Generalized hypertree width is W[1]-hard parameterized by incidence treewidth

Let $H$ be a hypergraph, and let the incidence treewidth of $H$ be the treewidth of its incidence graph. Generalized-hypertree-width conjecture. Generalized Hypertree Width is W[1]-hard with respect to the parameter incidence treewidth. The paper motivates this conjecture by the number of equivalence classes arising in its Myhill–Nerode construction; it does not establish the conjectured parameterized-hardness result.