References

XIIC

N. Cheung, Landmark XII-C, supplied manuscript, version 1. Source identifier supplied with the excerpts: e0611fd7. Locators: eq:finite-curvature, eq:ell3, eq:Ccoefficients, and thm:actualsource. The declared density and source are reproduced as finite definitions in this manuscript.

XIID

N. Cheung, Landmark XII-D, supplied manuscript, version 1. Source identifier supplied with the excerpts: e3e3f67d. Root interface: lem:root-kernel, as quoted in the supplied XVI-J; related compact-root locator: thm:root. Compactness and the $Z_2$ bound are explicit assumptions, not results independently proved here.

XIB

N. Cheung, Landmark XI-B, supplied manuscript, version 1. Locators: eq:ER, eq:EA, lem:Green, and thm:graviton. The ambient prescription and its slab restriction are explicitly specified in Section sec:propagator.

XIE

N. Cheung, Landmark XI-E, supplied manuscript, version 1. Locators: eq:W, eq:h, eq:Heven, and eq:antisym. The massless normalization $h_0=-W_0$ is retained.

XVIH

N. Cheung, Landmark XVI-H, supplied revised manuscript. Locators: the compact polarized representation and diagonal quadratic normalization. Used only for the insertion normalization stated in Input input:all.

XVII

N. Cheung, Landmark XVI-I, revised manuscript supplied in this conversation. Locators: the tensor derivatives of the insertion, the explicit ambient propagator, and the compressed root-attachment test. No selected normalization of its full extension family is imported into the narrower sector here.

BF

R. Brunetti and K. Fredenhagen, Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds, Communications in Mathematical Physics 208 (2000), 623–661. arXiv:math-ph/9903028. Sections 5.1–5.2, especially Theorems 5.2–5.3, give the point-extension framework. The extension action used here is specified explicitly in (eq:extension).

FR

K. Fredenhagen and K. Rejzner, Perturbative algebraic quantum field theory, arXiv:1208.1428v2. Section 7, Theorem 7.2, and equation (82). Only the point-extension background and identical-edge factorial convention are used; a full time-ordered family is not transferred.

BDH

C. Brouder, N. V. Dang, and F. Hélein, A smooth introduction to the wavefront set, Journal of Physics A: Mathematical and Theoretical 47 (2014), 443001. arXiv:1404.1778. Theorem 13 and Proposition 26 give the distributional product criterion and the Feynman wavefront description.

Hormander

L. Hörmander, The Analysis of Linear Partial Differential Operators I, second edition, Springer, 1990. Chapter VIII: wavefront sets, pullback under smooth maps, distributional products, and proper pushforward.