Copiousness conjecture for irreducible hypertrees

Let $T$ be an irreducible hypertree, and identify it with its graph $G$, whose edges are the pairs occurring in the triples of $T$. Irreducible hypertree copiousness conjecture. Every irreducible hypertree is copious. The paper proves this for irreducible hypertrees with $n\leq 10$ vertices and proves separately that every bipyramid is topologically copious, hence copious; the general assertion remains open.