Theorem: XX-D release and Q3 status

On the identical printed power-law background and original-rod prescription, this manuscript establishes:

1. the full second classical jet (eq:inverse)–(eq:qloc), including all embedding and induced-metric contributions and the proved absence of $Y_2$;

2. the native unsmoothed classical insertion on the spatial Schwartz domain;

3. compact microcausal Hessian admission after a source cutoff, without mistaking opposite-sign equal-time covectors for a microcausal exclusion;

4. explicit compact one-contraction Wick symbols and an alternative transverse numerical extension;

5. a conditional native cutoff-free symbol and compact regular-probe products, with distinct internal and external infrared hypotheses;

6. native same-class infrared non-determination and the unavoidable inverse-distance two-rod canonical term;

7. exact recovery of the classical formal symbol and a smooth pure-trace blind sector.

The data supplied in XX-C do not verify the infrared hypotheses for a selected representative or supply the covariance on the required two-endpoint noncompact domain. Accordingly the requested native quantum Q3 gate is not closed by the present release.

Proof. Item (i) is Theorem thm:jet and the explicit expansions. Item (ii) is Theorem thm:classicaldomain. Item (iii) is Proposition prop:microcausal. Item (iv) is Theorem thm:compactWick and Proposition prop:Taylor. Item (v) is Theorem thm:native. Item (vi) is Proposition prop:IRfailure and (eq:RRtail). Item (vii) is Theorem thm:symbol and Proposition prop:traceblind.

The hypotheses distinguishing the conditional native theorem from the unconditional compact construction have been explicitly retained. Their verification is not among the conclusions.