Proposition: Supported transport of the new results

The compactly smeared free identities and the supported reciprocity witness are unchanged by completion extensions agreeing near their relevant finite causal reserves. Chart transport through $\iota$ preserves their pairings and fixed-support continuity.

Proof. Finite propagation localizes the smooth free solutions and Green responses needed by a compact test to its finite causal shadow. The witness calculation is local in $w,u,v$; Proposition prop:localwitness places its support in the retained regular reserve.

Distribution transport is defined by transposition on tests and densities. On the fixed compact reserve, the chart and inverse have bounded derivatives of every required finite order. The corresponding test seminorms therefore give equivalent local descriptions.