Tripartite form universality for superbalanced holographic entropy inequalities

Establish that every superbalanced holographic entropy inequality can be written in tripartite form, namely as a positive sum of negative tripartite and conditional tripartite information quantities.

Background

Tripartite form (TF) is a compact representation of information quantities that has proven useful in identifying and organizing holographic entropy inequalities. Prior work has successfully used TF to generate many new inequalities for N = 6.

In this paper, the authors revisit TF and emphasize a conjecture from earlier work that all superbalanced HEIs admit such a representation. They note strong supporting evidence is forthcoming but do not provide a proof here, leaving the universality of TF for superbalanced HEIs open.

References

In , it was conjectured explicitly that all superbalanced HEIs can in fact be expressed in tripartite form, with strong supporting evidence to appear in .

— Combinatorial properties of holographic entropy inequalities  (2601.09987 - Grimaldi et al., 15 Jan 2026) in Discussion, subsection “Tripartite form”