Equity Appreciation Rights - Stock-based compensation cost by award type (Details) - Madison Industries IAQ Solutions Corporation - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2026	Mar. 31, 2025
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Total Equity Appreciation Rights cost	$ 10.4	$ 5.2
EAR Plan
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Total Equity Appreciation Rights cost	0.0	5.2
Amended EAR Plan
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Total Equity Appreciation Rights cost	$ 10.4	$ 0.0