References

CheungPhilosophy

N. Cheung, The Philosophy of Enter: Destructive Readout, Quantum Recovery, and the Refusal of Identification, EntPhil, version 2. Enter Calculus Companion. Introductory essay, not a theorem premise. https://enter.grok.me/enter.

CheungEnter

N. Cheung, “The Enter Calculus: A Linear Quantum Lambda Calculus with an Operational Characterization of Measurement.” Frontiers in Physics, volume 14 (2026). DOI https://doi.org/10.3389/fphy.2026.1954943. Publisher author name: Ngo Cheung.

CheungI

N. Cheung, Manuscript I, version 2. Enter Calculus Companion. Supplied finite measurement-characterization passages.

CheungEn07B

N. Cheung, En07-B, version 1. Enter Calculus Companion. Supplied complete-complement criterion, four same-model endpoint obligations, and resolution-certificate passages.

CheungHawk01B

N. Cheung, Hawk01-B, version 1. Enter Calculus Companion. Supplied exact correction, complete endpoint, and entropy–recovery separation passages.

CheungOai280C

N. Cheung, Oai280-C, version 1. Enter Calculus Companion. Supplied full-code criterion and subsystem/algebra target distinctions.

CheungHawk03A

N. Cheung, Hawk03-A, version 1. Enter Calculus Companion. Supplied encoded-partner and independent-factor comparisons; not a horizon-smoothness theorem.

CheungHawk04A

N. Cheung, Hawk04-A, version 1. Enter Calculus Companion. Supplied fixed finite autonomous recurrence and access-preserving comparison passages.

CheungHawk04D

N. Cheung, Hawk04-D, version 1. Enter Calculus Companion. Supplied complete-channel transfer, positive-mass clock, and conditional endpoint certificate.

Hawk05B

Hawk05-B, version 1. Supplied predecessor manuscript passages: finite Haar Page mean, destructive record mean, decoupling, and entropy–recovery separation. Authorship of the supplied file is not inferred here.

Hawk05C

Hawk05-C: Conditional Page-Curve Extrapolations under Enter. Supplied predecessor text in this exchange, version 1. Finite capacity compatibility, two return types, sector entropy, and independent recovery allowances. No independent archival or publication verification is asserted.

CheungEn02B

N. Cheung, En02-B, version 1. Enter Calculus Companion. Supplied resource-certified decoder and benchmark-specific streaming workspace passages.

CheungEn02C

N. Cheung, En02-C, version 1. Enter Calculus Companion. Supplied sequential soundness and one-live-qubit benchmark obstruction.

CheungEn07A

N. Cheung, En07-A, version 1. Enter Calculus Companion. Supplied readout-and-drop identity and prop:no-landauer-from-channel.

CheungEm03A

N. Cheung, Em03-A, version 1. Enter Calculus Companion. Supplied fixed-background scalar emission law; not a complete gravitational evaporation channel.

CheungEm03F

N. Cheung, Em03-F, version 1. Enter Calculus Companion. Supplied entanglement-breaking packet channel and recovery obstruction.

CheungEm03G

N. Cheung, Em03-G, version 1. Enter Calculus Companion. Supplied ordered source-field and packet-decoder comparisons; not a local Schwarzschild coherent receiver.

HaydenPreskill

P. Hayden and J. Preskill, “Black holes as mirrors: quantum information in random subsystems.” Journal of High Energy Physics 2007(09), 120. DOI https://doi.org/10.1088/1126-6708/2007/09/120. https://arxiv.org/abs/0708.4025.

KnillLaflamme

E. Knill and R. Laflamme, “Theory of quantum error-correcting codes.” Physical Review A 55 (1997), 900–911. DOI https://doi.org/10.1103/PhysRevA.55.900.

KSW

D. Kretschmann, D. Schlingemann, and R. F. Werner, “The information-disturbance tradeoff and the continuity of Stinespring's representation.” IEEE Transactions on Information Theory 54 (2008), 1708–1717. DOI https://doi.org/10.1109/TIT.2008.917696. https://arxiv.org/abs/quant-ph/0605009.

