Oooh, this is very interesting and timely. Thank you, reading it now.

Out of curiosity, what's the motivation for Bitcoin-Core? Is it comparing mempool txs?

Transaction relay.

Ideally nodes have lots of connections so that attackers can't so easy block transaction and block propagation and censor information. But lots of connections means lots of network bandwidth wasted relaying redundant information nodes already know about.

From day one bitcoin relayed transactions by offering just their hashes and only requesting what wasn't known. But even sending hashes ends up being a lot of data in total, and the bandwidth scales with peers*transactions. Using set reconciliation changes that to more like peers+transactions.

When using setrecon for authentication its important that the scheme is as close to information theoretically optimal as possible-- which makes approaches like pinsketch important.

For the transaction case faster but less communications efficient methods might be better except that latency is also a consideration for Bitcoin and minimizing latency means running reconciliation often. This stresses the inefficiencies of alternative tools as well as covers up for the quadratic decode cost of pinsketch.

I'm not aware of anyone using our minisketch library for authentication-ish uses but I'd be interested in seeing it.