References

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 handoff, restriction-ideal obstruction, ordering counterexample, and unresolved completion boundary.

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. Copied witness and the exact scope of classical cancellation.

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. Assembly sign, completion formulas, compact balanced kernels, and scalar-sourced slot.

XIID

N. Cheung, Landmark XII-D: Retarded response and carrier admission for the cubic-only density-weighted Einstein source. Supplied manuscript XII-D.tex. Inherited roots, response normalization, source coefficients, and causal plateau proposition.

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. Polynomial product, action causal matrix, full-shell ideal, free differential, and admissible ordering class.

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. Boundary only: retained Einstein–Hilbert action and named invariant-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. Inverse coefficient $-1$ and free ghost normalization.

FR

K. Fredenhagen and K. Rejzner, Perturbative algebraic quantum field theory, arXiv:1208.1428v2, 2013. Sections 6–7: time ordering, retarded constructions, and the declared domains of local and multilocal renormalization.

FRModels

K. Fredenhagen and K. Rejzner, Perturbative Construction of Models of Algebraic Quantum Field Theory, arXiv:1503.07814, 2015. Comparison framework for the separation of free products and renormalized perturbative constructions.

Hormander

L. Hörmander, The Analysis of Linear Partial Differential Operators I, second edition, Springer, 1990. Distribution products and proper-pushforward wavefront bounds used in the one-line proof.

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 wave Green operators, transposition, causal support, and finite propagation.