Burn proof**
Discussion
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