References

Hawking1975

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

Hawking1976

S. W. Hawking, “Breakdown of predictability in gravitational collapse,” Physical Review D 14 (1976), 2460–2473. doi:10.1103/PhysRevD.14.2460.

Stinespring

W. F. Stinespring, “Positive functions on $C^{\ast }$-algebras,” Proceedings of the American Mathematical Society 6 (1955), 211–216. doi:10.1090/S0002-9939-1955-0069403-4.

Watrous

J. Watrous, The Theory of Quantum Information, Cambridge University Press, 2018. doi:10.1017/9781316848142.

KnillLaflamme

E. Knill and R. Laflamme, “Theory of quantum error-correcting codes,” Physical Review A 55 (1997), 900–911. doi:10.1103/PhysRevA.55.900. arXiv:quant-ph/9604034.

BraunsteinPati

S. L. Braunstein and A. K. Pati, “Quantum information cannot be completely hidden in correlations: Implications for the black-hole information paradox,” Physical Review Letters 98 (2007), 080502. doi:10.1103/PhysRevLett.98.080502. arXiv:gr-qc/0603046.

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:10.1109/TIT.2008.917696. arXiv: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:10.1142/S0129055X03001709. arXiv:quant-ph/0302031.

Bennett1973

C. H. Bennett, “Logical reversibility of computation,” IBM Journal of Research and Development 17 (1973), 525–532. doi:10.1147/rd.176.0525.

Landauer1961

R. Landauer, “Irreversibility and heat generation in the computing process,” IBM Journal of Research and Development 5 (1961), 183–191. doi:10.1147/rd.53.0183.

ReebWolf

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

Page1993

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

GaikwadEtAl

A. Gaikwad, A. Kaushal, G. Mandal, and S. R. Wadia, “A microscopic model of black hole evaporation in two dimensions,” Journal of High Energy Physics 08 (2023), 171. doi:10.1007/JHEP08(2023)171. arXiv:2210.15579.

CheungHawk04A

N. Cheung, Hawk04-A, version 1. Supplied manuscript Hawk04-A.tex, n.d. Enter Calculus Companion. Documentary comparison: complete preservation, exact complete-complement recovery, and featureless-output boundary.

CheungHawk04B

N. Cheung, Hawk04-B, version 2. Supplied manuscript Hawk04-B.tex, n.d. Enter Calculus Companion. Documentary comparison: typed decoder/readout/discard interfaces; :gravity; endpoint and receiver limits.

CheungEn07A

N. Cheung, En07-A, version 1. Supplied manuscript En07-A.tex, n.d. Enter Calculus Companion. Documentary comparison: reversible recycling, readout-and-drop, three ledgers, and :no-landauer-from-channel.

CheungEn04A

N. Cheung, En04-A, version 1. Supplied manuscript En04-A.tex, n.d. Enter Calculus Companion. Documentary comparison: complete restoration, residual response, and :noimplication.

CheungHawk01B

N. Cheung, Hawk01-B, version 1. Supplied manuscript Hawk01-B.tex, n.d. Enter Calculus Companion. Documentary comparison: complete-complement criteria, residual certificates, and entropy/recovery separation.

CheungHawk02E

N. Cheung, Hawk02-E, version 1. Supplied manuscript Hawk02-E.tex, n.d. Enter Calculus Companion. Documentary comparison: regulated interacting SYK–scalar certification, not a gravitational endpoint.

CheungHawk03A

N. Cheung, Hawk03-A, version 1. Supplied manuscript Hawk03-A.tex, n.d. Enter Calculus Companion. Documentary comparison: finite partner algebra, two-purifier and information–disturbance certificates, not a physical firewall resolution.

CheungEm03H

N. Cheung, Em03-H, version 8. Supplied manuscript Em03-H-v8.tex, n.d. Enter Calculus Companion. Documentary comparison: complete channels and stored-packet certificates for one fixed quartic bath.

CheungEn02B

N. Cheung, En02-B, version 1. Supplied manuscript En02-B-v1.tex, n.d. Enter Calculus Companion. Documentary comparison: :B5, with its declared streaming delivery and storage contract.

