References

CKLW

S. Carpi, Y. Kawahigashi, R. Longo, and M. Weiner. From vertex operator algebras to conformal nets and back. Memoirs of the American Mathematical Society 254 (2018), no. 1213. doi:10.1090/memo/1213. arXiv:1503.01260.

CTW

S. Carpi, Y. Tanimoto, and M. Weiner. Local energy bounds and strong locality in chiral CFT. Communications in Mathematical Physics 390 (2022), 169–192. doi:10.1007/s00220-021-04291-9. arXiv:2103.16475.

CTWCorrection

S. Carpi, Y. Tanimoto, and M. Weiner. Correction to: Local Energy Bounds and Strong Locality in Chiral CFT. 2023 correction, including the Hermitian hypotheses in the locality statements. Author-deposited correction: https://real.mtak.hu/130780/7/corrections.pdf.

CarpiTomassini

S. Carpi and L. Tomassini. Energy bounds for vertex operator algebra extensions. arXiv:2303.14097. Cited for its stated sufficient conditions, not for the universal Family 280 conclusion.

GuiUnbounded

B. Gui. Unbounded field operators in categorical extensions of conformal nets. Inventiones Mathematicae 244 (2026), no. 3, 899–965. arXiv:2001.03095. The author's listed errata are relevant to applications.

GuiQSystems

B. Gui. Q-systems and extensions of completely unitary vertex operator algebras. International Mathematics Research Notices 2022, no. 10, 7550–7614. arXiv:1908.03484.

GuiExtensions

B. Gui. Comparison of Extensions of Unitary Vertex Operator Algebras and Conformal Nets. arXiv:2505.03235. The stated hypotheses and example classes are retained.

HenriquesTener

A. G. Henriques and J. E. Tener. Every conformal net has an associated unitary VOA. arXiv:2507.20735. Cited as an independently stated converse-direction construction, not proved in this companion.

KLM

Y. Kawahigashi, R. Longo, and M. Müger. Multi-interval subfactors and modularity of representations in conformal field theory. Communications in Mathematical Physics 219 (2001), 631–669. doi:10.1007/PL00005565. arXiv:math/9903104.

ThomFusion

A. Thom. A remark about the Connes fusion tensor product. arXiv:math/0601045. Relative tensor products of von Neumann algebra correspondences.

BartelsDouglasHenriques

A. Bartels, C. L. Douglas, and A. Henriques. Conformal nets III: fusion of defects. arXiv:1310.8263. Defect and sector fusion under its stated finite-index hypotheses.

Rehren

K.-H. Rehren. Algebraic holography. arXiv:hep-th/9905179. Cited to distinguish an explicit spacetime-region correspondence from the extension record used here.

Pedersen

G. K. Pedersen. {$C^{\ast }$-Algebras and Their Automorphism Groups}. Academic Press, 1979. Jordan decomposition and standard $C^{\ast }$-algebraic separation.

Watrous

J. Watrous. The Theory of Quantum Information. Cambridge University Press, 2018. Finite-dimensional channels, references, Choi matrices, and completely bounded trace norms.

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.

FuchsVanDeGraaf

C. A. Fuchs and J. van de Graaf. Cryptographic distinguishability measures for quantum-mechanical states. IEEE Transactions on Information Theory 45 (1999), 1216–1227. arXiv:quant-ph/9712042.

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.

OpenAI280

OpenAI, as attributed in the supplied document. Strongly rational unitary vertex operator algebras and conformal nets. 25 September 2026. User-supplied .pdf, identified in the dossier as Family 280-01. Theorem 1.1, Corollary 9.3, and the relevant conventions are source records, not independently verified premises.

OpenAI290

OpenAI, as attributed in the supplied dossier. Bounded recovery for modular spectral averages. 23 September 2026. Family 290-02 source record. Its modular hypotheses are not instantiated on $A_V$ here.

Dossier

User-supplied Oai280-A development plan and comparative source dossier. Includes Family 280 catalogue attribution, the reported .lean scope note, other family records, and manuscript excerpts. Retrieval label 6f2e9611. No comprehensive corpus scan or verification is asserted.

Oai211A

Oai211-A: Operational Marks on Conditioned Block Trees. Earlier conversation draft. Cited only for the explicitly conditional operational comparison architecture. No independent registration, compilation, or proof verification is asserted.

CheungPortal

N. Cheung. Enter Calculus Companion. https://enter.grok.me. Searchable source companion, not a proof checker. Individual manuscript identifiers and supplied versions control the attributions below.

CheungEn05C

N. Cheung. En05-C, version 1. Undated supplied manuscript 05-C.tex. Especially :comparison and the normal-state and preparation-class qualifications. Tensor-free snapshot–channel–adjoint comparison. Enter Calculus Companion.

CheungEn05A

N. Cheung. En05-A, version 1. Undated supplied manuscript 05-A.tex. Especially :cone and :comparison. Scheduled past, adjoint support, and prescribed metric envelope. Enter Calculus Companion.

CheungEn03A

N. Cheung. En03-A, version 1. Undated supplied manuscript 03-A.tex. Especially :locality. Complete finite schedule support and its metric upper bound. Enter Calculus Companion.

CheungVIIE

N. Cheung. VII-E, version 1. Undated supplied manuscript -E.tex. Especially :locality. Prescribed schedule locality, not a field-theoretic light cone. Enter Calculus Companion.

