The symmetry-minimising-eigenfunction conjecture for the area-constrained rectangle

Let $\Omega_{a,b}$ be a rectangle, and consider the variational problem defining the lowest positive Dirac eigenvalue under the area constraint, with right-hand side denoted by the source's equation (area). Let $\psi$ be a minimiser, and let (symmetry) denote the symmetry condition defined earlier in the paper. Symmetry conjecture. There exists a minimiser $\psi$ of the right-hand side of (area) which satisfies (symmetry). The conjecture concerns the structure of minimisers used in the spectral optimisation argument; the supplied context does not state whether it has been resolved.