I don't have proofs. I haven't gone into any level of rigor with any of this.

Here is a recent example: https://files.spritely.institute/papers/petnames.html

The idea of a naming system can be (1) decentralized, (2) globally unique, (3) human meaningful. It talks about the onion DID names which achieves decentralized and globally-unique, and proposes a petname system that maps local names to achieve all three when combined with the onion names.

It sounds similar to me to the mathematical concept of an atlas. Atlases originally came about trying to map a non-Euclidian topology to a local, Euclidian topology. No Euclidian topology can fully describe the non-Euclidian topology, but a set of those can, and together would form an atlas.

Someone with more math chops than I can prove (or disprove) that the petname system forms an atlas over the set of globally-unique names (identifiers). The biggest anti-pattern I can see coming out of it is when people using this attempt to make the local petnames globally unique instead of working with it as a local mapping that can never fully describe the global space of unique names.