Falsification Thresholds and Warning Thresholds Why action against irreversible risk need not wait for falsification

Abstract Falsifiability is the discipline of science: judging a model wrong requires pre-registered tests, adequate samples and long enough observation. Faced with irreversible risk, however, this discipline is often carried into decisions about action, producing an argument that sounds rigorous: since the conditions for falsification have not been met, there is no need to act. This paper shows that the argument conflates two questions. A falsification threshold answers "is the model right?"; its standard must be strict and roughly symmetric between the two kinds of error. A warning threshold answers "do we act now?"; its position is set by the ratio of the costs of the two errors. Proposition 1 (tier A): for a preventive action that can be withdrawn, with false-alarm cost c_FA and miss cost c_M, the optimal action threshold is the posterior probability p* = c_FA/(c_FA + c_M); whenever c_M/c_FA exceeds the odds implied by the falsification standard (19 for a posterior of 0.95), the warning threshold lies strictly below the falsification threshold, and when a miss cannot be recovered the ratio has no upper bound. Proposition 2 (tier A) gives the time account: under sequential detection, the time for evidence to reach a threshold is roughly the log-odds distance to it divided by the per-step distinguishability; if waiting for falsification plus the lead time coordination needs exceeds the time the risk takes to complete, waiting itself crosses the irreversible line. In an example starting from a 1% prior with 0.02 nats of distinguishability per step, the falsification standard takes about 377 steps to reach, while the warning threshold for a cost ratio of 20 takes about 80. The paper then gives a registration protocol for both thresholds, the asymmetric standard for withdrawal, and rules against two opposite abuses: picking favourable signals after the fact, and postponing indefinitely on the ground that nothing has been falsified yet. It also explains why a triggered warning cannot count as confirmation of the model. The asymmetric stopping boundaries of clinical-trial data monitoring committees, earthquake early warning and aircraft groundings are ready precedents for the distinction.