Segment Information - Segment Results (Details) - Madison Industries IAQ Solutions Corporation - USD ($) $ in Millions		3 Months Ended
		Mar. 31, 2026	Mar. 31, 2025
Revenue from External Customer [Line Items]
Total net sales		$ 923.7	$ 690.4
Segment selling, general and administrative expenses	[1]	(154.3)	(105.6)
Central and other costs		(7.6)	0.4
Allocated Madison Industries costs		(10.7)	(4.5)
Segment EBITDA add-backs (excluding depreciation)		0.0	(3.4)
Depreciation		(13.0)	(10.1)
Intangible asset amortization		(40.9)	(25.2)
Restructuring expenses		(2.3)	(0.1)
Equity appreciation rights expense		(10.4)	(5.2)
Transaction related expenses		(4.0)	(0.8)
Interest and financing expenses		(90.7)	(65.8)
Other income (expense)		(0.4)	3.0
Income (loss) from continuing operations before income taxes		60.3	59.9
Litigation settlement, gain			3.9
Commercial
Revenue from External Customer [Line Items]
Total net sales		609.7	493.6
Residential
Revenue from External Customer [Line Items]
Total net sales		314.0	196.8
Operating Segments
Revenue from External Customer [Line Items]
Total segment adjusted EBITDA		240.3	171.6
Operating Segments | Commercial
Revenue from External Customer [Line Items]
Total net sales		609.8	493.6
Segment cost of goods sold		(380.1)	(308.8)
Segment selling, general and administrative expenses		(75.1)	(65.6)
Segment EBITDA add-backs		6.4	9.2
Total segment adjusted EBITDA		161.0	128.4
Depreciation		(6.5)	(6.2)
Operating Segments | Residential
Revenue from External Customer [Line Items]
Total net sales		315.6	197.5
Segment cost of goods sold		(193.4)	(128.0)
Segment selling, general and administrative expenses		(49.4)	(30.6)
Segment EBITDA add-backs		6.5	4.3
Total segment adjusted EBITDA		79.3	43.2
Depreciation		(6.5)	(3.9)
Intersegment Sales
Revenue from External Customer [Line Items]
Total net sales		(1.7)	(0.7)
Intersegment Sales | Commercial
Revenue from External Customer [Line Items]
Total net sales		0.1	0.0
Intersegment Sales | Residential
Revenue from External Customer [Line Items]
Total net sales		$ 1.6	$ 0.7

[1] Inclusive of equity appreciation rights expense of $10.4 and $5.2 for the three months ended March 31, 2026 and 2025, respectively.