References

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.

Watrous

J. Watrous, The Theory of Quantum Information, Cambridge University Press, 2018.

VeitchEtAl

V. Veitch, S. A. H. Mousavian, D. Gottesman, and J. Emerson, “The resource theory of stabilizer quantum computation,” New Journal of Physics 16 (2014), 013009. doi: 10.1088/1367-2630/16/1/013009. arXiv:1307.7171.

FattalEtAl

D. Fattal, T. S. Cubitt, Y. Yamamoto, S. Bravyi, and I. L. Chuang, “Entanglement in the stabilizer formalism,” arXiv:quant-ph/0406168, 2004.

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. Preprint title: “General Entanglement Breaking Channels,” arXiv:quant-ph/0302031.

Kato

T. Kato, Perturbation Theory for Linear Operators, Classics in Mathematics, Springer, 1995. Reprint of the second edition. doi: 10.1007/978-3-642-66282-9.

Cao2024

C. Cao, “Non-trivial area operators require non-local magic,” Journal of High Energy Physics 11 (2024), 105. doi: 10.1007/JHEP11(2024)105. arXiv:2306.14996. Cited with its operator-algebra and code hypotheses, not as a generic magic-to-complement-nonconstancy theorem.

CaoEtAl2026

C. Cao, G. Cheng, K. Karthikeyan, C. Li, and J. Preskill, “State-dependent geometries from magic-enriched quantum codes,” arXiv:2603.13475v1, 2026. Perturbative skewed subsystem codes, proto-area entropy, and tripartite non-local Choi magic. No generic identification with ${\delta }_{\mathrm{full}}$ is imported.

Moosa2026

M. Moosa, “Type III von Neumann algebras are magical,” arXiv:2608.12512v1, 2026. Continuum/thermodynamic-limit comparison only; no finite-carrier residual-response conclusion is imported.

CheungI

N. Cheung, Landmark I, version 2. Supplied unpublished manuscript excerpts, n.d. Source identifiers I.tex and I_v2.tex in the supplied records. In particular, thm:main, “Characterization.” Born probabilities and positive-branch destructive residuals within the declared strategy class.

CheungEn03A

N. Cheung, En03-A, version 1. Supplied unpublished manuscript excerpts En03-A.tex, n.d. Minimal linear typed interface and relation to a larger calculus. No field preparation or gate-library universality is imported.

CheungHawk04A

N. Cheung, Hawk04-A: Unitary Information Preservation and Radiation Recovery: A Complete-Complement Formulation of the Black-Hole Information Problem, version 1. Supplied unpublished manuscript record and excerpts, n.d. In particular, thm:global, thm:exact, cor:nohiding, thm:four-majorana, and the endpoint and recurrence interfaces. The required channel statements are proved locally.

CheungHawk04B

N. Cheung, Hawk04-B: Quantum Recovery, Destructive Readout, and Complete Residuals, supplied manuscript and revised typed-program source, n.d. Quantum return, readout-and-drop, apparatus dilation, exact four-Majorana residual accounting, certificates, and access-preserving endpoints.

CheungHawk02E

N. Cheung, Hawk02-E: Coherent Diaries and Complete-Residual Certification in a Regulated Interacting SYK–Scalar Model, version 1. Supplied unpublished manuscript Hawk02-E-v1.tex, n.d. Regulated architecture, finite-proxy comparisons, source-energy separation, and fixed-proxy recurrence.

CheungEn02B

N. Cheung, En02-B, version 1. Supplied unpublished manuscript excerpts En02-B-v1.tex, n.d. In particular, thm:B1, resource-certified decoder soundness, complete branch maps, and live-name accounting.

CheungEn02C

N. Cheung, En02-C, version 1. Supplied unpublished manuscript excerpts En02-C-v1.tex, n.d. Reference-preserving sequential soundness and the separation of availability, decoder existence, and executable recovery.

CheungEn02E

N. Cheung, En02-E, version 2. Supplied unpublished manuscript excerpts En02-E-v2.tex, n.d. Gaussian packet states and flagged-cutoff comparisons; commuting-state hypotheses are retained.

CheungEm03C

N. Cheung, Em03-C, version 1. Supplied unpublished manuscript excerpts Em03-C-v1.tex, n.d. Joint apparatus interfaces, finite records, coherent comparisons, and physical receiver boundaries.

CheungXIVH

N. Cheung, Landmark XIV-H: Internal kernel relations on the operator route, version 1. Supplied unpublished manuscript excerpts XIV-H.tex, n.d. Internal maps, regular charts, and the stated H2 stop. Documentary separation only.

CheungXIVI

N. Cheung, Landmark XIV-I, version 1. Supplied unpublished manuscript excerpts XIV-I.tex, n.d. Constructed I2 internal amplitude module and unresolved I3 joint characteristic map. Documentary separation only.

CheungXIVJ

N. Cheung, Landmark XIV-J, version 1. Supplied unpublished manuscript excerpts XIV-J.tex, n.d. In particular, prop:descent, lem:null, thm:reference, thm:conditionalextension, thm:J2, and cor:noadmission. Supported-sector references do not admit the full coefficient.

CheungXVB

N. Cheung, Landmark XV-B, version 1. Supplied unpublished manuscript excerpts XV-B.tex, n.d. Relative-lifting and extension interfaces; no inherited full characteristic contraction or quantum admission is supplied.

CheungXVIN

N. Cheung, Landmark XVI-N, version r12. Supplied unpublished manuscript excerpts XVI-N.tex, n.d. In particular, thm:massless-obstruction. Conditional specified-instance result, not a universal completion or the missing characteristic-map construction.

SuppliedCatalogue

OpenAI, as attributed in the supplied companion record, Enter Calculus Companion: OpenAI family catalogue excerpts. Supplied documentary record describing Families 227, 279, 274, and 276; the supplied Family 279 record is labelled rem:oai-279 and dated 7 October 2026. Attribution, proofs, and publication status are not independently verified here. No family is a theorem premise.