Declarations

of the release. This manuscript gives the proved-obstructed branch for one explicitly frozen classical prescription. It does not present an obstructed construction as a gauge-invariant observable.

to the supplied series. The supplied manuscripts are cited only for the specific comparison statements identified in Section sec:introduction. No series theorem about a sharp insertion, boundary topology, free product, or support certificate is used as a theorem about the regulated coordinate map defined here.

and quantum scope. All products used in the proofs are products of smooth classical functions or pairings with smooth compact kernels. No quantum contraction or renormalization operation is performed.

equations. The action and its retained Euler equations are specified. The sourced diagnostic solves the scalar equation for an off-shell metric configuration. It is not a coupled Einstein–scalar existence result.

and verification. The positive witness is analytic. No numerical calculation or executed symbolic computation is used. No successful pdflatex compilation, proof-assistant verification, or independent referee review is claimed.