Refuse, Don't Rank: Verifiability Is a Property of the Record

Machine generators now propose scientific hypotheses faster than laboratories can test them, so the field has framed verification as an allocation problem: rank the proposals, spend the budget where it buys most. Ranking presupposes that effort converts into evidence at some positive rate, so that a hypothesis unresolved today is one awaiting a larger budget. For hypotheses about systems observed through a single fixed record, that is false. It is false in a way you can detect before fitting anything, and such hypotheses should be refused outright rather than ranked lower. The obstacle is not a weak verifier or a small budget but the geometry of the record. The Cramér-Rao floor on a threshold date is $\sigma^2/(\mu_1^2 T \Lambda_m)$, where $\Lambda_m$ is the Christoffel function of the record's own sampling measure: a classical object from optimal design, computable from sample moments in one matrix solve, before any drift model is fitted. On the subpolar-gyre sea-surface temperature record used to date a possible AMOC collapse, it permits no 90% interval narrower than 82 years, against 93 for honest inference. One widely cited published interval is already narrower than the floor allows. A second instance shows the same failure inside a surrogate: the linearisation underlying all early-warning practice promises unlimited resolution at threshold, delivers none, and confines its entire error to the variance channel, the one statistic practitioners compute. The floor belongs to a particular record, not to a phenomenon or an instrument class. Ours is a favourable draw, sitting at the 16th percentile of a 224-year median across realisations of the same fitted system. So "is this hypothesis verifiable?" has no answer until a record is named, and any other record can be checked the same way.