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Intangible assets and goodwill - Indefinite-lived Intangibles (Details) $ in Thousands | 3 Months Ended | 12 Months Ended |
--- | --- | --- | ---
Dec. 31, 2022 USD ($) | Dec. 31, 2022 USD ($) | Dec. 31, 2021 USD ($)
Indefinite-lived intangibles |  |  |
Impairment |  | $ (33,384) |
Intangible assets, net | $ 705,891 | 705,891 | $ 724,841
Indefinite-lived intangible assets |  |  |
Indefinite-lived intangibles |  |  |
Beginning Balance |  | 576,500 |
Reclass from Indefinite-Lived to Definite-Lived |  | (89,550) |
Impairment |  | (33,384) |
Ending Balance | $ 453,566 | $ 453,566 |
Indefinite-lived intangible assets | Significant unobservable inputs (Level 3) | Income Method | Discount Rate |  |  |
Indefinite-lived intangibles |  |  |
Indefinite-lived intangible asset, measurement input | 0.15 | 0.15 |
Indefinite-lived intangible assets | Significant unobservable inputs (Level 3) | Income Method | Probability of success | Weighted Average |  |  |
Indefinite-lived intangibles |  |  |
Indefinite-lived intangible asset, measurement input | 0.88 | 0.88 |
Indefinite-lived intangible assets | Upstaza |  |  |
Indefinite-lived intangibles |  |  |
Beginning Balance |  | $ 358,700 |
Reclass from Indefinite-Lived to Definite-Lived |  | (89,550) |
Impairment | $ (33,400) | (33,384) |
Ending Balance | 235,766 | 235,766 |
Indefinite-lived intangible assets | PTC-FA |  |  |
Indefinite-lived intangibles |  |  |
Beginning Balance |  | 112,500 |
Impairment |  | 0 |
Ending Balance | 112,500 | 112,500 |
Indefinite-lived intangible assets | PTC-AS |  |  |
Indefinite-lived intangibles |  |  |
Beginning Balance |  | 105,300 |
Ending Balance | $ 105,300 | $ 105,300 |

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- Definition Amount of assets, excluding financial assets and goodwill, lacking physical substance and having a projected indefinite period of benefit reclassed to definite-lived assets. + References No definition available. + Details
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- Definition Amount of impairment loss resulting from write-down of assets, excluding financial assets and goodwill, lacking physical substance and having a projected indefinite period of benefit to fair value. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -SubTopic 30 -Section 50 -Paragraph 3 -Subparagraph (b) -URI https://asc.fasb.org/extlink&oid=66006027&loc=d3e16373-109275 Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef -Publisher FASB -Name Accounting Standards Codification -Topic 230 -SubTopic 10 -Section 45 -Paragraph 28 -Subparagraph (b) -URI https://asc.fasb.org/extlink&oid=126954810&loc=d3e3602-108585 + Details
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