Complex sentence: This fact is a problem for the DP-hypothesis because it means that the fixed words of the idiom are interrupted in the vertical dimension; the hierarchical arrangement of the fixed is interrupted by the possessor, which is not part of the idiom.
Split into simpler sentences: This fact is a problem for the DP-hypothesis because it means that the fixed words of the idiom are interrupted in the vertical dimension. That is, the hierarchical arrangement of the fixed words is interrupted by the possessor, which is not part of the idiom.