Reduction problem for multivariable dilogarithm identities

Determine whether every functional identity of the classical dilogarithm with rational functions of more than one variable as arguments is reducible to the trivial identity by successive application of the pentagon identity. Characterize the precise scope of such reducibility beyond the one‑variable case proven by Wojtkowiak.

Background

Wojtkowiak proved that any functional identity of the dilogarithm with one variable is reducible to the trivial identity by successive use of the pentagon identity. Extending this to multivariable rational arguments has been an outstanding question in the literature.

The monograph answers this question in the affirmative for the specific class of identities arising from periods in cluster patterns and loops in cluster scattering diagrams by showing infinite reducibility. However, the general reduction problem for arbitrary multivariable identities remains unsettled and lacks a systematic paper.