I am familiar with PoL. It was a key concept for eHash.
Does merkleization make it so every burn Perot isn't nrccessary for auditing the entire set? Just using a subset of the merkle tree to validate inclusion should give assurances?
Its pretty insane. Not limited to but primarily motivated by building an efficient proof of liabilities system for mints. We can also use trees to prove correct state transitions for the mint during operation.
PoL: https://gist.github.com/callebtc/ed5228d1d8cbaade0104db5d1cf63939
Discussion
Burn proof**
The goal is that clients won't have to download the entire db to run the PoL but only need inclusion proofs for their coins.
Can't sparse Merkle trees be used for this?
Yes, sparse merkle sum trees to be precise
Will the proofs include the merkle path somehow?
Something similar was discussed here. The proof data the client is holding should have some assurance as to where in the merkle tree this would be included.
https://delvingbitcoin.org/t/pplns-with-job-declaration/1099/19