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In a previous paper by one of the authors, a Lagrangian 3-form structure wasestablished for a generalised Darboux system, originally describing orthogonalcurvilinear coordinate systems, which encodes the Kadomtsev-Petviashvili (KP)hierarchy. Here a hierarchy of Lagrangian multiforms is established for thesame system, viewed as a hierarchy of Chern-Simons actions in aninfinite-dimensional space of Miwa variables, constituting the variational formof a universal 3D integrable system embedded in this infinite-dimensionalspace.

The Darboux-KP system as an integrable Chern-Simons multiform theory in infinite dimensional space