What may and may not be handed to X-B

The available classical material is:

1. the off-shell coefficients (eq:Ozero)–(eq:Otwo);

2. the joint kernels (eq:uone) and (eq:utwo);

3. the named configuration and test spaces;

4. the support and continuity statements of Section sec:kernels;

5. the action identity (eq:switchedNoether);

6. the nonzero regulator defect (eq:infdefect);

7. the single first interaction

   $$V_1(g)=\int g{\ell }_1,$$

   including both its gravitational and scalar terms.

There is no cleared classical gauge-invariant handoff for this prescription. A later paper cannot treat the defect as absent. A changed regulator or coordinate prescription would define a new problem and would require a new classical proof before being used as the invariant input of X-B.

No kernel is labeled quantum-admitted here. No product, extension, causal factorization identity, or quantum normalization is defined. Smooth classical kernels do not by themselves constitute the required end-to-end quantum construction.