g_B = 2c/(3 pi^2) for the compression direction of every diffeomorphism-covariant net (corollary of Theorem B)

Status: proved — a complete structured proof. Stated under hypotheses H1, H2, H3, quoted below.

Area: Theorem B: universality for diffeomorphism-covariant nets · Card type: constant · Knowledge-base id: const-gb-general-nets

Statement

For every diffeomorphism-covariant net on S^1 of central charge c satisfying the standing hypotheses of Theorem B (separable, CDIT axioms, Bisognano-Wichmann, Haag duality, Reeh-Schlieder), the Bures form of the zero-collar compression direction is g_B = 4 dist(T(g_tot) Omega, closure(A(I)'_sa Omega))^2 = 2c/(3 pi^2), so -log F = (s^2/8) g_B + o(s^2). This is the value statement of Theorem B (card thm-b-universality), whose hypotheses (H1)-(H3) hold for every such net (card implementer-hypotheses); the constant is fixed by c-linearity and the free-fermion value at c = 1 (card const-gb).

Hypotheses

The statement is made under named hypotheses. The sentences are quoted from the statement above; read the status badge only together with them.

Hypothesis labels used: H1, H2, H3.

This is the value statement of Theorem B (card thm-b-universality), whose hypotheses (H1)-(H3) hold for every such net (card implementer-hypotheses); the constant is fixed by c-linearity and the free-fermion value at c = 1 (card const-gb).

How to verify

rigor/universality_theorem_B.tex thm:B (value step thm:value); (H1)-(H3): rigor/implementation_C11.tex thm:main.

Evidence

• rigor/universality_theorem_B.tex — document, at thm:B
• rigor/implementation_C11.tex — document, at thm:main

Related claims

• Free-fermion one-particle metrics of the compression direction: g_B = 2r/(3 pi^2), g_KM = r/6 (c = r) — proved
• g_KM = c/6 for the compression direction of a general conformal net (conjecture; only the analytically continued value exists) — conjectural

Review

Review record: passed 2026-09-23 by REF-DEP-CFT-B3.

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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