Fun read.

One upside of the deterministic schemes is they include provenance/lineage. Can literally "trace up" the path the history back to the original ID giver.

Kinda has me curious about how much information is required to represent any arbitrary provenance tree/graph on a network of N-nodes/objects (entirely via the self-described ID)?

(thinking in the comment: I guess if worst case linear chain, and you assume that the information of the full provenance should be accessible by the id, that scales as O(N x id_size), so its quite bad. But, assuming "best case" (that any node is expected to be log(N) steps from root, depth of log(N)) feels like global_id_size = log(N) x local_id_size is roughly the optimal limit? so effectively the size of the global_id grows as log(N)^2? Would that mean: from the 399 bit number, with lineage, would be a lower limit for a global_id_size be like (400 bit)^2 ~= 20 kB (because of carrying the ordered-local-id provenance information, and not relative to local shared knowledge)

Two ways to frame it:

Provenance is a DAG, so you get a partial order for free by topological sort. That can be extended to a compatible total order. Then provenance for a node is just its ordering. This kind of mapping from objects to the first N consecutive naturals is also a minimal perfect hash function, which have n log n overhead. We can't navigate the tree to track ancestry, but equality implies identical ancestry.

Alternatively, we could track the whole history in somewhat more bits with a succinct encoding, 2N if it's a binary tree.

In practice, deterministic IDs usually accept a 2^-N collision risk to get log n.

The ATProto underlying BlueSky social network is similar. It uses a content-addressed DAG.

Each “post” has a CID, which is a cryptographic hash of the data. To “prove” ownership of the post, there’s a witness hash that is sent that can be proved all the way up the tree to the repo root hash, which is signed with the root key.

Neat way of having data say “here’s the data, and if you care to verify it, here’s an MST”.