4 problems

Let $G$ be a symmetry group and let $\cE=\operatorname{Rep}(G)$. A modular extension $\cM$ of $\cE$ is a UMTC containing $\cE$ fully faithfully and satisfying the defining centrali…

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

Threshold conjecture. A proper $N$-body ground-state wave function $\Psi^{(Z,N)}_{\mathrm{Bose}}$ exists whenever $Z>Z_*(N)$.