References

XXB

XX-B: Coupled Gauge-Fixed Free Input for the Original-Rod Lapse: A Q1 Construction on the Frozen XX-A Background, anonymous draft supplied in the present manuscript exchange, -B.tex, n.d. Relevant displayed objects: the action Hessian, gauge normalization, causal matrices, algebraic Hadamard class, and smooth subsidiary contraction defect. No registered authorship or independent verification is inferred.

XXA

XX-A, classical-freeze draft referred to in the supplied XX-B manuscript, n.d. The equations used here are the explicitly reproduced XX-B freeze. An unavailable complete XX-A source is not represented as having been inspected.

CheungEm02E

N. Cheung, Em02-E, version 1, supplied registered manuscript record, 02-E-v1.tex, n.d. Enter Calculus Companion. Relevant supplied locators: :lapse, :release, and “The quantum input gate and the first contraction target.” Original inflaton-slice harmonic rods and incomplete quantum audit.

CheungXIXD

N. Cheung, XIX-D, version 1, supplied registered manuscript record, -D.tex, n.d. Enter Calculus Companion. Relevant supplied locators: “CE: the original-rod relational lapse,” :state, :repair, and :main. Covariance non-determination, positivity qualifications, and actual-image repair.

CheungXVIIIA

N. Cheung, Landmark XVIII-A: Prepared Relational Observables: Non-Determination, Normalization Compatibility, and Conditional Ultraviolet Matching, version 2, supplied registered manuscript record, -A-v2.tex, n.d. Enter Calculus Companion. Relevant supplied locators: :witness, :smoothwitness, :ward, and :release. Selected contractions do not authenticate full kernels; exact repair uses the actual image.

CheungXVIIIB

N. Cheung, Landmark XVIII-B, version 2, supplied registered manuscript record, -B-v2.tex, n.d. Enter Calculus Companion. Relevant supplied locators: “Evaluated target and proof boundary,” :spectral, and :release. A free massive-scalar stress-response benchmark on classical Minkowski space, not the coupled relational lapse.

CheungXIXA

N. Cheung, XIX-A, version 1, supplied registered manuscript record, -A.tex, n.d. Enter Calculus Companion. Relevant supplied locators: :original-rods, :rod-detection, :elliptic-hyperbolic, and :main. Original versus modified rods and clock non-identification.

CheungXIXC

N. Cheung, XIX-C, version 1, supplied registered manuscript record, -C.tex, n.d. Enter Calculus Companion. Relevant supplied locators: :limit, :two-limits, and :main. Finite scheduled support and continuum non-determination, not native covariance estimates.

Hack

T.-P. Hack, “Quantization of the linearised Einstein–Klein–Gordon system on arbitrary backgrounds and the special case of perturbations in inflation,” Classical and Quantum Gravity 31 (2014), 215004. DOI: 10.1088/0264-9381/31/21/215004. arXiv:1403.3957. Gauge-invariant coupled-field framework. Its scalar and tensor subsectors are not silently identified with the complete local observable space.

BFHPR

R. Brunetti, K. Fredenhagen, T.-P. Hack, N. Pinamonti, and K. Rejzner, “Cosmological perturbation theory and quantum gravity,” Journal of High Energy Physics 08 (2016), 032. DOI: 10.1007/JHEP08(2016)032. arXiv:1605.02573. Relational-observable context. No rod, covariance, or state identification is imported.

BGP

C. Bär, N. Ginoux, and F. Pfäffle, Wave Equations on Lorentzian Manifolds and Quantization, ESI Lectures in Mathematics and Physics, European Mathematical Society, Zürich, 2007. DOI: 10.4171/037. arXiv:0806.1036. Normally hyperbolic Cauchy theory, fundamental solutions, and local Hadamard/Riesz constructions.

IS

O. Islam and A. Strohmaier, “On microlocalisation and the construction of Feynman propagators for normally hyperbolic operators,” Communications in Analysis and Geometry 32 (2024), 1811–1883. DOI: 10.4310/CAG.241204020919. arXiv:2012.09767. Bundle-valued distinguished parametrices and Hadamard bisolutions. The local microlocal construction is used; physical gauge-quotient positivity is not inferred.

FS

C. J. Fewster and A. Strohmaier, “On the construction of Hadamard states from Feynman propagators,” arXiv:2510.11492, version 2, 30 April 2026. Additional positivity and real-structure requirements in passing from Feynman propagators to states. Their positive-definite bundle state theorem is not applied to the indefinite gauge-fixed bundle in this paper.

HWlocal

S. Hollands and R. M. Wald, “Local Wick polynomials and time ordered products of quantum fields in curved spacetime,” Communications in Mathematical Physics 223 (2001), 289–326. DOI: 10.1007/s002200100540. arXiv:gr-qc/0103074. Local composite-field normalization, distinct from global state and infrared selection.