Theorem: Transfer to the prescribed regular host

Transport all stated chart objects, coefficient densities, and test families through the developing embedding. The first stages, canonical tree outputs, four presentation injectivity results, charge separations, and truncated partial product hold on the corresponding supported host presentation.

Every response and charge witness used in the proof remains inside the retained regular laboratory. No global conical covariance, Green operator, or product around the worldsheet is constructed.

Proof. Distribution transport through a diffeomorphism is defined by transposition on tests and densities. The developing embedding preserves the local metric, tensor species, and compact supports. The response identities are supported Cauchy identities by Proposition prop:saturation. The compact directions in Lemma lem:restricted are supported in $V$. The sharp trace witness uses an initial point within distance $t_0$ of an observation point, hence in $K_{\ast }$.

The remaining operations are compact distributional pairings, proper pushforwards, fixed transpositions, and algebraic maps on the actual polynomial spaces. Their identities are unchanged by this presentation transport. Compact coordinate changes modify finite seminorm constants but not the proved finite orders. No step defines anything across the defect.