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Income taxes - Component of Income Taxes (Detail) - USD ($)
$ in Thousands
3 Months Ended
Mar. 31, 2025
Mar. 31, 2024
Income taxes    
Expected tax expense, at U.S. federal statutory income tax rate of 21% $ 273 $ 1,744
Rate differences on equity in earnings of Kronos, net of dividends (319) (782)
U.S. state income taxes and other, net 23 26
Income tax expense (benefit) $ (23) $ 988