Declarations

scope. The Cauchy reduction, the pure-trace cubic coefficient, the counter-propagating symbol and its Bianchi check, the solution-pairing lemma, the kernel lemma, the covector transport, the admission criterion, the plane-wave asymptotics, the rapid-decay lemma, the class obstruction, the inherited covector, and the general detection statement are proved on smooth configurations and compact distributional kernels in the displayed conventions. The Einstein subshell question and smaller observation classes with $\mathsf{b}\equiv 0$ are stated as undecided.

. X-A supplies finite propagation and the Cauchy facts. XI-A supplies the signed action and the gauge-fixed versus Einstein distinction. XI-B supplies the normalization, the causal kernels, and the free shell. XI-E supplies the algebra, its domain, the admission map, and the finite cubic coefficient. XI-F supplies the kernel representation, Theorem F1 and its data, and the open remark. Hörmander supplies Definition 8.1.2, Proposition 8.1.3, (8.1.11), and Theorems 8.2.4, 8.2.9, 8.2.12, 8.2.13, 8.3.1. Bär–Ginoux–Pfäffle supplies the retarded and advanced inverses on distributions.

. The identity of the class invariant, the split form of the forbidden covector, the plane-wave witness, the blindness of Einstein-shell pairs, the status of the one-slot rewriting, and the uninstantiated constructed branch 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.