References

XA

N. Cheung. {Landmark X-A: Classical covariance of one fixed-regulator switched relational scalar through order ${\kappa }^2$}. Supplied manuscript X-A.tex.

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.

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.

XD

N. Cheung. Landmark X-D: Convergence of the completed ramp relational scalar as the regulator width tends to zero. Supplied manuscript X-D-v3.tex.

XE

N. Cheung. Landmark X-E: A specified gravitational action for the ramp relational scalar, and the first graviton tree. Supplied manuscript X-E.tex.

VIIC

Landmark VII-C: A mixed-Wick obstruction to a normal-topology boundary extension for sharp Cauchy harmonic insertions. Supplied manuscript VII-C.tex. Used for the copied assumption 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.

BF

R. Brunetti and K. Fredenhagen. Microlocal analysis and interacting quantum field theories: renormalization on physical backgrounds. Comm.\ Math.\ Phys. 208 (2000), 623–661.

BFR

R. Brunetti, K. Fredenhagen, and K. Rejzner. Quantum gravity from the point of view of locally covariant quantum field theory. Comm.\ Math.\ Phys. 345 (2016), 741–779. Named for the whole-Lagrangian switch; not used.

DF

M. Dütsch and K. Fredenhagen. The master Ward identity and generalized Schwinger–Dyson equation in classical field theory. Comm.\ Math.\ Phys. 243 (2003), 275–314. Cited in Remark rem:structural only.

DH

J. J. Duistermaat and L. Hörmander. Fourier integral operators II. Acta Math. 128 (1972), 183–269.

FR

K. Fredenhagen and K. Rejzner. Batalin–Vilkovisky formalism in the functional approach to classical field theory. Comm.\ Math.\ Phys. 314 (2012), 93–127.

Hor

L. Hörmander. The Analysis of Linear Partial Differential Operators I, 2nd ed. Springer, 1990. Theorems 8.2.3, 8.2.9, 8.2.10, 8.2.14.

LL

L. D. Landau and E. M. Lifshitz. The Classical Theory of Fields, 4th ed. Pergamon, 1975.

Rej

K. Rejzner. Perturbative Algebraic Quantum Field Theory. Mathematical Physics Studies. Springer, 2016.