Coverage and numerical conservatism

The reported empirical coverage is $140/140=1$. This does not prove uniform coverage over all channels, establish the calibration assumptions, or replace Theorem thm:binomial.

For perspective, if a single case's repeated datasets were independent ideal draws with coverage probability $p_{\mathrm{cov}}$, observing 20 covered datasets gives the one-sided 95% exact lower confidence endpoint

This is an illustration of Monte Carlo uncertainty, not a new laboratory confidence statement. Seven separate cases require an additional multiplicity allowance for simultaneous Monte Carlo intervals. The heterogeneous suite cannot simply be treated as 140 iid observations of one channel's coverage probability.

The report's statement that any coverage miss would be a “failure of the statistical procedure itself” needs qualification. Even a correct procedure can miss on an allowed tail event. Under the model, its miscoverage probability is bounded, not zero. Outward arithmetic prevents inward numerical approximation from weakening the intended intervals; it does not eliminate statistical tail events, implementation bugs, or violations of assumptions.