src/ts/examples/tutorials/ex28.c (though the comment is wrong, the example did run for me).
TSView() to binary stores the ENTIRE TS state needed to run (yes including the function pointers provided by the user) and TSLoad() loads it back up ready to run again :-)
Barry
Note 1) it is still only proof of concept, I don't do anything with user contexts etc etc.
Note 2) it, course, doesn't save state inside SNES, KSP, PC, or Mat nor should it ever. Those will all get rebuilt when the next TSSolve() is called.