References

CheungEm02E

N. Cheung, Em02-E, version 1, supplied unpublished manuscript, 02-E-v1.tex, n.d. Enter Calculus Companion.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

CheungXVIIIA

N. Cheung, Landmark XVIII-A: Prepared Relational Observables: Non-Determination, Normalization Compatibility, and Conditional Ultraviolet Matching, version 2, supplied unpublished manuscript, -A-v2.tex, n.d. Relevant supplied locators: :witness, :smoothwitness, :hbar, :ward, and :release. Pure-trace, formal-order, and actual-image controls.

CheungXVIIIB

N. Cheung, Landmark XVIII-B, version 2, supplied unpublished manuscript, -B-v2.tex, n.d. Relevant supplied locators: :spectral, :ward, :residual, and :release. Separately frozen massive stress-response benchmark; not the original-rod lapse.

CheungXVID

N. Cheung, Landmark XVI-D: Prepared witness response and completion domains, version 1, supplied unpublished manuscript, -D.tex, n.d. Relevant supplied locators: :Slambda, :Xcand, :coordinate-compatibility, and :response-package. Smooth witness response and conditional coordinate compatibility; not slice-elliptic rod uniqueness.

CheungXVIN

N. Cheung, XVI-N, version r12, supplied unpublished manuscript, -N.tex, n.d. Relevant supplied locator: :massless-obstruction. Conditional massless special-family obstruction and separate undischarged spatially compact Route B.

CheungXVIQ

N. Cheung, XVI-Q, release Q11, supplied unpublished manuscript, -Q.tex, n.d. Relevant supplied locators: :o1, :qds, :sigma, :classification, :insertion, and :package. Scoped bulk two-point report and its explicit nontransfer and verification qualifications.

CheungXVB

N. Cheung, XV-B, version 2, supplied unpublished manuscript, -B.tex, n.d. Relevant supplied locators: :interface, :lifting, :jetnull, and :release. Technical lifting and extension interfaces; no inherited full-map or quantum-admission conclusion is imported.

CheungOai069

N. Cheung, Oai069-A, version 1, supplied unpublished manuscript, 069-A.tex, n.d. Finite Ward-defect and local-system comparison scopes only.

CheungOai282

N. Cheung, Oai282-B, version 1, supplied unpublished manuscript, 282-B.tex, n.d. Local free-scalar Ward action and declared finite coverage; not a gravitational dictionary or catalogue verification.

XIXA

XIX-A: Clock Separation Before Coordinate Identification: Four Labelled Objects and Five Non-Identifications, version 1, supplied manuscript record, -A.tex, n.d. Classical comparison and original/modified rod distinctions. No independent source verification or authorship authentication is inferred.

XIXB

XIX-B: A Witness Mismatch Between Two Coordinate Cauchy Prescriptions: Unswitched Harmonic Coordinates and Prepared Coordinate Completion, version 1, supplied manuscript record, -B.tex, n.d. Declared direct first-coordinate mismatch, not a quantum anomaly or an intrinsic obstruction to every VI prescription.

XIXC

XIX-C: Finite Incidence Registers and the Missing Continuum Evolution: Matching, Records, Promised Tokens, and Scheduled Support, version 1, supplied manuscript record, -C.tex, n.d. Finite interfaces and continuum non-determination comparison.

XIXD

XIX-D: Quantum-Certificate Inventory for Separated Clock Prescriptions, version 1, supplied manuscript record, -D.tex, n.d. Relevant supplied locator: :slots. Q1–Q5 and same-target quantum admission discipline.

XIXE

XIX-E: Boundary of the Clock-Separation Programme: Nontransfer, Physical Interpretation, and Unchanged Obligations, anonymous draft supplied in the present manuscript exchange, -E.tex, n.d. Boundary inventory, not a universal impossibility theorem.

Catalogue

OpenAI catalogue and companion scope records, attributed to OpenAI in the supplied documentary record, dated 7 October 2026. Relevant comparisons: Families 069, 282, and 271. The reported Lean scope names 271-04 only. Attribution, proof validity, and execution are not independently authenticated here.

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. Coupled linearized field and gauge framework; not this observable's covariance or quantum admission.

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 framework and cosmological perturbative context; no native rod-prescription identification is inferred.

Frob

M. B. Fröb, “Gauge-invariant quantum gravitational corrections to correlation functions,” Classical and Quantum Gravity 35 (2018), 055006. DOI: 10.1088/1361-6382/aaa74c. arXiv:1710.00839. Relational quantum-correlator context; not the original-rod lapse calculation.

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. DOI: 10.1007/s00220-016-2676-x. arXiv:1306.1058. Perturbative gravity and BV framework; no native identity or ultraviolet-completeness result is imported.

Hormander

L. Hörmander, The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis, second edition, Springer, 1990. Theorems 8.2.4 and 8.2.10: pullbacks and products under their wavefront hypotheses.

Radzikowski

M. J. Radzikowski, “Micro-local approach to the Hadamard condition in quantum field theory on curved space-time,” Communications in Mathematical Physics 179 (1996), 529–553. DOI: 10.1007/BF02100096. Theorem 5.1 and its scalar-field hypotheses; not a selection of a cosmological state.

SV

H. Sahlmann and R. Verch, “Microlocal spectrum condition and Hadamard form for vector-valued quantum fields in curved spacetime,” Reviews in Mathematical Physics 13 (2001), 1203–1246. DOI: 10.1142/S0129055X01001010. arXiv:math-ph/0008029. Vector-valued microlocal framework under the stated field and quantization hypotheses.

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. DOI: 10.1007/s002200050004. arXiv:math-ph/9903028. Finite-scaling-degree extension framework; not applied to an undefined native nonlocal product.

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 Wick products and normalization analysis.

HWexistence

S. Hollands and R. M. Wald, “Existence of local covariant time ordered products of quantum fields in curved spacetime,” Communications in Mathematical Physics 231 (2002), 309–345. DOI: 10.1007/s00220-002-0719-y. arXiv:gr-qc/0111108. Existence for the stated local scalar-field construction; not automatic admission of the present nonlocal lapse.