Whitham tau-function conjecture for toric Calabi–Yau brane partition functions

Let the space be a toric Calabi–Yau 3-manifold or 3-orbifold with Aganagic–Vafa outer D-branes, let its partition function be the corresponding brane partition function, and let its local mirror curve be the associated mirror spectral curve. Whitham tau-function conjecture. The partition function of a toric Calabi-Yau 3-manifold or 3-orbifold with Aganagic-Vafa outer D-branes is a tau-function of the universal Whitham hierarchy associated with its local mirror curve. This would connect topological-string partition functions and mirror curves to universal Whitham hierarchies; the source derives the proposal from the BKMP remodeling conjecture but gives no general resolution.