Declarations

scope. The proofs given here concern the dependency audit, local Euler variation, the explicit pure-trace Einstein–Hilbert coefficient, and variational integrability. They do not constitute the proposed admission and retarded response construction.

scope. XI-B, XI-E, XI-G, and XII-A-v2 are used in their supplied forms. Their inherited statements are distinguished from the calculations proved here. The changed-model freeze is not attributed to a predecessor that does not contain it.

-go scope. The integrability result concerns the source ${\sigma }_{\epsilon }{J}_3$ as an Euler derivative on the unrestricted off-shell class. It is not a no-go for density-ramped actions with their actual layer terms, nonvariational forcing prescriptions, larger algebras, or future admission constructions.

. No successful pdflatex execution, proof-assistant check, independent referee review, or journal acceptance is asserted. The source uses standard theorem environments and defines all internal reference targets.