4 problems

Upper-bound conjecture. There should exist absolute constants $a$ and $b$, independent of $B$, such that

Let $Z$ be the atomic number of an atom. For a molecule, let $K$ be the number of nuclei and let $Z$ be its total nuclear charge. Maximum excess-charge conjecture. An atom of atomi…

Monotonicity conjecture. The map $N\mapsto\Lambda_*(N)$ is monotonically increasing.

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