Differences among 50 U.S. states fell for each period's top 100 male names but rose for 17 shared names between 1960–1964 and 2020–2024

We tested whether common baby names became more similar among 50 U.S. states. We used Social Security Administration files with a March 1, 2026 record date. We compared 1960–1964 with 2020–2024 and showed 13 five-year periods. Each state had the same weight. Jensen-Shannon divergence fell from 0.09987 to 0.07368 bits for each period's national top 100 male names. It fell from 0.08719 to 0.06859 bits for female names. For the same 17 male names in both endpoint lists, divergence rose from 0.03364 to 0.03904 bits. We bounded every absent annual count from zero to four under the source rule. The male top-100 change lay in [−0.03933, −0.02266] bits. The shared male name change lay in [0.00258, 0.00601] bits. Removing John from the shared set removed its estimated rise. The sets differ in size and membership. They do not isolate a cause of the change. We also found 318 conflicts in 70,265 national and state margin checks. The bounds do not cover other source errors. These results concern selected names, not all births or culture as a whole. The package contains source archives, code, provenance, tables, figures, a proof of the bound, and offline instructions. A separate run reproduced all eight main output files byte for byte.

baby names · cultural change · state differences · Jensen-Shannon divergence · withheld counts · reproducibility · Social Security Administration