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Income taxes - Component of Income Taxes (Details) - USD ($) $ in Thousands | 3 Months Ended | 9 Months Ended
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Sep. 30, 2025 | Sep. 30, 2024 | Sep. 30, 2025 | Sep. 30, 2024
Income taxes |  |  |  |
Expected tax expense (benefit), at U.S. federal statutory income tax rate of 21% | $ (1,726) | $ 9,425 | $ (1,241) | $ 13,217
Rate differences on equity in earnings (losses) of Kronos, net of dividends | 856 | (954) | 262 | (2,512)
U.S. state income taxes and other, net | 16 | 37 | 59 | 93
Income tax expense (benefit) | $ (854) | $ 8,508 | $ (920) | $ 10,798

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