References

XIXA

XIX-A: Clock Separation Before Coordinate Identification: Four Labelled Objects and Five Non-Identifications, anonymous draft supplied in the present manuscript exchange, -A.tex, n.d. Classical comparison, not quantum certification.

XIXB

XIX-B: A Witness Mismatch Between Two Coordinate Cauchy Prescriptions: Unswitched Harmonic Coordinates and Prepared Coordinate Completion, anonymous draft supplied in the present manuscript exchange, -B.tex, n.d. Specified direct first-coordinate comparison only.

XIXC

XIX-C: Finite Incidence Registers and the Missing Continuum Evolution: Matching, Records, Promised Tokens, and Scheduled Support, anonymous draft supplied in the present manuscript exchange, -C.tex, n.d. Finite-interface and continuum non-determination comparison.

XIXD

XIX-D: Quantum-Certificate Inventory for Separated Clock Prescriptions: Non-Determination, Counterterm Images, and Unclosed Quantum Gates, anonymous draft supplied in the present manuscript exchange, -D.tex, n.d. Quantum audit and self-contained comparison arguments; no native quantum certificate is inferred.

CheungVI

N. Cheung, Relational Einstein–scalar observables at second order: classical descent and a compact-switch obstruction, Landmark VI, version 1, supplied unpublished manuscript, .tex, n.d. Enter Calculus Companion. Classical descent, separate switch defect, and RG-open quantum finite-renormalization audit.

CheungVIIIA

N. Cheung, Landmark VIII-A, version 3, supplied unpublished manuscript, -A-v3.tex, n.d. Enter Calculus Companion. Finite matching and record–residual interfaces; relevant supplied locator: :thm:residual.

CheungVIIIB

N. Cheung, Landmark VIII-B, version 3, supplied unpublished manuscript, -B-v3.tex, n.d. Enter Calculus Companion. Packet dictionary, finite source and promised tokens, and parameter–lapse separation.

CheungVIIIC

N. Cheung, Landmark VIII-C, version 3, supplied unpublished manuscript, -C-v3.tex, n.d. Enter Calculus Companion. Frozen-packet incidence, guarded composition, and the separate mixed-germ, acquisition, embedding, and dynamics interfaces.

CheungXA

N. Cheung, X-A, version 1, supplied unpublished manuscript, -A.tex, n.d. Enter Calculus Companion. Fixed density ramp, transition response test, and the plateau-supported classical identity.

CheungXAconv

N. Cheung, X-A-conv, version 1, supplied unpublished manuscript, -A-conv.tex, n.d. Enter Calculus Companion. Distinct fixed convolution prescription and its stated first-order covariance obstruction.

CheungEm02E

N. Cheung, Em02-E, version 1, supplied unpublished manuscript, 02-E-v1.tex, n.d. Enter Calculus Companion. Original inflaton-slice rods, classical relational lapse, and incomplete quantum audit. Relevant supplied locators: :lapse, :release.

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. Enter Calculus Companion. Witness, complete kernel, class, normalization, and quantum admission remain distinct.

CheungXVIIIB

N. Cheung, Landmark XVIII-B, version 2, supplied unpublished manuscript, -B-v2.tex, n.d. Enter Calculus Companion. Free massive scalar stress response on a classical Minkowski background; not a native clock or insertion certificate.

CheungXVIB

N. Cheung, Landmark XVI-B: Prepared-source diagnostics and the complete-insertion boundary, version 1, supplied unpublished manuscript, -B.tex, n.d. Enter Calculus Companion. Source, response, root pairing, and class-kernel interfaces.

CheungXVID

N. Cheung, Landmark XVI-D: Prepared witness response and completion domains, version 1, supplied unpublished manuscript, -D.tex, n.d. Enter Calculus Companion. Smooth response, coordinate candidate, and conditional inherited-coordinate compatibility.

CheungXVIH

N. Cheung, Landmark XVI-H: Compact polarized kernel and witness recovery, version 1, supplied unpublished manuscript, -H.tex, n.d. Enter Calculus Companion. General-test compact kernel under root inputs; selected witness contraction and admission remain distinct.

