Income Taxes (Details) - Madison Industries IAQ Solutions Corporation - USD ($)	3 Months Ended
Mar. 31, 2026	Mar. 31, 2025
Income Tax Disclosure [Line Items]
Effective income tax rate	28.70%	24.50%
Income tax expense, Pillar Two model	$ 0

Percentage of current income tax expense (benefit) and deferred income tax expense (benefit) pertaining to continuing operations.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 12
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482685/740-10-50-12

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 231
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482663/740-10-55-231

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Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration