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Contract Assets and Liabilities (Tables)
9 Months Ended
Sep. 30, 2023
Revenue from Contract with Customer [Abstract]  
Components of contract assets and contract liabilities
The components of contract assets and contract liabilities consisted of the following:
September 30,December 31,
20232022
(in thousands)
Contract assets - current:
Unbilled revenue$9,944 $5,706 
Total contract assets - current$9,944 $5,706 
Contract assets - long-term:
Unbilled revenue - long-term$2,411 $1,287 
Contract assets - long-term590 681 
Total contract assets - long-term(1)
$3,001 $1,968 
Contract liabilities - current:
Deferred revenue - current$6,621 $6,783 
Total contract liabilities - current$6,621 $6,783 
Contract liabilities - long-term:
Other contract liabilities - long-term$96 $109 
Total contract liabilities - long-term$96 $109 
Changes in short-term and long-term contract assets and contract liabilities for the nine months ended September 30, 2023 were as follows:
Contract AssetsContract Liabilities
(in thousands)
Balance as of January 1, 2023$7,674 $6,892 
Billings or revenue recognized that was included in the beginning balance(2,955)(6,117)
Changes in contract assets or contract liabilities, net of reclassification to receivables8,617 5,757 
Cumulative catch-up adjustment arising from changes in estimates to complete(92)49 
Cumulative catch-up adjustment arising from contract modifications(208)149 
Changes in costs to fulfill and amortization of commission costs (91)— 
Changes in contract commission costs— (13)
Balance as of September 30, 2023$12,945 $6,717