SHA3-512 troubleshooting - is there a worked example for hashing the "zero-length string"?
Does anyone know of some document or tutorial that gives a worked example of each step in using SHA3-512 to generate a digest of the message "" (or some other short message), giving detailed step-by-step values for all variables in the algorithm?


What you are looking for is called a "test vector" (with intermediate values) and NIST offers them for all their standardised primitives.

The one for SHA3-512 for 0-bit input is this PDF. Because it's 38 pages full of data, I won't post it here but it has the state after intermediate function application for all rounds for an empty message.