WatrousBook

J. Watrous, The Theory of Quantum Information. Cambridge University Press, 2018. Author's manuscript: https://cs.uwaterloo.ca/ watrous/TQI/TQI.pdf.

WatrousSDP

J. Watrous, “Semidefinite programs for completely bounded norms.” Theory of Computing 5 (2009), 217–238. https://theoryofcomputing.org/articles/v005a011/. https://arxiv.org/abs/0901.4709.

WatrousSimpler

J. Watrous, “Simpler semidefinite programs for completely bounded norms.” Chicago Journal of Theoretical Computer Science 2013, article 8. https://arxiv.org/abs/1207.5726.

Barenco

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation.” Physical Review A 52 (1995), 3457–3467. DOI https://doi.org/10.1103/PhysRevA.52.3457. https://arxiv.org/abs/quant-ph/9503016.

ChenPetz

C.-F. Chen, G. Penington, and G. Salton, “Entanglement wedge reconstruction using the Petz map.” Journal of High Energy Physics 2020(01), 168. DOI https://doi.org/10.1007/JHEP01(2020)168. https://arxiv.org/abs/1902.02844.

YoshidaKitaev

B. Yoshida and A. Kitaev, Efficient decoding for the Hayden–Preskill protocol. arXiv:1710.03363. https://arxiv.org/abs/1710.03363.

PageAverage

D. N. Page, “Average entropy of a subsystem.” Physical Review Letters 71 (1993), 1291–1294. DOI https://doi.org/10.1103/PhysRevLett.71.1291. https://arxiv.org/abs/gr-qc/9305007.

Sen

S. Sen, “Average entropy of a subsystem.” Physical Review Letters 77 (1996), 1–3. DOI https://doi.org/10.1103/PhysRevLett.77.1. https://arxiv.org/abs/hep-th/9601132.

Baumgratz

T. Baumgratz, M. Cramer, and M. B. Plenio, “Quantifying coherence.” Physical Review Letters 113 (2014), 140401. DOI https://doi.org/10.1103/PhysRevLett.113.140401. https://arxiv.org/abs/1311.0275.

EntanglementBreaking

M. Horodecki, P. W. Shor, and M. B. Ruskai, “Entanglement breaking channels.” Reviews in Mathematical Physics 15 (2003), 629–641. DOI https://doi.org/10.1142/S0129055X03001709. https://arxiv.org/abs/quant-ph/0302031.

Teleportation

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels.” Physical Review Letters 70 (1993), 1895–1899. DOI https://doi.org/10.1103/PhysRevLett.70.1895.

EngelhardtWall

N. Engelhardt and A. C. Wall, “Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime.” Journal of High Energy Physics 2015(01), 073. https://arxiv.org/abs/1408.3203.

IslandReview

A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, “The entropy of Hawking radiation.” Reviews of Modern Physics 93 (2021), 035002. DOI https://doi.org/10.1103/RevModPhys.93.035002. https://arxiv.org/abs/2006.06872.

Penington

G. Penington, Entanglement Wedge Reconstruction and the Information Paradox. arXiv:1905.08255. External gravitational comparison, not an identification theorem for the finite vault. https://arxiv.org/abs/1905.08255.

CheungXIVI

N. Cheung, XIV-I, version 1. Enter Calculus Companion. Supplied constructed I2 internal amplitude and unresolved I3 boundary.

CheungXIVJ

N. Cheung, XIV-J, version 1. Enter Calculus Companion. Supplied reconstruction descent, supported-sector reference, J2 boundary, and no-admission record.

CheungXVB

N. Cheung, XV-B, version 2. Enter Calculus Companion. Supplied lifting and extension interfaces; the graph-specific complete map remains unresolved.

CheungXVIN

N. Cheung, XVI-N, version r12. Enter Calculus Companion. Supplied conditional massless special-family obstruction and undischarged universal obligation.

CheungXVIO

N. Cheung, XVI-O, revision o70-sync. Enter Calculus Companion. Supplied separation of kernel-subsector progress from bulk $O.1=\text{NOT\_CLOSED}$.