The Universe is a hierarchy of orders; quarks and gluons, atoms, molecules, cells, multi-cellular and on. So hyperoperators form a natural hierarchy to model multilevel systems. Feynman's Path Integral with the integral removed is just tetration. So I believe the higher operators through self organization/renormalization are directly associated with specific levels of reality, but except for QFT I have no suspicion as to which hyperoperators might be associated with levels of physics. Here is how it might work. Hexation might model chemistry while heptation could model simple biological systems. Thanks for asking. This is fun stuff to work on.