References

CheungVIIA

N. Cheung, Landmark VII-A: Plateau-compatible relational scalars: a second-order classical intertwiner. Supplied manuscript VII-A.tex, n.d. Restricted gauge domain, classical coefficients, and Cauchy intertwining.

CheungVIIB

N. Cheung, Landmark VII-B: Cauchy harmonic insertions and second-order retarded products: a sharp-boundary obstruction in an off-shell polynomial domain. Supplied manuscript VII-B.tex, n.d. Sharp adjoint, off-shell obstruction, and linear free-shell repair.

CheungVIIC

N. Cheung, Landmark VII-C: A mixed-Wick obstruction to a normal-topology boundary extension for sharp Cauchy harmonic insertions. Supplied manuscript VII-C.tex, n.d. Fixed covariance and numerical mixed-triple obstruction.

CheungVIID

N. Cheung, Landmark VII-D: Finite part of the regulated Cauchy-reflection triangle: a strong numerical distributional limit for the VII-C family. Supplied manuscript VII-D.tex, n.d. Complete numerical asymptotic and real regulator conversion.

CheungVIIE

N. Cheung, Landmark VII-E: Observation boundaries for destructive quantum readout and external geometry. Supplied manuscript VII-E.tex, n.d. Includes the conditional distributional observation dictionary.

CheungVIIG

N. Cheung, Landmark VII-G: Completely positive observation boundaries for finite matter–geometry feedback. Supplied manuscript VII-G.tex, n.d. Finite instruments and their expressly limited operational scope.

CheungVIIH

N. Cheung, Landmark VII-H: Normalization-independent connected quantum responses: complete ambiguity, observable descent, and a nonzero free-field benchmark. Manuscript VII-H.tex, supplied in the preceding exchange, n.d. A separate free Wick-square benchmark.

CheungIXA

N. Cheung, Landmark IX-A. Manuscript IX-A.tex, version 1, n.d. Supplied excerpts concerning the classical boundary carrier and nonconvergence of unchanged regular approximants.

CheungIXB

N. Cheung, Landmark IX-B. Manuscript IX-B-v2.tex, version 2, n.d. Supplied calibration and missing-second-multiplication statements.

CheungIXE

N. Cheung, Landmark IX-E. Manuscript IX-E.tex, version 1, n.d. Supplied entering-state ledger: relative partial free product versus absent sharp time-ordered and retarded maps.

CheungXA

N. Cheung, {Landmark X-A: Classical covariance of one fixed-regulator switched relational scalar through order ${\kappa }^2$}. Manuscript X-A.tex, n.d. Supplied classical density-ramp comparison.

CheungXAconv

N. Cheung, Landmark X-A-conv. Manuscript X-A-conv.tex, version 1, n.d. Supplied comparison separating convolution and density preparation.

CheungXIIA

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, n.d.

CheungXIIB

N. Cheung, Landmark XII-B: Admission and one retarded response of the ramped cubic Einstein source, at fixed regulator width: handoff audit, variational consistency, and the unresolved release. Supplied manuscript XII-B.tex, n.d.

CheungXIID

N. Cheung, Landmark XII-D: Retarded response and carrier admission for the cubic-only density-weighted Einstein source. Supplied manuscript XII-D.tex, n.d.

CheungXIIF

N. Cheung, {Landmark XII-F: The gauge-fixed remainder of ${{\Phi }_{\mathrm{D}}}^{(2)}$: companion support, the auxiliary pairing, and what is not a Ward identity}. Supplied manuscript XII-F.tex, n.d.

CheungXIVH

N. Cheung, Landmark XIV-H. Manuscript XIV-H.tex, version 1, n.d. Supplied internal-kernel and H2 boundary excerpts.

CheungXIVI

N. Cheung, Landmark XIV-I. Manuscript XIV-I.tex, version 1, n.d. Supplied I2 construction and unresolved I3 joint-map statements.

CheungXIVJ

N. Cheung, Landmark XIV-J. Manuscript XIV-J.tex, version 1, n.d. Supplied reconstruction, null-presentation, supported-reference, and J2 statements.

CheungXVB

N. Cheung, Landmark XV-B. Manuscript XV-B.tex, version 1, n.d. Supplied conditional extension interfaces; no full admission.

CheungXVF

N. Cheung, Landmark XV-F. Manuscript XV-F-v3.tex, version 3, n.d. Supplied internal-expression and normal-jet ambiguity statements.

CheungXVIN

N. Cheung, Landmark XVI-N. Manuscript XVI-N.tex, revision r12, n.d. Supplied conditional completion obstruction and unresolved prepared-insertion scope.

CheungXVIO

N. Cheung, Landmark XVI-O. Manuscript XVI-O.tex, revision o70-sync, n.d. Supplied kernel-level versus bulk/insertion scope distinctions.

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.

Hormander

L. Hörmander, The Analysis of Linear Partial Differential Operators I, second edition, Springer, 1990. Wavefront product, pullback, composition, and pushforward calculus.

BDH

C. Brouder, N. V. Dang, and F. Hélein, “Continuity of the fundamental operations on distributions having a specified wave front set (with a counter example by Semyon Alesker),” Studia Mathematica 232 (2016), 201–226. arXiv:1409.7662.

BF

R. Brunetti and K. Fredenhagen, “Microlocal analysis and interacting quantum field theories: Renormalization on physical backgrounds,” Communications in Mathematical Physics 208 (2000), 623–661. arXiv:math-ph/9903028.

HRV

E. Hawkins, K. Rejzner, and B. Visser, A novel class of functionals for perturbative algebraic quantum field theory. arXiv:2312.15203. The fixed-kernel polynomial and equicausal frameworks are background; no sharp-Cauchy admission theorem is attributed to them.

Duetsch

M. Dütsch, Perturbative QFT: off-shell fields, deformation quantization and causal perturbation theory. arXiv:2306.17698v2, 2023.

BDF

R. Brunetti, M. Dütsch, and K. Fredenhagen, Perturbative algebraic quantum field theory and the renormalization groups. arXiv:0901.2038.

FRBV

K. Fredenhagen and K. Rejzner, Batalin–Vilkovisky formalism in perturbative algebraic quantum field theory. arXiv:1110.5232. Renormalized BV framework; not a sharp-insertion extension theorem.

BFR

R. Brunetti, K. Fredenhagen, and K. Rejzner, “Quantum gravity from the point of view of locally covariant quantum field theory,” Communications in Mathematical Physics 345 (2016), 741–779. arXiv:1306.1058.

FrobWard

M. B. Fröb, “Anomalies in time-ordered products and applications to the BV-BRST formulation of quantum gauge theories,” Communications in Mathematical Physics 372 (2019), 281. arXiv:1803.10235.

FrobCorrelation

M. B. Fröb, “Gauge-invariant quantum gravitational corrections to correlation functions,” Classical and Quantum Gravity 35 (2018), 055006. arXiv:1710.00839. Comparison calculation, not the fixed zero-Cauchy prescription.

FrobLima

M. B. Fröb and W. C. C. Lima, Propagators for gauge-invariant observables in cosmology. arXiv:1711.08470. Causal relational-coordinate comparison.