External sources, and whether you can obtain them

The split between open access and needs library access is a guess, not a measurement: refs/restore.sh reports both as MANUAL, so this page classifies them by keywords in the Source column of refs/REFERENCES.md. Expect misfilings; at the time of writing DaleckiiKrein and Petz96 are two of them. Only the fetchable group is verified, by comparison with a live refs/restore.sh --list.

This page covers the 36 table rows of refs/REFERENCES.md. It is not a list of every external result the project relies on: further sources are cited in that file as bullet entries rather than table rows (4 of them below the table), and the source documents themselves are third-party material that this repository does not redistribute. For the full picture read refs/REFERENCES.md, which also records the exact result used from each source.

Three ways to obtain a row:

refs/restore.sh with no argument lists what it would download and reports everything else as MANUAL; it does not distinguish open-access MANUAL rows from paywalled ones, which is the distinction this page adds.

Fetchable by refs/restore.sh (20)

Open access, fetch by hand (9)

Needs library access (7)

What is taken from each source

Quoted from the Results used column of refs/REFERENCES.md; an empty entry means the file records none.

• LongoXu — Thm 3.18 (free-fermion MI), Thm 4.1 (generalized MI, positivity, finite-dim limit), Thm 4.2 (G-identity, singular limit), Rmk 4.3; mutual-information formula for two intervals; Hardy-projection realization of the vacuum
• CasiniHuerta09 — modular Hamiltonian / eigenfunctions of the interval Hardy compression; spectrum 1/(1+e^kappa); thermal form
• BGL93 — geometric modular group of interval algebras (Bisognano-Wichmann for conformal nets), modular conjugation geometric
• Wiesbrock93 — hsm inclusion <-> Borchers translations; interval algebras with a common endpoint are hsm
• Borchers92 — Borchers' commutation relations Delta^{it} U(s) Delta^{-it} = U(e^{-2 pi t} s), J U(s) J = U(-s)
• FHSW20 — rotated Petz maps alpha_{sigma,t}; Sec 4.2 hsm inclusions (Petz map = Borchers translation, rotated = translation by 1+e^{-+2 pi t}); strengthened DPI with p(t)=pi/(cosh 2 pi t +1) (integrated form); standard-form Petz formula J_N V^* J_M x J_M V J_N
• FH22 — 2-positive channels version
• JRSWW — universal recovery with the p(t) average
• SFR — no result recorded in the table
• FR — no result recorded in the table
• HJPW — direct-sum decomposition of exact Markov states
• Petz86 — sufficiency <-> equality of relative entropies <-> Connes cocycle in N
• Petz88 — no result recorded in the table
• PowersStormer70 — quasi-equivalence criterion for gauge-invariant quasi-free states (S^{1/2}-T^{1/2} and (1-S)^{1/2}-(1-T)^{1/2} Hilbert-Schmidt); Powers-Stormer inequality
• Araki71 — quasi-equivalence of quasi-free states (self-dual formalism)
• Araki76 — Araki relative entropy definition
• Araki77 — monotone (martingale) convergence of relative entropy along increasing subalgebras (exact hypotheses!)
• OhyaPetz — Cor 5.12 (relative entropy convergence)
• Alberti83 — F(phi,psi)^2 = inf_{x>0} phi(x) psi(x^{-1})
• Uhlmann76 — Uhlmann fidelity, standard-form formula <Omega, Delta_{phi,omega}^{1/2} Omega>
• ArakiRaggio82 — no result recorded in the table
• Jencova02 — monotone metrics on vN algebra state spaces
• Petz96 — no result recorded in the table
• DaleckiiKrein — second-order expansion of Tr X log X
• VWZ — eqs (1.3),(1.8),(2.1),(2.13),(2.14),(3.15),(3.24); lambda statements; Fig 5 exponents; App A.5
• SwingleWang19 — Gaussian Petz map formulas
• CDIW21 — extension to D^s(S^1), which s?
• TakhtajanTeo06 — WP class, Hilbert-Schmidt condition
• NagSullivan95 — Segal-Shale condition <-> H^{1/2}
• Shen18 — characterization log phi' in H^{1/2}
• FewsterHollands05 — energy bounds / smearing class for T(f)
• KirillovYuriev87 — no result recorded in the table
• CalabreseCardy04 — thermal single-interval entropy
• CasiniHuerta04 — entropic c-function
• CTT17 — null Markov property
• Camassa12 — no result recorded in the table

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