CheungXIVH

N. Cheung, Landmark XIV-H: Internal kernel relations on the operator route, version 1, supplied unpublished manuscript, -H.tex, n.d. Relevant supplied locators: :K5exact, :H2, :release. H2 is the stop within this sheet.

CheungXIVI

N. Cheung, Landmark XIV-I, version 1, supplied unpublished manuscript, -I.tex, n.d. Enter Calculus Companion. Relevant supplied locators: :I2, :I3, :release. Internal amplitude construction and remaining complete joint-map gap.

CheungXIVJ

N. Cheung, Landmark XIV-J, version 1, supplied unpublished manuscript, -J.tex, n.d. Enter Calculus Companion. Relevant supplied locators: :descent, :null, :reference, :J2, :noadmission. Supported-sector reference is not full characteristic admission.

CheungXVB

N. Cheung, XV-B, version 2, supplied unpublished manuscript, -B.tex, n.d. Enter Calculus Companion. Technical descent, relative lifting, finite normal jets, and extension interfaces; no complete inherited coefficient or downstream quantum admission is inferred.

CheungXVIN

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

CheungXVIP

N. Cheung, XVI-P, version p23, supplied unpublished manuscript, -P.tex, n.d. Enter Calculus Companion. Declared two-point prescription, external-leg scheme, and separately scoped identity checks.

CheungXVIQ

N. Cheung, XVI-Q, release Q11, supplied unpublished manuscript, -Q.tex, n.d. Enter Calculus Companion. Relevant supplied locators: :o1, :qds, :p6, :insertion, :package. Scoped two-point closure report, verification qualifications, and unchanged inherited insertion and admission boundaries.

CheungXVIO

N. Cheung, XVI-O, version o70-sync, supplied unpublished manuscript, -O.tex, n.d. Enter Calculus Companion. Kernel two-point Ward subsector under its own prescription, not the enlarged Q11 prescription or bulk BV restoration.

CheungEm02A

N. Cheung, Em02-A, version 6, supplied unpublished manuscript, 02-A-v6.tex, n.d. Enter Calculus Companion. Relevant supplied locator: :transition. Localization coefficients in $ϵ$, not smoothing coefficients in $\delta$.

CheungEm02D

N. Cheung, Em02-D, version 4, supplied unpublished manuscript, 02-D-v4.tex, n.d. Enter Calculus Companion. Relevant supplied locator: :main. Inverse-cubic leading distribution for one fixed model; no transferred finite part or quantum lapse coefficient.

CheungVIIE

N. Cheung, Landmark VII-E, version 1, supplied unpublished manuscript, -E.tex, n.d. Enter Calculus Companion. Observation interfaces and prescribed scheduled support.

CheungVIIJ

N. Cheung, Landmark VII-J, version 1, supplied unpublished manuscript, -J.tex, n.d. Enter Calculus Companion. Timed dependency, actual influence, physical containment, and fixed-cone transport comparisons.

CheungEn05B

N. Cheung, En05-B, version 1, supplied unpublished manuscript, 05-B.tex, n.d. Enter Calculus Companion. Isotropic matched operational-limit construction on its declared experiment family and prescribed speed. No incidence continuum identification is imported.

CheungEn05C

N. Cheung, En05-C, version 1, supplied unpublished manuscript, 05-C.tex, n.d. Enter Calculus Companion. Relevant supplied locator: :comparison. Tensor-free snapshot–channel–adjoint dependence, not metric reconstruction.

CheungEn06A

N. Cheung, En06-A, version 1, supplied unpublished manuscript, 06-A.tex, n.d. Enter Calculus Companion. Corrected layer account and distinct operational, observable-product, and frame-covariance interfaces.

CheungEn06B

N. Cheung, En06-B, version 1, supplied unpublished manuscript, 06-B.tex, n.d. Enter Calculus Companion. Prescribed routes, speed, complete payload transport, and legal scheduling; not derived geometry.

CheungVIIH

N. Cheung, Landmark VII-H, version 1, supplied unpublished manuscript, -H.tex, n.d. Enter Calculus Companion. Free massless scalar susceptibility, retarded prescription, logarithmic extension, and contact ambiguity. Not a gravitational dictionary.

