Possible PSPACE-completeness of the hunting-number threshold problem

Determine whether deciding, for an input graph G and integer k, whether h(G) <= k is PSPACE-complete, or otherwise establish its precise complexity classification.

Background

The threshold problem deciding whether h(G) <= k can be represented as a special case of the integer matrix mortality problem, which places it in PSPACE. The paper does not establish PSPACE-hardness, nor does it provide evidence that the problem belongs to NP; consequently, its exact complexity remains unresolved.