References

Oai265A

Oai265-A: Static Area Laws, Quantum Recovery, and Gravitational Entropy: A Separation Theorem with a Source and Attachment Audit. Version 1, 12 October 2026. User-supplied manuscript 265-A.tex. No independent compilation or proof-assistant verification is asserted here.

ExecutionReport

Oai265-B Appendix Code Execution Report. Undated user-supplied file (30).txt. Reports execution of the version-1 supplementary script with seed 265, 20 repetitions per case, 40 shots per setting, ${\alpha }_{\mathrm{s}}=1/20$, and $b_{\mathrm{cal}}=b=0$. Contains first-repetition rational endpoints and aggregate coverage counts. The execution is not independently reproduced in this revision.

KlieschRoth

M. Kliesch and I. Roth. Theory of quantum system certification—a tutorial. PRX Quantum 2 (2021), 010201. arXiv:2010.05925, version 3. https://arxiv.org/abs/2010.05925.

FlammiaLiu

S. T. Flammia and Y.-K. Liu. Direct fidelity estimation from few Pauli measurements. Physical Review Letters 106 (2011), 230501. arXiv:1104.4695. https://arxiv.org/abs/1104.4695.

DaSilvaEtAl

M. P. da Silva, O. Landon-Cardinal, and D. Poulin. Practical characterization of quantum devices without tomography. Physical Review Letters 107 (2011), 210404. arXiv:1104.3835. https://arxiv.org/abs/1104.3835.

FuchsVanDeGraaf

C. A. Fuchs and J. van de Graaf. Cryptographic Distinguishability Measures for Quantum Mechanical States. arXiv:quant-ph/9712042. https://arxiv.org/abs/quant-ph/9712042.

Watrous

J. Watrous. Simpler semidefinite programs for completely bounded norms. arXiv:1207.5726, version 2, 2012. https://arxiv.org/abs/1207.5726.

Hoeffding

W. Hoeffding. Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58 (1963), 13–30. doi:10.1080/01621459.1963.10500830.

ClopperPearson

C. J. Clopper and E. S. Pearson. The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika 26 (1934), 404–413. doi:10.1093/biomet/26.4.404.

GST

E. Nielsen, J. K. Gamble, K. Rudinger, T. Scholten, K. Young, and R. Blume-Kohout. Gate set tomography. Quantum 5 (2021), 557. arXiv:2009.07301. https://arxiv.org/abs/2009.07301.

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. arXiv:quant-ph/0605009. https://arxiv.org/abs/quant-ph/0605009.

CheungEn07C

N. Cheung. En07-C, version 1, undated manuscript. Supplied 07-C.tex excerpts: :choi, :constant-error, :featureless, :entropy, and complete-residual scope statements. Enter Calculus Companion. https://enter.grok.me. Citations identify supplied excerpts, not independent verification.

CheungHawk04B

N. Cheung. Hawk04-B: Black-Hole Information as an Access Problem: Enter, Quantum Recovery, and Complete Residuals. Version 2, undated manuscript. Especially :certificate, :interval, and :QND. Enter Calculus Companion. https://enter.grok.me/browse/Hawk04-B.

CheungEn07A

N. Cheung. En07-A, version 1, undated manuscript. Supplied excerpts on complete channels, selected entropy, and the distinction between channel identities and Landauer cost. Enter Calculus Companion. https://enter.grok.me.

CheungEn07B

N. Cheung. En07-B, version 1, undated manuscript. Supplied 07-B.tex, especially :featureless and :entropy. Enter Calculus Companion. https://enter.grok.me.

CheungEn02B

N. Cheung. En02-B, version 1, undated manuscript. Supplied 02-B-v1.tex, especially :B1, complete branch accounting, and the declared decoder-module resource class. Enter Calculus Companion. https://enter.grok.me.

CheungEn02C

N. Cheung. En02-C, version 1, undated manuscript. Supplied 02-C-v1.tex, reference-preserving sequential soundness and :constant. Enter Calculus Companion. https://enter.grok.me.

CheungEn01C

N. Cheung. En01-C, version 1, undated manuscript. Supplied 01-C.tex, :certificate: bounded complete-record statistics, loss-model restrictions, and calibration failure risk. Enter Calculus Companion. https://enter.grok.me.

CheungI

N. Cheung. I, version 2, undated manuscript. Supplied .tex, :path and :adequacy. Finite path maps and circuit/instrument adequacy. Enter Calculus Companion. https://enter.grok.me.

CheungEn06B

N. Cheung. En06-B, version 1, undated manuscript. Supplied 06-B.tex, :Bellinstrument and the separate Bell-specimen discussion. Enter Calculus Companion. https://enter.grok.me.

CheungEm05B

N. Cheung. Em05-B, version 1, undated manuscript. Supplied 05-B-v1.tex, :Choi and the flagged-instrument interface. Enter Calculus Companion. https://enter.grok.me.

CheungEm03E

N. Cheung. Em03-E, version 1, undated manuscript. Supplied 03-E-v1.tex, the Pauli-channel distance identity and :recovery. Optimality is restricted to its declared channel. Enter Calculus Companion. https://enter.grok.me.

CheungEm03G

N. Cheung. Em03-G, version 1, undated manuscript. Supplied 03-G-v1.tex, :leakageBell. Complete-environment consequences of decoded Bell overlap. Enter Calculus Companion. https://enter.grok.me.

CheungEn04A

N. Cheung. En04-A, version 1, undated manuscript. Supplied 04-A.tex, :certificate and :noimplication. Quantum return, channel allowances, and non-Clifford-resource non-identification. Enter Calculus Companion. https://enter.grok.me.

CheungXVB

N. Cheung. Landmark XV-B: Relative Lifting and Reconstruction Descent for the Full Joint Characteristic Target. Version 2, undated manuscript. Supplied -B.tex, technical-continuation distinction and :release. Enter Calculus Companion. https://enter.grok.me/browse/XV-B.

CheungXIVJ

N. Cheung. XIV-J, version 1, undated manuscript. Supplied -J.tex, :J2 and :noadmission. The characteristic-map and quantum-admission interfaces are separate from finite-memory certification. Enter Calculus Companion. https://enter.grok.me.