It would be convenient if there was a data structure that could store the set of unspent transactions as a sparse tree, and easily add/remove transactions witho

It would be convenient if there was a data structure that could store the set of unspent transactions as a sparse tree, and easily add/remove transactions without knowing the full tree. Perhaps as a merkle tree. There might be something more efficient. I think that if this has was included in each block, then a user of bitcoin could download the block headers starting from their last known-good block. Then download the structure containing the transaction set from a recent block (6-10 blocks back, perhaps) to prevent having invalid blocks with good proof of work at the end, as those wouldn't be built upon by other miners. Then download the transactions from the blocks after the one you have the transaction set from and only verify those blocks.