The maximality conjecture for semi-crabs

Let $gh$ and $g$ be integers for which the preceding semi-crab construction defines the plane integral point set $\mathcal{P}=\operatorname{decompose}(gh,g)$. Semi-crab maximality conjecture. For each such pair of integers $gh$ and $g$, the point set $\mathcal{P}=\operatorname{decompose}(gh,g)$ is maximal whenever $|\mathcal{P}|\geq 7$. The construction gives integral point sets isomorphic to semi-crabs, while the source does not provide a proof that all of these sets are maximal.