reminds me a lot of Ford Circle / Farey Diagram / Stern Brocot tree

Basically a tree of fractions where you take two rational points on a number line, a/b and c/d, then the next point in the tree is (a+b) / (c+d). Turns out that every single point you create this way has a unique position and never duplicate each other, and it forms a tree like structure.

https://en.wikipedia.org/wiki/Ford_circle

not sure if this would be useful, but basically it could be a fractional index that has a built in tree structure, since it basically means any fraction is a leaf on a Stern-Brocot tree.