Are all F_{σδ} ideals Farah ideals?

Determine whether every F_{σδ} ideal on the natural numbers ω (viewed as a subset of the Cantor space {0,1}^ω with the product topology) is a Farah ideal; equivalently, decide whether the class of F_{σδ} ideals coincides with the class of Farah ideals defined by the existence of a sequence of hereditary compact subsets (K_n)⊆P(ω) such that S∈I iff ∀n∃k S\[0,k]∈K_n.

Background

The paper recalls that an ideal I on ω is Farah if there exists a sequence (K_n) of hereditary compact subsets of P(ω) such that S∈I iff for all n there exists k with S[0,k]∈K_n. It is known that all analytic P-ideals are Farah and every Farah ideal is F_{σδ}.

The authors explicitly note that the converse direction is not settled: whether every F_{σδ} ideal is Farah. This is a well-known open problem in the structure theory of ideals on ω, relevant to understanding how descriptive-set-theoretic complexity aligns with structural representations of ideals.