I am glad that you liked our paper :) (the distributed bloom filter paper requires serious editing though).
Current sparse Merkle multiproofs require an index and a hash inside the proof. So in our hypothetical example that would be 30-40 indices and 30-40 hashes. Only then can a recipient of the proof perform the operations in the right order to recreate the original merkle root. With our proposal on the other hand, for this hypothetical example, we would need 30-40 hashes, and only 5 indices for a recipient to be able to recreate the correct Merkle root.
Current sparse Merkle multiproofs require an index and a hash inside the proof. So in our hypothetical example that would be 30-40 indices and 30-40 hashes. Only then can a recipient of the proof perform the operations in the right order to recreate the original merkle root. With our proposal on the other hand, for this hypothetical example, we would need 30-40 hashes, and only 5 indices for a recipient to be able to recreate the correct Merkle root.
Here's by the way a great repo that can create sparse Merkle multiproofs https://github.com/wealdtech/go-merkletree