Longo-Xu Remark 4.3: adjacent-interval CMI (c/6) log(1+z) for every rational conformal net (conjecture)

Status: conjectural — believed, with partial evidence; not proved.

Area: Foundations: CMI as a Markov defect (Notes 1-3) · Card type: conjecture · Knowledge-base id: longo-xu-cmi-general-c

Statement

Conjecture (Longo-Xu, Remark 4.3): for every rational conformal net of central charge c, the vacuum conditional mutual information of adjacent intervals A = (-a,0), B = (0,b), C = (b,b+l) is I(A:C|B) = (c/6) log[(a+b)(b+l)/(b(a+b+l))] = (c/6) log(1+z). Proved only for the free fermion net A_r (c = r), its finite-index subnets and the finite-index extensions of Longo-Xu (card longo-xu-cmi); the project states that the general claim is not proved and does not use it (adjacent_interval_cmi_longo_xu.tex scope box l. 327-330; paper1 rem:LX-scope).

How to verify

paper1/sec_setting.tex rem:LX-scope (l. 101-107); adjacent_interval_cmi_longo_xu.tex scope box (l. 327-330); refs/LongoXu_1712.07283.pdf Remark 4.3.

Evidence

• paper1/sec_setting.tex — document, at rem:LX-scope
• refs/LongoXu_1712.07283.pdf — source; held privately, not redistributed

Related claims

• Longo-Xu CMI of adjacent intervals for the free fermion net A_r, its finite-index subnets and extensions — proved

Review

Review record: passed 2026-09-23 by REF-DEP-CFT-B4.

The referee's report and the card's event log stay in the private knowledge base; only the verdict, the date and the referee are published here.

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