Abstract

We prove the source-level consequences of the supplied density-weighted cubic preparation on the XI-G pure-trace plane-wave pair. The polarized correction is first order in the frequency, its spatial traceless projection vanishes, and the prepared bulk source retains the stated second-order coefficient. We also prove the distinction between comparison with the unramped source and comparison with a sharp-onset source, and derive the weighted-representative residual under compact interior variations.

These results do not identify a source with its retarded response, a response with the completed insertion, or an insertion with a compact free-shell kernel. The XI-G obstruction transfers only after a same-class comparison of actual observable kernels. The supplied later sheets are recorded separately: XVI-D constructs the witness response, XVI-E supplies a polarized root pairing, and XVI-F-v2 supplies an independently defined auxiliary evaluation. Their remaining compatibility checks are not discharged by the source calculation. No new quantum retarded coefficient or admission theorem is claimed.