The collapsing conjecture for facets of hierarchical model polytopes

Let $p\leq q\leq r$ be positive integers, and let $P_\Delta^{p,q,r}$ denote the polytope associated with the hierarchical model in the paper. A facet is obtained by collapsing if it arises from a facet of a smaller table through the paper's collapsing operation.

Collapsing conjecture. Suppose that

$$p \leq q \leq r.$$

Then all facets of $P_\Delta^{p,q,r}$ are obtained by collapsing from facets of $P_\Delta^{p,q,q}$.

The conjecture is motivated by computational results summarized in the paper's table, although the authors also exhibit a non-collapsible facet of $P_\Delta^{4,4,4}$, showing that not every facet arises by collapsing to a binary table. The conjecture remains open in the supplied source.