4 problems

Let $S$ be a positive semidomain. It is a bi-LFS if both $(S,+)$ and $S^\bullet$ are length-factorial monoids (LFMs), and a bi-UFS if both $(S,+)$ and $S^\bullet$ are unique-factor…

Molecularity conjecture for $\mathcal{C}_3$. The class $\mathcal{C}_3$ is molecular.

Realizability conjecture. For every $n \in \mathbb{N}_{\ge 2}$ there exists a numerical monoid $N$ such that

Primary full-system conjecture. For every dimension $d\geq 3$, there exists a primary monoid in $\mathcal{C}_d$ having full system of sets of lengths.