References

XIIIC

N. Cheung, Landmark XIII-C: The joint two-line extension of one selected binary pair, on the unchanged carrier. Supplied manuscript XIII-C.tex. Inventory, partial-diagonal class, primitive extensions, characteristic cancellation, and four successor obligations.

XIIIB

N. Cheung, Landmark XIII-B: One binary causal datum for the displayed coefficient, on the unchanged carrier. Supplied manuscript XIII-B.tex. Tree datum, properness, retarded convention, ordered values, and unresolved two-line gate.

XIIIA

N. Cheung, Landmark XIII-A: Classical cancellation on a fixed subclass, and the obstruction to a coefficientwise restriction quotient. Supplied manuscript XIII-A.tex. Evaluation-only boundary and non-ideal theorem.

XIIID

N. Cheung, Landmark XIII-D: One bounded classical completion of the auxiliary pairing, or its obstruction on the unchanged sheet. Supplied manuscript XIII-D.tex. Class-qualified classical obstruction and distinction between an admitted cochain and an integrated completion.

XIIF

N. Cheung, {Landmark XII-F: The gauge-fixed remainder of ${{\Phi }^{(2)}}_{\mathrm{D}}$: companion support, the auxiliary pairing, and what is not a Ward identity}. Supplied manuscript XII-F.tex. Retained full-shell witness and its classical scope.

XIIE

N. Cheung, Landmark XII-E: Assembly of the second-order relational coefficient after admission of the density-weighted cubic insertion. Supplied manuscript XII-E.tex. Displayed coefficient, insertion sign, and scalar-sourced slot.

XIIC

N. Cheung, Landmark XII-C: One declared cubic weighting: actual Euler source, changed Noether identity, and the coupled-jet question. Supplied manuscript XII-C.tex. Unchanged selected action.

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. Microlocal product continuity, scaling degree, and extension across points and submanifolds.

Dang

N. V. Dang, “The extension of distributions on manifolds, a microlocal approach,” Annales Henri Poincaré 17 (2016), 819–859, arXiv:1412.2808. Scaling and wavefront conditions for submanifold extensions.

FR

K. Fredenhagen and K. Rejzner, Perturbative algebraic quantum field theory, arXiv:1208.1428. Functional domains, time ordering, and renormalization; not an imported joint-extension theorem for the selected pair.

Hormander

L. Hörmander, The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis, second edition, Springer, 1990. Submersion pullback, distribution products, differential-operator wavefront bounds, and proper pushforward.