References

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 only for standard smooth wave Cauchy theory and finite propagation.

Frob

M. B. Fröb. Gauge-invariant quantum gravitational corrections to correlation functions. Classical and Quantum Gravity 35 (2018), 055006. arXiv:1710.00839. Relational-coordinate comparison background only; no quantum result is transferred to the present regulator.

III

Descent of first-order relational scalars, and the free-product obstruction. Landmark III, unpublished manuscript supplied with this project, version as supplied in III.tex. Used only to distinguish its equation-space and quotient questions from the off-shell problem studied here.

VI

Relational Einstein–scalar observables at second order: classical descent and a compact-switch obstruction. Landmark VI, unpublished manuscript supplied with this project, version as supplied in VI.tex. Comparison for the separation of geometric descent, switched assignments, and coefficientwise obstructions.

VIIA

Plateau-compatible relational scalars: a second-order classical intertwiner. Landmark VII-A, unpublished manuscript supplied with this project, version as supplied in VII-A.tex. Comparison only; its harmonic-coordinate equation is unswitched and unregulated.

VIIB

Cauchy harmonic insertions and second-order retarded products: a sharp-boundary obstruction in an off-shell polynomial domain. Landmark VII-B, unpublished manuscript supplied with this project, version as supplied in VII-B.tex. Comparison only; its sharp insertion and quantum domain are not the definitions of the present classical prescription.

IXA

An off-shell admission domain and boundary-sensitive topology for sharp Cauchy relational insertions. Landmark IX-A, unpublished manuscript supplied with this project, version as supplied in IX-A.tex. Comparison only; its carrier and topology are not imported, and no quantum product is inferred.