In the default configuration, the checksum database currently has 657 level-0 tiles. The raw log data associated with each level-0 tile seems to be about 50KB. You could store the entire current checksum database log in about 30 MiB. You could store the level-0 hash tiles in 5 MiB.
This makes sense right? Cargo, the rust package manager, does replicate the entire package index using git and it is ~250 MiB (~150MiB in .git/) (The cargo index stores much more metadata in a more verbose JSON format). It seems like a very reasonable bet considering prior art.
Care to maybe check real quick before making bets?