CheungIX

N. Cheung, IX sharp-insertion and partial-product records, supplied unpublished manuscripts: -A.tex, version 1; -B-v2.tex, version 2; -C.tex, version 1; -Free.tex, version 1; -E.tex, version 1; -E-2.tex, version 1; -E-3.tex, version 1; n.d. Enter Calculus Companion. Version-qualified comparison collection, not one theorem or a completed clock-product domain.

CheungIXFreeTwo

N. Cheung, IX-Free-2, version 1, supplied unpublished manuscript, -Free-2.tex, n.d. Enter Calculus Companion. Relative truncated partial product and selected-word coherence through ${\hslash }^3$; not time ordering or full quantum algebra.

CheungIXD

N. Cheung, Landmark IX-D, version 3, supplied unpublished manuscript, -D-v3.tex, n.d. Enter Calculus Companion. Separate sharp time-ordered extension and normalized retarded maps remain outside its supplied release.

CheungOai282B

N. Cheung, Oai282-B, version 1, supplied unpublished manuscript, 282-B.tex, n.d. Enter Calculus Companion. Local free-scalar conformal Ward construction within its declared homogeneous class; not OpenAI family verification.

CheungOai069A

N. Cheung, Oai069-A, version 1, supplied unpublished manuscript, 069-A.tex, n.d. Enter Calculus Companion. Finite Ward-defect and finite-monodromy/local-system benchmarks. No gravitational dictionary is imported.

CheungI

N. Cheung, Landmark I, version 2, supplied unpublished manuscript, .tex, n.d. Enter Calculus Companion. Finite destructive measurement characterization inside a stated structural class; not a field instrument.

CheungEnter

N. Cheung, “The Enter Calculus: A Linear Quantum Lambda Calculus with an Operational Characterization of Measurement,” Frontiers in Physics 14 (2026), article 1954943. DOI: 10.3389/fphy.2026.1954943. Accepted-article record dated 28 September 2026; article number and DOI as supplied. Finite operational context only.

CheungHawk04A

N. Cheung, Hawk04-A, version 1, supplied unpublished manuscript, 04-A.tex, n.d. Enter Calculus Companion. Complete preservation and recovery through declared access are separate tasks.

CheungHawk04B

N. Cheung, Hawk04-B, version 2, supplied unpublished manuscript, 04-B.tex, n.d. Enter Calculus Companion. Classical readout and quantum-return decoding retain different interfaces.

Catalogue

OpenAI mathematics catalogue and companion scope records, attributed to OpenAI in the supplied documentary record, dated 7 October 2026. Recorded comparison families: 260, 271, 362, 376, 282, and 069. Family 271's reported Lean scope names 271-04 only. Catalogue attribution, source proofs, and Lean execution are not independently authenticated by this manuscript. No catalogue theorem is a premise.

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, not an identification of native clock prescriptions.

HW

S. Hollands and R. M. Wald, “Quantum fields in curved spacetime,” Physics Reports 574 (2015), 1–35. DOI: 10.1016/j.physrep.2015.02.001. arXiv:1401.2026. States, composite observables, and products on classical globally hyperbolic backgrounds.

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. Distributional products and extension framework; not applied to an undefined inherited graph.

Watrous

J. Watrous, The Theory of Quantum Information, Cambridge University Press, Cambridge, 2018. DOI: 10.1017/9781316848142. Complete channels, references, and diamond-norm comparison.

Fritz

T. Fritz, “Velocity polytopes of periodic graphs and a no-go theorem for digital physics,” Discrete Mathematics 313 (2013), 1289–1301. DOI: 10.1016/j.disc.2013.02.010. arXiv:1109.1963v3. The revised arXiv version includes the historical-attribution corrigendum. Fixed periodic-graph context only; no obstruction is transferred to changing refinement families.

ADH

A. Almheiri, X. Dong, and D. Harlow, “Bulk locality and quantum error correction in AdS/CFT,” Journal of High Energy Physics 04 (2015), 163. DOI: 10.1007/JHEP04(2015)163. arXiv:1411.7041. External holographic comparison under its own duality hypotheses.

DHW

X. Dong, D. Harlow, and A. C. Wall, “Reconstruction of bulk operators within the entanglement wedge in gauge-gravity duality,” Physical Review Letters 117 (2016), 021601. arXiv:1601.05416. External reconstruction context, not an incidence or clock-programme premise.