Applicability of Quillen’s connectivity theorem to derived ideal powers

Determine whether Quillen’s connectivity theorem applies to the derived powers of the derived ideal constructed from the fiber of an augmented simplicial algebra E to its discrete quotient π_0E, as defined by Hekking, so that these powers can be used to obtain the required filtration-vanishing and an alternative proof of the nilpotence result.

Background

The paper gives a primary proof of its boundedness theorem using ordinary degreewise powers of a simplicial ideal. It then sketches an alternative approach using derived ideals and their derived powers, citing Hekking’s construction.

That alternative approach requires Quillen’s connectivity theorem to hold for the derived ideal powers. The author explicitly states that it is not immediately clear whether this hypothesis is valid, leaving the applicability of the theorem as an unresolved technical question.