Boundedness of relative dimension for interval orders

Determine whether the relative dimension is bounded over the family of all interval orders.

Background

The paper introduces relative dimension as an average-frequency refinement of local dimension. It proves that the canonical interval orders have relative dimension less than 4, even though interval orders can have unbounded local dimension. The authors note that relative dimension is not monotone under taking subposets, so the boundedness result for canonical interval orders does not extend automatically to all interval orders. They therefore leave open whether a uniform bound exists for the entire class.