I need *your* definition and explanation of the hierarchy phenomenon, then. It seems to just be one of those naturally-ordered things that an intelligence would certainly be able to believe exists/perceive.

With my recent learning/discovery of the concept of "cladism", I see that more than one "hierarchy" system might exist in minds somewhere. A perceived hierarchy may not be the "real" one. That's what "wars" are able to sort out?

Many definitions occur on Google, and it's not easy to prioritise them, is it?

Hierarchy

"
A hierarchy (in Greek: often used in Geographic studies, it is derived from hieros, sacred, and arkho, rule) is a system of ranking and organizing things or people, where each element of the system (except for the top element) is subordinate to a ...

en.wikipedia.org/wiki/Hierarchy

In mathematics, a hierarchy is a preorder, i.e. an ordered set. The term is used to stress a natural hierarchical relation among the elements. In particular, it is the preferred terminology for posets whose elements are classes of objects of increasing complexity. ...

en.wikipedia.org/wiki/Hierarchy (mathematics)"