Monotonic binding conjecture for bosonic electron numbers

Let $Z>0$ be a nuclear charge, let $N_{\mathrm{max}}(Z)$ be the maximum number of bosonic electrons that a nucleus of charge $Z$ can bind, and write $\Psi^{(Z,N)}_{\mathrm{Bose}}$ for a proper $N$-body ground-state wave function of the Coulomb Hamiltonian.

Monotonic binding conjecture. A proper $N$-body ground-state wave function $\Psi^{(Z,N)}_{\mathrm{Bose}}$ exists for every integer $N$ satisfying

$$1\leq N\leq N_{\mathrm{max}}(Z).$$

Equivalently, if the nucleus binds $N$ electrons, it also binds every smaller positive number of electrons. This is stated as an open problem in the cited literature and is known from Zhislin's theorem only in the range $N<Z+2$.