References

CheungHawk01A

N. Cheung, Hawk01-A, version 1, unpublished manuscript, n.d. User-supplied excerpts; locators listed in Appendix app:locators. Corpus companion: https://enter.grok.me.

CheungEm03A

N. Cheung, Em03-A, version 1, unpublished manuscript, n.d. Fixed-background scalar emission law, thm:main; user-supplied excerpts.

CheungEm03E

N. Cheung, Em03-E, version 1, unpublished manuscript, n.d. Complete complementary output, thm:complement; user-supplied excerpts.

CheungEm03F

N. Cheung, Em03-F, version 1, unpublished manuscript, n.d. Exterior source–scalar evolution and channel; user-supplied excerpts.

CheungEm05A

N. Cheung, Em05-A, version 1, unpublished manuscript, n.d. Marginal/recovery separation, cor:separation; user-supplied excerpts.

CheungEm05B

N. Cheung, Em05-B, version 1, unpublished manuscript, n.d. Constant-complement criterion, thm:constantComplement; user-supplied excerpts.

CheungEm06B

N. Cheung, Em06-B, version 1, unpublished manuscript, n.d. Classical input-stability allowance, thm:input-stability; user-supplied excerpts.

CheungEn02E

N. Cheung, En02-E, version 2, unpublished manuscript, n.d. Finite Gaussian packet state and cutoff interface; user-supplied excerpts.

CheungPsy02B

N. Cheung, Psy02-B, version 2, unpublished manuscript, n.d. Complete-process equality, thm:process; user-supplied excerpts.

CheungEn03A

N. Cheung, En03-A, version 1, unpublished manuscript, n.d. Residual-state obstruction, thm:obstruction; user-supplied excerpts.

CheungXIVH

N. Cheung, XIV-H, version 1, unpublished manuscript, n.d. Internal kernels and H2 release boundary; user-supplied excerpts.

CheungXIVI

N. Cheung, XIV-I, version 1, unpublished manuscript, n.d. Constructed I2 internal amplitude and unresolved I3 joint map; user-supplied excerpts.

CheungXIVJ

N. Cheung, XIV-J, version 1, unpublished manuscript, n.d. Reconstruction descent, supported-sector reference, conditional extension, and J2/no-admission boundary; user-supplied excerpts.

CheungXVB

N. Cheung, XV-B, version 1, unpublished manuscript, n.d. Relative-lifting interface, thm:lifting; user-supplied excerpts.

CheungXVIL

N. Cheung, XVI-L, version 1, unpublished manuscript, n.d. Complete-source two-edge graph contribution and stated renormalization/matching boundaries; user-supplied excerpts.

CheungXVIM

N. Cheung, XVI-M, version 1, unpublished manuscript, n.d. Graph-specific counterterm and scale ledgers; user-supplied excerpts.

CheungXVIN

N. Cheung, XVI-N, version r12, unpublished manuscript, n.d. Conditional massless prepared-insertion obstruction, thm:massless-obstruction; user-supplied excerpts.

CheungXVIO

N. Cheung, XVI-O, version o70-sync, unpublished manuscript, n.d. Kernel-subsector prescription and separate bulk/BV verdicts; user-supplied excerpts.

Hawking1975

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

Page1976

D. N. Page, “Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole,” Physical Review D 13, 198–206 (1976). doi:10.1103/PhysRevD.13.198.

Mathur

S. D. Mathur, “The information paradox: A pedagogical introduction,” Classical and Quantum Gravity 26, 224001 (2009). arXiv:0909.1038.

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, 1708–1717 (2008). arXiv:quant-ph/0605009.

LiebRuskai

E. H. Lieb and M. B. Ruskai, “Proof of the strong subadditivity of quantum-mechanical entropy,” Journal of Mathematical Physics 14, 1938–1941 (1973). doi:10.1063/1.1666274.

Audenaert

K. M. R. Audenaert, “A sharp continuity estimate for the von Neumann entropy,” Journal of Physics A: Mathematical and Theoretical 40, 8127–8136 (2007). Preprint title: “A sharp Fannes-type inequality for the von Neumann entropy.” arXiv:quant-ph/0610146.

Donoghue

J. F. Donoghue, “General relativity as an effective field theory: The leading quantum corrections,” Physical Review D 50, 3874–3888 (1994). arXiv:gr-qc/9405057.

HollandsWald2001

S. Hollands and R. M. Wald, “Local Wick polynomials and time ordered products of quantum fields in curved spacetime,” Communications in Mathematical Physics 223, 289–326 (2001). arXiv:gr-qc/0103074.

HollandsWald2002

S. Hollands and R. M. Wald, “Existence of local covariant time ordered products of quantum fields in curved spacetime,” Communications in Mathematical Physics 231, 309–345 (2002). arXiv:gr-qc/0111108.

BrunettiFredenhagen

R. Brunetti and K. Fredenhagen, “Microlocal analysis and interacting quantum field theories: Renormalization on physical backgrounds,” Communications in Mathematical Physics 208, 623–661 (2000). arXiv:math-ph/9903028.

HuVerdaguer

B. L. Hu and E. Verdaguer, “Stochastic gravity: Theory and applications,” Living Reviews in Relativity 11, 3 (2008). arXiv:0802.0658.

delRio2026

A. del Río and F. J. Marañón-González, “Black-hole evaporation from the semiclassical Einstein equations in 3+1 dimensions,” arXiv:2607.11737v1 (2026). Submitted July 13, 2026. Cited as a semiclassical comparison, not a premise of the certification theorem.

HaydenPreskill

P. Hayden and J. Preskill, “Black holes as mirrors: Quantum information in random subsystems,” Journal of High Energy Physics 2007(09), 120 (2007). arXiv:0708.4025.

Penington

G. Penington, “Entanglement wedge reconstruction and the information paradox,” Journal of High Energy Physics 2020(09), 002 (2020). Preprint title: “The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole.” arXiv:1905.08762.

ReplicaWormholes

A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, “Replica wormholes and the entropy of Hawking radiation,” Journal of High Energy Physics 2020(05), 013 (2020). arXiv:1911.12333.

Shirokov

M. E. Shirokov, “Energy-constrained diamond norms and their use in quantum information theory,” arXiv:1706.00361 (2017).