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Summary of Significant Accounting Policies (Details) - USD ($)
$ / shares in Units, $ in Thousands
 3 Months Ended 9 Months Ended
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2024
Sep. 30, 2023
Summary of Significant Accounting Policies [Line Items]        
Common units percentage     99.80%  
Economic interest     99.80%  
Asset liabilities percentage     100.00%  
Reduce net income (in Dollars) $ (39,228) $ (36,004) $ (89,418) $ (102,424)
Reduce basic earnings (in Dollars per share) $ (0.36) $ (0.34) $ (0.84) $ (0.99)
Reduce diluted earnings (in Dollars per share) $ (0.36) $ (0.34) $ (0.84) $ (0.99)
Minimum [Member]        
Summary of Significant Accounting Policies [Line Items]        
Reduce net income (in Dollars) $ 9,000   $ 9,000  
Reduce basic earnings (in Dollars per share) $ 0.08   $ 0.08  
Reduce diluted earnings (in Dollars per share) $ 0.08   $ 0.08  
Purple LLC [Member]        
Summary of Significant Accounting Policies [Line Items]        
Common units percentage     0.20%  
Economic interest     0.20%