Divergence of nodal domains along infinite eigenvalue sequences in the square

Consider the Neumann problem in the square and a sequence of eigenfunctions associated with an infinite sequence of eigenvalues. Nodal-domain divergence conjecture. The number of nodal domains of the eigenfunctions tends to $+\infty$ along the sequence.

The claim would give a general asymptotic lower bound on nodal complexity for arbitrary eigenfunction sequences associated with infinitely many eigenvalues, beyond the specific families analyzed in the paper. The source offers it as a conjecture; no resolution is given here.