References

XIID

N. Cheung, Landmark XII-D: Retarded response and carrier admission for the cubic-only density-weighted Einstein source. Supplied manuscript XII-D.tex. Response, two-leg insertion, roots, admission, class, ordering correction, signed ledger, and causal plateau proposition.

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. Action, source expansion, gauge-fixing Euler term, empty jet.

XIIB

N. Cheung, Landmark XII-B: Admission and one retarded response of the ramped cubic Einstein source, at fixed regulator width. Supplied manuscript XII-B.tex. Density versus source weighting only.

XIIA

N. Cheung, Landmark XII-A: One graded polynomial carrier for the finite-ramp multiplet, with ordering-stable composites and a robust observation exclusion. Supplied manuscript XII-A-v2.tex. Carrier, shell, descent, ordering transport, named sector, exclusion.

XIG

N. Cheung, Landmark XI-G: The free-shell class of the cubic Einstein kernel: the onset covector is inherited by every representative. Supplied manuscript XI-G.tex. Retained exclusion; not reopened.

XIE

N. Cheung, Landmark XI-E: On-shell admission of the fixed-width tree, a localized first-order identity, and the held-fixed defect. Supplied manuscript XI-E.tex. Scalar-sourced slot $r_g$, identification of the coordinate leg with $-\mathcal{T}$, switching display, and the evaluated witness $I>0$.

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. Inverse normalization, free identities, trivial plateau residual algebra.

XA

N. Cheung, {Landmark X-A: Classical covariance of one fixed-regulator switched relational scalar through order ${\kappa }^2$}. Supplied manuscript X-A.tex. Scalar completion formula, affine $k$-dependence, on-shell covariance with fixed free input, pure-gauge identity for the scalar operator, transposition lemma. Classical statements only.

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. Smooth Cauchy theory, causal Green operators, finite propagation.

Hormander

L. Hörmander, The Analysis of Linear Partial Differential Operators I, second edition, Springer, 1990. Theorems 8.2.4, 8.2.10, and 8.2.12: pullback, product, and pushforward wavefront bounds.

FR

K. Fredenhagen and K. Rejzner, Perturbative algebraic quantum field theory, arXiv:1208.1428. Comparison background for classical response functionals and their kernels; no quantum retarded product is imported.