References

XXA

XX-A: Original-Rod Lapse: Classical Freeze and Quantum Admission Contract, supplied draft, -A.tex, n.d. Complete text supplied in the present manuscript exchange. Relevant locators: :rel-lapse, :coupled, :regular-wick, and :repair.

XXB

XX-B: Coupled Gauge-Fixed Free Input for the Original-Rod Lapse, supplied draft, -B.tex, n.d. Complete text supplied in the present manuscript exchange. Relevant locators: :NH, :residual, :intertwining, :contractions, and :closure.

XXC

XX-C: State, Subtraction, and Spatial-Tail Audit for the Original-Rod Lapse, supplied draft, -C.tex, n.d. Complete text supplied in the present manuscript exchange. Relevant locators: :subtraction, :conditional, :IRfailure, :tworod, and :repair.

XXD

XX-D: The Original-Rod Relational Lapse: Composite Formula and Product Domains, supplied draft, -D.tex, n.d. Complete text supplied in the present manuscript exchange. Relevant locators: :qloc, :classicaldomain, :compactWick, :native, and :release.

CheungEm02E

N. Cheung, Em02-E, version 1, 02-E-v1.tex, n.d. Enter Calculus Companion, https://enter.grok.me. Supplied registered record: 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, -A-v2.tex, n.d. Enter Calculus Companion, https://enter.grok.me. Relevant supplied locators: :witness, :smoothwitness, :ward, and :release.

CheungXVIIIB

N. Cheung, Landmark XVIII-B, version 2, -B-v2.tex, n.d. Enter Calculus Companion, https://enter.grok.me. Separately frozen free massive-scalar stress-response benchmark; not the present lapse.

CheungXIXA

N. Cheung, XIX-A, version 1, -A.tex, n.d. Enter Calculus Companion, https://enter.grok.me. Supplied prescription and clock-separation record, including original-versus-modified rods.

CheungXIXB

N. Cheung, XIX-B, version 1, -B.tex, n.d. Enter Calculus Companion, https://enter.grok.me. Supplied direct-coordinate mismatch and formal-order nontransfer record.

CheungXIXC

N. Cheung, XIX-C, version 1, -C.tex, n.d. Enter Calculus Companion, https://enter.grok.me. Relevant supplied locator: :main. Finite incidence, records, residuals, scheduled support, and refinement non-determination.

CheungXIXD

N. Cheung, XIX-D, version 1, -D.tex, n.d. Enter Calculus Companion, https://enter.grok.me. Relevant supplied sections: “CE: the original-rod relational lapse” and “Exact affine cancellation criterion.” Q1–Q5 same-target audit.

CheungXIXE

N. Cheung, XIX-E, version 1, -E.tex, n.d. Enter Calculus Companion, https://enter.grok.me. Supplied boundary inventory and unchanged obligations.

CheungXVIQ

N. Cheung, XVI-Q, release Q11, -Q.tex, n.d. Enter Calculus Companion, https://enter.grok.me. Relevant supplied locators: :o1, :qds, :insertion, and :package. Narrow bulk two-point report; no lapse identity or series-wide verification is imported.

CheungXVIN

N. Cheung, XVI-N, version r12, -N.tex, n.d. Enter Calculus Companion, https://enter.grok.me. Relevant supplied locator: :massless-obstruction. Conditional special-family insertion obstruction; spatially compact Route B remains separate.

CheungXVB

N. Cheung, XV-B, version 2, -B.tex, n.d. Enter Calculus Companion, https://enter.grok.me. Supplied relative-lifting and extension interfaces. No inherited full-map or downstream quantum-admission conclusion is imported.

CheungOai069

N. Cheung, Oai069-A, version 1, 069-A.tex, n.d. Enter Calculus Companion, https://enter.grok.me. Finite-monodromy and free Ward comparison record; not a gravitational counterterm premise.

CheungOai282

N. Cheung, Oai282-B, version 1, 282-B.tex, n.d. Enter Calculus Companion, https://enter.grok.me. Declared free-scalar local Ward action and finite coverage class; not the present cosmological identity.

Catalogue

OpenAI, OpenAI mathematics catalogue and companion scope records, supplied record dated 7 October 2026, .tex. Enter Calculus Companion, https://enter.grok.me. Documentary family comparisons only. No proof or authorship authentication is inferred.

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. DOI: 10.4171/037. arXiv:0806.1036. Normally hyperbolic Cauchy uniqueness and causal Green operators.

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. Extension and normalization framework for already specified distributional constructions.

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 normalization and covariance conditions. No automatic nonlocal Newton insertion theorem is imported.

FRBV

K. Fredenhagen and K. Rejzner, “Batalin–Vilkovisky formalism in perturbative algebraic quantum field theory,” Communications in Mathematical Physics 317 (2013), 697–725. arXiv:1110.5232. Renormalized BV operations and their relation to the anomalous Master Ward Identity. No native lapse application is inferred.

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. Locally covariant effective perturbative gravity and renormalized BV framework.

BDFrR

R. Brunetti, M. Dütsch, K. Fredenhagen, and K. Rejzner, “Unitary, anomalous Master Ward Identity and its connections to the Wess–Zumino condition, BV formalism and $L_{\infty }$-algebras,” arXiv:2210.05908. DOI: 10.1007/s00023-023-01388-w. Primary anomaly-consistency framework; not a calculation of the present nonlocal lapse breaking.

FR

K. Fredenhagen and K. Rejzner, Perturbative algebraic quantum field theory, arXiv:1208.1428. Functional products, formal perturbative orders, and the distinction between algebraic constructions and state interpretation.