With exact totals, the first count threshold that leaves name entropy order unresolved ranges from 49 to 299 across paired SSA tables for 1980–2017

We tested how count suppression changes what name tables can establish about diversity. We used paired name counts and applicant totals from babynames 1.0.1 for 38 SSA birth years, 1980 to 2017. We kept totals exact. At each artificial threshold t, we kept counts of at least t and allowed every omitted name to have one to t minus one applicants. We used finite-count bounds to find the first threshold that left the female versus male entropy order unresolved. This threshold ranged from 49 to 299, with median 123.5. It was 299 in 1980 and 49 in 2017. The first unresolved threshold for same-name probability ranged from 2,041 to 11,029. At threshold five, female entropy was higher in all 38 years, but either sex could have more distinct names. The 31 years shared with a prior SCI study matched in all 62 year-sex cells. Male entropy increased by 0.210 to 0.568 nats more than female entropy between 1980 and 2017 under every allowed endpoint completion. The threshold search is exploratory. The results require exact matching totals and the stated omission rule. They describe eligible applicants in one snapshot, not all births or a cause of name choice. Two source readers, small partition searches, 241,923 direct threshold checks, and exact repeated outputs support the calculations. The package preserves source data, hashes, code, results, figures, proof, and repeat steps.

name diversity · count suppression · Shannon entropy · partial identification · cultural change · Social Security Administration · reproducible research