Rational K(pi,1) complements and ordinary K(pi,1) complements

Determine whether the complement of every complex hyperplane arrangement that is a rational K(pi,1) space is necessarily a K(pi,1) space.

Background

The paper distinguishes between the ordinary K(pi,1) property of an arrangement complement and the stronger rational K(pi,1) property, defined through the Bousfield–Kan rational completion. Examples are known of arrangement complements that are K(pi,1) but not rational K(pi,1), while the converse implication remains unresolved.

This question asks whether rational asphericity of an arrangement complement forces ordinary asphericity, clarifying the relationship between the topological condition and the rational homotopy-theoretic condition equivalent to Koszulness of the Orlik–Solomon algebra.