I've been thinking about proofs for Hivemind for a while, as I realized earlier on that there aren't any.
Short of a periodic hash fucntion tied to a data set that changes every block, but doesn't take too much to compute, I can't think of anything right now.
I also thought of hashing the various live objects that make up the Hivemind codebase, and have that exposed via API so people can poll randomly, or have the nodes broadcast it on chain, timestamped. I'm still reading on the inspect.getsource() function in Python, which gives results on actual live code. Still studying it so I can't say that it can work. Obviously taking a hash of code that's not live can be faked.
It's not feasible to hash the whole DB at intervals because read speeds and calc times are long.
Thank you for thinking about the issue, it seems like a lot of people don't even care. I'm not familiar with Hivemind, so I can't comment on the technical feasibility, but zero-knowledge proofs would be the ideal solution. See zk Rollups on ethereum's layer 2