Influenza swept through an English boarding school, and the nurses counted the boys confined to bed each day. Slide through the outbreak to see what those counts could prove at the time and what they could not. Compatibility and incompatibility claims have certificates you can re-check yourself, in this browser, in exact arithmetic.
Stop the clock on 26 January, after five days of counts. Using only those counts (the search never sees later data), Twindex finds two explanations that both fit, and a next-day measurement that would distinguish them under a stated future allowance. Then we compare with the count that was actually recorded, using its own historical allowance. This is a replay of historical data, run as if on 26 January.
The same exact checker covers drug dosing, neurons, epidemics and PDEs. Each card replays a real certificate from the repository.
Two parameter sets, here two values of R₀, each have a true SIR solution that stays within the assumed counting error of every count seen so far. The proof bounds the gap between a polynomial approximation and the true solution in exact rational arithmetic, using outward rational bounds; the proof does not rely on numerical solver convergence. As a consequence, no method can estimate R₀ from those counts with a worst-case error below half the gap.
Anonymous (1978), "Influenza in a boarding school", British Medical Journal 1:578. Values as distributed in the R package outbreaks 1.9.0 (dataset influenza_england_1978_school, GPL ≥ 2), read from the package's own data file. The original data were published as a figure, so transcriptions differ slightly between sources.