Is there a hash or string that represents a stockfish evaluation of a position to a certain depth? Is there a hash or string that represents a stockfish evaluation of a position to a certain depth?  For example for a given FEN, can you analyze to a depth of say 10 and get a hash to represent that position AND depth of analysis?  That would allow you to come back later and, if wanted, continue analysis to a greater depth at a later point.
I doubt that can be possible.

An analysis to a certain depth contains the generated position tree and the calculated values, which is quickly becoming a very large amount of data.
For depth 10, you probably need several megabytes of memory to represent the analysis result in a way that it could be used to continue searching deeper. There is simply no way to compress this into a small hash or anything else.