The linked paper "Hierarchical Complexity: A Formal Theory" is very interesting and quite short. If you ignore the references it is only 12 pages long. It starts from the very simple case of explaining how to formalize the idea that (1+2)*3 is more complicated than (1+2)+3. The paper develops its mathematical theory rather quickly. I was surprised the authors managed to create a psychological theory that was concrete enough to apply in practice. The authors describe the results when they used their theory to analyze two different studies.

Of course many methodologcal issues remain. However I was very impressed. If you are comfortable reading abstract math I recomend the paper.

It's short, but here's the money quote/tl;dr

MHC takes developmental psychology and reverses its normal etiology. Rather than positing stages that give rise to behaviors, MHC considers individual behaviors and then gives a system of classifying their complexity. The classification is hierarchical, so behaviors in higher complexity classes are necessarily constructed from combinations of less complex behaviors, and the classifications match the shape of developmental psychology as discovered by Piaget and Erikson, but the hierarchy is derived independently via a mathematical abstraction.