What is the most dense way (fewest characters) that I can store a complete SHA-256 hash?
Calling .digest() on a hashlib.sha256 object will return a 32-byte string -- the shortest possible way (with 8-bit bytes as the relevant unit) to store 256 bits of data which is effectively random for compressibility purposes.
Since 8 * 32 == 256, this provably has no wastage -- every bit is used.
In Python, represent a SHA-256 hash using the fewest characters possible