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.” Bibliographic entry supplied in EntPhil version 2: Frontiers in Physics, volume 14 (2026), DOI https://doi.org/10.3389/fphy.2026.1954943. The companion describes an accepted article with final formatted version forthcoming; that publisher status is not independently certified by this manuscript.

CheungI

N. Cheung, Manuscript I, version 2. Enter Calculus Companion. Supplied finite destructive-measurement characterization, including thm:main. https://enter.grok.me/browse/I.

Hawk05A

Hawk05-A: Enter, Page-Type Entropy Turnover, and the Classical-Record Obstruction. Supplied source Hawk05-A.tex, dated 15 October 2026. Author field unspecified. The reversed-weight equation in its flagged theorem is corrected in Section sec:repairs and Appendix app:flag.

CheungHawk02B

N. Cheung, Hawk02-B: Hamiltonian-Derived Emission and Quantitative Recovery in a Finite Evaporation Model, version 2. Enter Calculus Companion. Supplied labels thm:B3, thm:B7. https://enter.grok.me/browse/Hawk02-B.

CheungHawk01B

N. Cheung, Hawk01-B: Complete Quantum-Code Preservation in a Sequential Evaporation Model: Radiation Correlations, Residual Leakage, and the Page-Curve–Recovery Gap, version 1. Enter Calculus Companion. Supplied thm:entropyseparation. https://enter.grok.me/browse/Hawk01-B.

CheungHawk03A

N. Cheung, Hawk03-A, version 1. Enter Calculus Companion. Supplied complete-complement, independent-factor, and partner comparisons. Their model-specific hypotheses are not imported. https://enter.grok.me/browse/Hawk03-A.

CheungHawk04D

N. Cheung, Hawk04-D: From Finite Enter Interfaces to Conditional Evaporation Certificates: Controlled Limits, Mass Laws, and Quantum Recovery, version 1. Enter Calculus Companion. Relevant supplied labels: thm:swap, thm:flagged, thm:endpoint. https://enter.grok.me/browse/Hawk04-D.

CheungEn07A

N. Cheung, En07-A, version 1. Enter Calculus Companion. Supplied readout/discard and prop:no-landauer-from-channel records. https://enter.grok.me/browse/En07-A.

CheungEn07B

N. Cheung, En07-B, version 1. Enter Calculus Companion. Supplied endpoint and separate-ledger records. https://enter.grok.me/browse/En07-B.

CheungEn07C

N. Cheung, En07-C: Hawking Radiation under Destructive Enter, version 1. Enter Calculus Companion. Supplied def:four, thm:endpoint, and spectral/entropy separation records. https://enter.grok.me/browse/En07-C.

CheungEn02C

N. Cheung, En02-C, version 1. Enter Calculus Companion. Supplied reference-preserving sequential soundness, thm:C1. https://enter.grok.me/browse/En02-C.

CheungEn02D

N. Cheung, En02-D, version 4. Enter Calculus Companion. Supplied prepared-state turnover, thm:turnover. https://enter.grok.me/browse/En02-D.

CheungVIIG

N. Cheung, VII-G, version 1. Enter Calculus Companion. Supplied finite hybrid channel and history-instrument structure. https://enter.grok.me/browse/VII-G.

CheungEm05B

N. Cheung, Em05-B, version 1. Enter Calculus Companion. Supplied thm:constantComplement. https://enter.grok.me/browse/Em05-B.

CheungEm03A

N. Cheung, Em03-A, version 1. Enter Calculus Companion. Supplied fixed-background scalar emission law, thm:main; not a complete microscopic evaporation channel. https://enter.grok.me/browse/Em03-A.

CheungOai265A

N. Cheung, Oai265-A, version 2. Enter Calculus Companion. Supplied record/spectrum/recovery separation, thm:separation. Documentary comparison only. https://enter.grok.me/browse/Oai265-A.

CheungXIVI

N. Cheung, XIV-I, version 1. Enter Calculus Companion. Supplied I2 construction and I3 boundary. https://enter.grok.me/browse/XIV-I.

CheungXIVJ

N. Cheung, XIV-J, version 1. Enter Calculus Companion. Supplied reconstruction descent, supported reference, and J2 boundary. https://enter.grok.me/browse/XIV-J.

CheungXVB

N. Cheung, XV-B, version 2. Enter Calculus Companion. Supplied relative-lifting and extension interfaces; the inherited graph-specific map remains unresolved. https://enter.grok.me/browse/XV-B.

Watrous

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

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.

HorodeckiShorRuskai

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. Preprint title: General Entanglement Breaking Channels. https://arxiv.org/abs/quant-ph/0302031.

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.

PageRadiation

D. N. Page, “Information in black hole radiation.” Physical Review Letters 71 (1993), 3743–3746. DOI https://doi.org/10.1103/PhysRevLett.71.3743. https://arxiv.org/abs/hep-th/9306083.

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.

CollinsSniady

B. Collins and P. \'Sniady, “Integration with respect to the Haar measure on unitary, orthogonal and symplectic group.” Communications in Mathematical Physics 264 (2006), 773–795. https://arxiv.org/abs/math-ph/0402073.

Audenaert

K. M. R. Audenaert, “A sharp continuity estimate for the von Neumann entropy.” Journal of Physics A: Mathematical and Theoretical 40 (2007), 8127–8136. DOI https://doi.org/10.1088/1751-8113/40/28/S18. https://arxiv.org/abs/quant-ph/0610146.

Hawking

S. W. Hawking, “Particle creation by black holes.” Communications in Mathematical Physics 43 (1975), 199–220. DOI https://doi.org/10.1007/BF02345020.

ReebWolf

D. Reeb and M. M. Wolf, “An improved Landauer principle with finite-size corrections.” New Journal of Physics 16 (2014), 103011. DOI https://doi.org/10.1088/1367-2630/16/10/103011. https://arxiv.org/abs/1306.4352.

Penington

G. Penington, Entanglement Wedge Reconstruction and the Information Paradox. arXiv:1905.08255. External gravitational comparison; not a premise of the finite model. https://arxiv.org/abs/1905.08255.

AlmheiriEtAl

A. Almheiri, N. Engelhardt, D. Marolf, and H. Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole. arXiv:1905.08762. External gravitational comparison; not a premise of the finite model. https://arxiv.org/abs/1905.08762.