References

XIA

N. Cheung, Landmark XI-A: A switched Einstein–scalar action for the ramp relational scalar: sign conventions, Noether identities, and an empty fixed-input Einstein jet. Supplied manuscript XI-A.tex. Used for the signed vertex and the Einstein-jet obstruction.

XIB

N. Cheung, Landmark XI-B: The free de Donder multiplet for the ramp Einstein–scalar sheet: causal propagators, residual gauge, and the layer dressing. Supplied manuscript XI-B.tex. Used for the causal inverse, auxiliary multiplet, free differential, and stated finite-generator algebra.

XB

N. Cheung, Landmark X-B: Fixed-regulator admission and one retarded correction for the ramp relational scalar, with the metric kept classical. Supplied manuscript X-B-v3.tex. Used for the scalar-only first response and background identity, with its representative warning.

XC

N. Cheung, Landmark X-C: The missing second-order retarded maps for the ramp relational scalar, with the metric kept classical. Supplied manuscript X-C-v3.tex. Used for the explicitly named scalar-only completed coefficient and its classical background identity.

VIIC

Landmark VII-C: A mixed-Wick obstruction to a normal-topology boundary extension for sharp Cauchy harmonic insertions. Supplied manuscript VII-C.tex. Comparison only; no fixed Wick matrix or sharp insertion is imported.

BGP

C. Bär, N. Ginoux, and F. Pfäffle, Wave Equations on Lorentzian Manifolds and Quantization, ESI Lectures in Mathematics and Physics, European Mathematical Society, 2007. arXiv:0806.1036. Used for smooth Cauchy theory, finite propagation, and causal Green operators.

BDH

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),” Studia Mathematica 232 (2016), 201–226. arXiv:1409.7662. Used for wavefront multiplication and pushforward criteria.

FR

K. Fredenhagen and K. Rejzner, Perturbative algebraic quantum field theory, arXiv:1208.1428v2, 2013. Used for the distinction between regular polynomial generators and Hadamard-based polynomial extensions; no such extension is constructed here.

HRV

E. Hawkins, K. Rejzner, and B. Visser, A novel class of functionals for perturbative algebraic quantum field theory, arXiv:2312.15203v2, 2024. Background for keeping polynomial kernel statements separate from broader functional and continuity claims.