CheungEn02C

N. Cheung, En02-C, version 1. Supplied manuscript En02-C-v1.tex, n.d. Enter Calculus Companion. Documentary comparison: :C2 and :C3; information-theoretic and operational recovery are distinct.

CheungEn02E

N. Cheung, En02-E, version 2. Supplied manuscript En02-E-v2.tex, n.d. Enter Calculus Companion. Documentary comparison: finite Gaussian packet states and flagged cutoffs under their stated hypotheses.

CheungEm03B

N. Cheung, Em03-B, version 2. Supplied manuscript Em03-B-v2.tex, n.d. Enter Calculus Companion. Documentary comparison: packet marginal and apparatus-model readout; later reset is a separate task.

CheungEm03E

N. Cheung, Em03-E, version 1. Supplied manuscript Em03-E-v1.tex, n.d. Enter Calculus Companion. Documentary comparison: :evolution conserves the declared free Hamiltonian, not a thermodynamic reset cost.

CheungEn06B

N. Cheung, En06-B, version 1. Supplied manuscript En06-B.tex, n.d. Enter Calculus Companion. Documentary comparison: increasing-stencil finite-network transport and exact instrument preservation.

CheungEn05C

N. Cheung, En05-C, version 1. Supplied manuscript En05-C.tex, n.d. Enter Calculus Companion. Documentary comparison: tensor-free regional containment and explicit non-transfer boundaries.

CheungXVIIA

N. Cheung, XVII-A, version 1. Supplied manuscript XVII-A.tex, n.d. Enter Calculus Companion. Documentary comparison: finite sine-effect reconstruction and :timeband; no entanglement-wedge inference.

CheungEm06A

N. Cheung, Em06-A, version 1. Supplied manuscript Em06-A-v1.tex, n.d. Enter Calculus Companion. Documentary comparison: scalar-only coherent classical limit with prescribed metric data.

CheungEm06B

N. Cheung, Em06-B, version 1. Supplied manuscript Em06-B-v1.tex, n.d. Enter Calculus Companion. Documentary comparison: scalar-only family concentration and compact-test estimates; metric data remain inputs.

CheungXIVH

N. Cheung, Landmark XIV-H: Internal kernel relations on the operator route, version 1. Supplied manuscript XIV-H.tex, n.d. Documentary status: :H2 and :release.

CheungXIVI

N. Cheung, XIV-I, version 1. Supplied manuscript XIV-I.tex, n.d. Enter Calculus Companion. Documentary status: :I2, :I3, and :release.

CheungXIVJ

N. Cheung, XIV-J, version 1. Supplied manuscript XIV-J.tex, n.d. Enter Calculus Companion. Documentary status: :descent, :reference, :J2, and :noadmission.

CheungXVB

N. Cheung, XV-B, version 2. Supplied manuscript XV-B.tex, n.d. Enter Calculus Companion. Documentary status: relative lifting, normal-jet null criteria, closed-set extension, point-puncture correction, and the unconstructed inherited full map.

CheungXVIN

N. Cheung, XVI-N, revision r12. Supplied manuscript XVI-N.tex, n.d. Enter Calculus Companion. Documentary status: :massless-obstruction, its Route A domain, and the unfinished Route B.

CheungXVIO

N. Cheung, XVI-O, revision o70-sync. Supplied manuscript XVI-O.tex, n.d. Enter Calculus Companion. Documentary comparison: prescribed kernel subsector, not bulk closure; O.1 remains _CLOSED.

CheungXVIP

N. Cheung, XVI-P, revision p23. Supplied manuscript XVI-P.tex, n.d. Enter Calculus Companion. Documentary comparison: prepared and kernel-sector audits; no bulk O.1 closure or inherited quantum admission.

CatalogueRecord

OpenAI-labelled documentary record, OpenAI catalogue. Supplied companion manuscript OpenAI.tex. Cited only for the supplied non-premise and status ledger. No external catalogue verification, proof verification, or transfer of any family result is asserted.