The maximality conjecture for decompose crabs

Let $h$ be an integer, and let $\mathcal{P}=\operatorname{decompose}(h)$ be the plane integral point set constructed as a crab of the order specified in the source. Decompose-crab maximality conjecture. For each integer $h$, the point set $\mathcal{P}=\operatorname{decompose}(h)$ is maximal whenever $|\mathcal{P}|\geq 7$. The construction produces integral point sets, but the preceding discussion says maximality is not guaranteed and is only considered very likely; the conjecture asserts maximality for all cases with at least seven points.