References

PageWootters

D. N. Page and W. K. Wootters, “Evolution without evolution: Dynamics described by stationary observables,” Physical Review D 27 (1983), 2885–2892. https://doi.org/10.1103/PhysRevD.27.2885.

BoetteRossignoli

A. Boette and R. Rossignoli, “History states of systems and operators,” Physical Review A 98 (2018), 032108. https://doi.org/10.1103/PhysRevA.98.032108.

McClean

J. R. McClean, J. A. Parkhill, and A. Aspuru-Guzik, “Feynman's clock, a new variational principle, and parallel-in-time quantum dynamics,” Proceedings of the National Academy of Sciences 110 (2013), E3901–E3909. https://doi.org/10.1073/pnas.1308069110.

Diaz

N. L. Diaz, P. Braccia, M. Larocca, J. M. Matera, R. Rossignoli, and M. Cerezo, “Parallel-in-time quantum simulation via Page and Wootters quantum time,” Physical Review Research 7 (2025), 033294. https://doi.org/10.1103/wpnf-4nnn.

CheungEnter

N. Cheung, “The Enter Calculus: A Linear Quantum Lambda Calculus with an Operational Characterization of Measurement,” Frontiers in Physics 14 (2026), article 1954943. Accepted 28 September 2026; final formatted version forthcoming according to the publisher record consulted on 13 October 2026. https://doi.org/10.3389/fphy.2026.1954943.

CheungI

N. Cheung, Manuscript I, I.tex, version 2, n.d. Supplied manuscript record and theorem excerpts. In particular, thm:main characterizes Born probabilities and positive-branch destructive residual rays within its declared strategy class. Enter Calculus Companion, https://enter.grok.me/.

CheungPhilosophy

N. Cheung, The Philosophy of Enter: Destructive Readout, Quantum Recovery, and the Refusal of Identification, EntPhil-v2.tex, version 2, n.d. Introductory philosophical map, not a registered theorem premise. https://enter.grok.me/enter.

CheungEn08A

N. Cheung, Manuscript En08-A, En08-A.tex, version 1, n.d. Supplied manuscript record and excerpts, especially thm:main, “Failure of reconstruction from scheduler consistency.” Enter Calculus Companion, https://enter.grok.me/.

Trinity

P. A. Höhn, A. R. H. Smith, and M. P. E. Lock, “Trinity of relational quantum dynamics,” Physical Review D 104 (2021), 066001. https://doi.org/10.1103/PhysRevD.104.066001.

CheungXEnter

N. Cheung, Manuscript X-Enter, X-Enter.tex, version 1, n.d. Supplied manuscript record and excerpts, especially thm:relational, “Conditional selective relational readout.” Its encoded phase model is cited as a comparison only. Enter Calculus Companion, https://enter.grok.me/.

CheungVIII

N. Cheung, Manuscripts VIII-A, VIII-B, and VIII-C, VIII-A-v3.tex, VIII-B-v3.tex, and VIII-C-v3.tex, versions 3, n.d. Supplied records and excerpts concerning fixed-presentation matching, record–residual separation, affine acquisition obstructions, guarded packet flow, and residual ownership. In VIII-A, see A:thm:residual. These are comparison records, not geometric premises of En09-A. Enter Calculus Companion, https://enter.grok.me/.

CheungXIXC

N. Cheung, Manuscript XIX-C, XIX-C.tex, version 1, n.d. Supplied record and excerpts, especially thm:main, “Finite incidence does not determine continuum evolution,” and the identified prop:token, prop:affine, prop:two-limits, and prop:interpolation. Enter Calculus Companion, https://enter.grok.me/.

CheungEm02E

N. Cheung, Manuscript Em02-E, Em02-E-v1.tex, version 1, n.d. Supplied manuscript record and excerpts, especially thm:lapse, “Complete relational lapse through second order.” Its classical background-dependent lapse is not identified with the present clock record. Enter Calculus Companion, https://enter.grok.me/.

Watrous

J. Watrous, The Theory of Quantum Information, Cambridge University Press, 2018. Chapter 3: similarity and distance among states and channels. Author's manuscript and errata interface: https://cs.uwaterloo.ca/ watrous/TQI/.

CheungEn05A

N. Cheung, Manuscript En05-A, En05-A.tex, version 1, n.d. Supplied manuscript record and introductory excerpts. Finite-range schedule geometry, complete channel locality, and continuum-comparison cautions are cited as distinctions, not as automatic transfer theorems. Enter Calculus Companion, https://enter.grok.me/.

CheungXXIOutline

N. Cheung, XXI-A–C development-plan references, n.d. Outline-level material supplied with the En09-A proposal, concerning finite clock codes, hybrid event germs, and complete recorded-channel convergence. Full manuscript texts, versions, and publication metadata were not supplied. No unsupplied XXI theorem is used as a premise; the required budget is proved in Section sec:stability.

CheungVIIJ

N. Cheung, Manuscript VII-J, VII-J.tex, version 1, n.d. Supplied manuscript record and scope excerpts. Scheduled reachability, operational influence, complete decoded simulation, and separately certified physical embedding remain distinct. Enter Calculus Companion, https://enter.grok.me/.

CheungBoundaries

N. Cheung, Supplied analytic and classical boundary records, n.d. Manuscript VI, VI.tex, version 1; XIV-I, XIV-I.tex, version 1; XIV-J, XIV-J.tex, version 1; XV-B, XV-B.tex, version 2; and XVI-N, XVI-N.tex, version r12. The cited excerpts distinguish classical descent, internal amplitude construction, the unresolved full characteristic map, technical continuation, downstream admission, and the conditional massless obstruction. They are cited solely to preserve non-transfer and standing scope. Enter Calculus Companion, https://enter.grok.me/.