Uniqueness conjecture for TP-bases of positroid cells

Let a positroid cell in the nonnegative Grassmannian be given. A TP-basis is a minimal set of nonzero Plücker variables from which every other nonzero Plücker variable in the cell can be expressed as a subtraction-free rational function. Two TP-bases are mutation equivalent if one can be obtained from the other by Plücker mutations induced by 3-term Plücker relations.

TP-basis mutation-equivalence conjecture. For any positroid cell, all TP-bases are mutation equivalent.

The source presents this as a further conjecture after proving the canonical-basis statement for weakly-connected cells; no resolution beyond those results is given.