References

XVIH

Landmark XVI-H. Supplied revised XVI-H.tex, “Compact polarized kernel and witness recovery.” Locators: thm:Opol, thm:trep, prop:estimate, prop:tmatch, and thm:main. Used for the compact classical representation, continuity, and current witness matching. Its unproved full-kernel wavefront gate is not retroactively reported as proved there.

XVIE

Landmark XVI-E. Supplied revised XVI-E.tex, “Polarized root representation and witness-level completion compatibility.” Locators: lem:TD, lem:TC, and thm:compatibility. Used for matching the polarization convention and current witness compatibility.

XVIF

Landmark XVI-F. Supplied revised XVI-F.tex, “Auxiliary/root compatibility and direct witness completion.” Locators: prop:compat, thm:compatibility, and cor:family-pointwise. Used for the current auxiliary/root and direct-completion record, not a superseded residual stop.

XVIG

Landmark XVI-G. Supplied current XVI-G.tex, “Frequency-dependent witness testing and resonant asymptotics.” Locators: prop:import, prop:kernel-slot, and prop:resonant. Its scalar density is not substituted for the graph kernel.

XIID

Manuscript XII-D, version 1. Supplied identifier e3e3f67d. Additional supplied excerpts: def:completed, lines 556–569; thm:root, lines 628–674; thm:admission and eq:t-bounds, lines 805–841. The root $Z_2$ statement is reproduced in the supplied original XVI-I as lem:root-kernel. These interfaces are used as explicit inherited premises; the complete source is not independently audited.

XIIC

Manuscript XII-C, version 1. Supplied identifier e0611fd7. Density formulas reproduced in the supplied original XVI-I: eq:ell3, eq:finite-curvature, and eq:J3. Additional source excerpt: thm:actualsource, lines 636–678. The declared unintegrated density representative is retained.

XIG

Manuscript XI-G, version 1. Supplied identifier 3cae2be9. Supplied excerpts: def:class, lines 494–507; thm:criterion, lines 954–987; thm:obstruction, lines 1107–1134. The compact-kernel transport premise is reproduced in the supplied original XVI-I. The printed frozen-kernel criterion is not silently promoted to a universal theorem.

XIB

Manuscript XI-B, version 1. Supplied identifier 862627cd. Interfaces reproduced in the supplied XVI documents: the quadratic metric operator, lem:Green, thm:graviton, and the free differential eq:s. Used for the normalization and free-variation convention.

XIE

Manuscript XI-E. Two-point formulas reproduced in the supplied original XVI-I: eq:W, eq:h, eq:Heven, and eq:antisym. The massless $W_0$ and $h_0=-W_0$ conventions are retained. No complete XI-E source verification is asserted.

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. Section 5.1 and Theorems 5.2–5.3 are used for point extensions of finite scaling degree. The full interacting construction is not imported.

FR

K. Fredenhagen and K. Rejzner, Perturbative algebraic quantum field theory, arXiv:1208.1428v2. Equation (82) fixes the adopted identical-edge factorial convention. Sections 6–7 provide graph and extension background; no complete time-ordered-product family is transferred to the present nonlocal insertion.

BDHintro

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 supply the product criterion and the Feynman wavefront description. The Fourier-sign conversion is stated explicitly in Lemma lem:WF.

BDHops

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. Sections 5–6 give the pullback, product, and proper-pushforward interfaces used in the compressed root-attachment test. No stronger unrestricted continuity theorem is asserted.