Semisol on Nostr: you can implement one very easily create a list of hashes, where not all indexes ...

you can implement one very easily

create a list of hashes, where not all indexes (depths) have to be full
depth 0 = an entry
depth 1 = two depth 0 hashes joined together
depth 2 = two depth 1 hashes joined together
so on

to add a new entry you try to put it in depth 0, and if you fail to put it then you combine this item with the existing depth 0 one and try to put the result in depth 1, and if that fails you repeat

to prove that a hash exists you do what you do with merkle trees

to prove that no entries have been tampered with since your last request, request that the log proves that all hashes from the previous state exist in the current state

all operations are O(log n) maximum