Uniqueness and invariance conjecture for energy-minimizing biharmonic almost complex structures

Let $M$ be a compact, simply-connected, nonspin four-dimensional almost complex manifold. An energy-minimizing biharmonic almost complex structure on $M$ determines a homotopy class. Uniqueness and invariance conjecture. The homotopy class of energy-minimizing biharmonic almost complex structures is a differential invariant of the underlying almost complex manifold and is unique up to sign. The statement is motivated in the source as a consequence one might expect from the proposed transversality and generic-metric discussion; no resolution is given.