CheungEn06A

N. Cheung. En06-A, version 1. Undated supplied manuscript 06-A.tex. Especially :algmicro and its 6obs observable-limit hypotheses. Channel transport does not supply algebraic microcausality without the declared observable interface. Enter Calculus Companion.

CheungEn06B

N. Cheung. En06-B, version 1. Undated supplied manuscript 06-B.tex. Especially :identity and the supplied instrument-transport comparison. Routes, ports, and speed remain specified inputs. Enter Calculus Companion.

CheungHawk03A

N. Cheung. Hawk03-A, version 1. Undated supplied manuscript 03-A.tex. Especially :exact and the partner/access distinctions. Enter Calculus Companion.

CheungHawk04A

N. Cheung. Hawk04-A, version 1. Undated supplied manuscript 04-A.tex. Especially :exact. Complete-complement recovery with an explicit decoder. Enter Calculus Companion.

CheungHawk04B

N. Cheung. Hawk04-B, version 2. Undated supplied manuscript 04-B.tex. Exact recovery, complete preservation, and record-only limitations. Enter Calculus Companion.

CheungEn07A

N. Cheung. En07-A, version 1. Undated supplied manuscript 07-A.tex. Especially :exact and the dimension and holographic-identification distinctions. Enter Calculus Companion.

CheungEn07B

N. Cheung. En07-B, version 1. Undated supplied manuscript 07-B.tex. Especially :four, :endpoint, and :release. The same-model gravitational endpoint package is not constructed by its documentary use here. Enter Calculus Companion.

CheungEn07C

N. Cheung. En07-C, version 1. Undated supplied manuscript 07-C.tex. Exact complete-complement recovery and the separation of a thermal-spectrum input from a replacement-channel verdict. Enter Calculus Companion.

CheungOai265A

N. Cheung. Oai265-A, version 1. Undated supplied manuscript 265-A.tex. Especially :determination and :separation. Static records, selected entropy, recovery, and radiation histories remain separate. Enter Calculus Companion.

CheungOai265B

N. Cheung. Oai265-B, version 2. Undated supplied manuscript 265-B-v2.tex. Especially :main and its validation contract. Three-correlation certification for one implemented decoder. Reported datasets are not independently rerun here. Enter Calculus Companion.

CheungOai290A

N. Cheung. Oai290-A, version 1. Undated supplied manuscript 290-A.tex. Especially :exact, :effect, and :assembly. Typed finite channels, complete complements, and modular-band witnesses are not identified with one another. Enter Calculus Companion.

CheungEn02BC

N. Cheung. En02-B, version 1, and En02-C, version 1. Undated supplied manuscript excerpts. Complete programme channels, arbitrary references, live-register ledgers, and sequential access. A successful branch alone is not deterministic return. Enter Calculus Companion.

CheungI

N. Cheung. Landmark I, version 2. Undated supplied manuscript .tex. Especially :main. Born strategy and destructive projective residuals inside the stated finite structural class. No field instrument or gravitational identification is imported. Enter Calculus Companion.

CheungEm03A

N. Cheung. Em03-A, version 1. Undated supplied manuscript 03-A-v1.tex. Especially :release. Fixed normalized Schwarzschild background, scalar radiation, transmission, and the retained mass-loss and backreaction boundaries. Enter Calculus Companion.

CheungEm02E

N. Cheung. Em02-E, version 1. Undated supplied manuscript 02-E-v1.tex. Especially :lapse and :release. Relational lapse on a declared Einstein–scalar background; not a conformal Hamiltonian identification. Enter Calculus Companion.

CheungEm03FG

N. Cheung. Em03-F, version 1, and Em03-G, version 1. Undated supplied manuscript excerpts. Effective exterior-source channels, bounded-observable comparisons, radiative excess energy, and switching-work ledgers. No gravitational mass-loss or complete evaporation law is imported. Enter Calculus Companion.

CheungXIVH

N. Cheung. Landmark XIV-H: Internal kernel relations on the operator route, version 1. Supplied -H.tex excerpts. Historical H2 internal-amplitude stop. Enter Calculus Companion.

CheungXIVI

N. Cheung. Landmark XIV-I, version 1. Supplied -I.tex excerpts. Internal amplitude constructed at I2; joint characteristic map unresolved at I3. Especially :I2 and :I3. Enter Calculus Companion.

CheungXIVJ

N. Cheung. Landmark XIV-J, version 1. Supplied -J.tex excerpts. Especially :descent, :reference, :J2, and :noadmission. Partial supported-sector reference is not the full joint map. Enter Calculus Companion.

CheungXVB

N. Cheung. XV-B, version 2. Supplied -B.tex excerpts. Relative lifting, finite normal-jet null tests, and extension interfaces; inherited full graph unresolved at B1. Its existence is distinct from opening the downstream admission exit. Enter Calculus Companion.

CheungXVIN

N. Cheung. XVI-N, version r12. Supplied -N.tex excerpts. Conditional massless prepared-insertion obstruction and the separately undischarged spatially compact Route B. Enter Calculus Companion.

CheungXVIP

N. Cheung. XVI-P, version p23. Supplied -P.tex excerpt. Technical release and build-report provenance are documentary; .1 remains _CLOSED. No report execution is independently reproduced here. Enter Calculus Companion.