References

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. Primary remainder handoff, conditional cancellation, evaluated witness, nonzero full-shell class, and completion boundary.

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 with coefficient $-1$, completion formulas, affine slot identity, 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 and causal plateau cancellation proposition; no response or root is reconstructed here.

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. Off-shell auxiliary coordinate, free-shell ideal, product, causal blocks, ordering maps, and frozen free differential.

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 $-1$, ghost normalization, auxiliary shell relation, and trivial compact residual intersection.

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: the Einstein–Hilbert action is retained and the named invariant fixed-input jet is not repaired.

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. Chapter 3: smooth Cauchy existence, uniqueness, causal Green operators, and finite propagation.