References

Draft

Landmark XVI-A. User-supplied draft, filename XVI-A.tex. Source of the frozen declarations, the sign convention, obligations 4–6, and the schematic slot display. No external publication status is asserted.

XIB

Manuscript XI-B, version 1, XI-B.tex, supplied identifier 862627cd. Supplied excerpts: “Free-multiplet release,” lines 205–225; “Off-shell nilpotence,” lines 383–396; “Free causal polynomial algebra,” lines 743–762. The associated supplied coverage summary is used only within its stated scope.

XIF

Manuscript XI-F, version 2, XI-F-v2.tex, supplied identifier ef5fb4a8. Supplied excerpt: “The cubic response obeys the complete second-order law,” lines 954–980. This reference does not assert the corresponding law for the prepared XVI-A response.

XIG

Manuscript XI-G, version 1, XI-G.tex, supplied identifier 3cae2be9. Supplied excerpts: “Free-shell class,” lines 494–507; “Separation and the admission criterion,” lines 954–987; “The free-shell class of the cubic kernel is obstructed,” lines 1107–1134. The obstruction is used only for the frozen class and hypotheses reported there.

XF

Manuscript X-F, version 1, X-F.tex, supplied identifier 4c1ccd1e. Supplied coverage summary and source locators: field content and second-order metric, lines 450–486; fixed-regulator release, lines 1425–1469. The complete manuscript was not supplied.

XG

Manuscript X-G, version 1, X-G.tex, supplied identifier d362d49d. Supplied coverage summary of the source-preserving variational obstruction and its positive classical witness. Source locators include the exact-upgrade definition, lines 245–261, and the qualified release, lines 1841–1885. The full proof was not supplied.

BDHintro

C. Brouder, N. V. Dang, and F. Hélein, A smooth introduction to the wavefront set, arXiv:1404.1778 [math-ph] (2014). In particular, Theorem 13 and the discussion of fundamental wavefront-set properties.

BDHoperations

C. Brouder, N. V. Dang, and F. Hélein, Continuity of the fundamental operations on distributions having a specified wave front set (with a counter example by Semyon Alesker), arXiv:1409.7662v2 [math.FA] (2016). In particular, Proposition 5.1 and Theorems 6.1 and 6.3.

BDF

R. Brunetti, M. Dütsch, and K. Fredenhagen, Perturbative Algebraic Quantum Field Theory and the Renormalization Groups, arXiv:0901.2038v2 [math-ph] (2009). Used for the distinction between distributional operations and the separate extension and normalization problems of perturbative quantum products.