, which is not implied by the ramp's causal reserve.

We then connect the analytical result to the proposed X-Enter-ST operational package: scalar-only invariant readout is necessarily uninformative, while a complete destructive-clock instrument can report supplied finite evaluations and preserve every unmeasured finite residual. An independently charged second coefficient would permit a conditional relational circuit, but is not constructed. Scheduled locality and reference-preserving SWAP transport concern these finite reports, not acquisition of the continuum coefficient.

The contribution is a controlled analytical–operational non-repair theorem on one retained host. The parent obstruction is credited to X-A–Convolution; the new supported audit makes its domain and interpretation explicit. No convolution repair, quantum characteristic coefficient, interacting differential, ultraviolet completion, or spacetime emergence is established.