SubTree Unified Merkle Path (STUMP) Format
A proof spanning a whole block is larger than needed when the transactions of interest sit close together. This encodes the path within a subtree instead, which is smaller for that common case.
Siggi Oskarsson
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119
228 Unlinkable Payments under the Identity Paradigm
Sending someone a bit of digital cash normally means telling them who you are, because the payment format includes your long-term identity key. That's fine for a friend or a business you trust, but it means every coffee tip or casual peer payment lets the recipient permanently tag it to your identity and link it to every other payment you've ever made them. There was no easy way to pay someone spendable coins for a one-off transaction while keeping your long-term identity out of the record.
136 Block-Anchored Overlay Synchronization via Block-Aligned Sparse Merkle Trees (BASM)
An index cannot easily prove it has seen everything relevant in a block rather than most of it. This gives a per-block summary that makes completeness checkable rather than assumed.