Declarations

scope. The kernel representation, the wavefront witness, the fermion computation, the finite transformation law, the variation identity, the ledger, and the support statement are proved on smooth configurations in the displayed conventions. The on-shell representative question for ${\mathcal{C}}_3$ is stated as open.

. X-A supplies the Cauchy facts, kernel lemma, preflight argument, and Theorem (v). XI-A supplies the signed action and the gauge-fixed versus Einstein distinction. XI-B supplies the fermion, normalization, and free shell. XI-C and XI-D supply the tree sign and the affine lemma. XI-E supplies the algebra, its domain, the cubic variation, and the witness. Hörmander supplies the wavefront tools.

. The admission mechanism, the value of the gauge-fixing companion, the double count in the three-term sum, the origin of the quadratic flow term, the non-plateau support of the de Donder parameter, and the retained Einstein-shell term are corrected relative to the production sheet.

. No successful pdflatex execution, proof-assistant check, executed symbolic computation, independent referee review, or journal acceptance is asserted. All nonzero and zero witnesses are analytic.