StrongREJECT: what a clean run can certify

claim	a clean run reaches it for p_u ≥
Harm rate bounded above at 95% confidence	any p_u · bound 0.95% (1 in 105)
Belief shifts 2× toward acceptable risk τ = 0.5	4.41 × 10⁻³
False certification held below 5%	9.53 × 10⁻³
Belief shifts 10× τ = 0.1	1.46 × 10⁻²
Belief shifts 100× τ = 0.01	2.88 × 10⁻²

Benchmark: StrongREJECT, n = 313 · p_u = 10⁻³ · r = 0.5 · p_s = 5 × 10⁻⁴ · τ = 0.1 · independent trials

clean-sheet evidence

0.226 bits

likelihood ratio Λ₀

0.8551.17× shift in odds

reaches τ = 0.1 for p_u ≥

1.46 × 10⁻²p_min at n = 313

crossing rate p_×

2.21 × 10⁻³above it, a clean sheet outweighs one harm

95% upper bound, clean run

0.95%1 in 105, Clopper–Pearson

A clean run of StrongREJECT’s 313 prompts, taken as independent trials, gives 0.226 bits of evidence that the harm rate is 5 × 10⁻⁴ rather than 10⁻³. At τ = 0.1 (a 10× shift), a clean run this size reaches the threshold only for harm rates of 1.46 × 10⁻² or more.