Periodic
The same unit, on loop.
The digit string is a unit of length ≥ 2 repeated wholesale: 1212 (12×2), 123123 (123×2), 454545 (45×3). A unit that is itself one repeated digit (1111) doesn’t count — that’s Solid territory, and the two are mutually exclusive.
Your record
Only 1,053 periodic numbers exist site-wide, about 1 in 950, and the count is hand-checkable: four-digit abab gives 9×9=81 (a≠0, a≠b); six-digit ababab gives 81 and abcabc gives 9×10×10−9=891 (minus 9 all-same units) — exactly 1,053.
Periodicity is the most visual rarity: no arithmetic needed, the loop is visible at a glance. It also stacks well — 1212 is simultaneously Two Pairs, Balanced, Two Symbols and Alternating Parity.
The mutual exclusion is deliberate: without it, 111111 would count as 1×6, 11×3 and 111×2 all at once, paying the same information four times. The registry assigns it to Solid alone — rarity is never billed twice.