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| Stock-based compensation | 17. Stock-based compensation Stock-based compensation expense was $53.6 million and $435.0 million for the three months ended June 30, 2026 and 2025, respectively, and $105.4 million and $447.7 million for the six months ended June 30, 2026 and 2025, respectively. The capitalized stock-based compensation expense related to internally developed software was $13.8 million and $65.6 million for the three months ended June 30, 2026 and 2025, and $23.2 million and $68.3 million for the six months ended June 30, 2026 and 2025, respectively. Stock options Granted stock options generally have vesting periods ranging from 12 months to 48 months, and expire 10 years after the initial grant date. A summary of outstanding stock options activities for the six months ended June 30, 2026 and 2025 is presented below:
As of June 30, 2026, unrecognized stock-based compensation cost net of estimated forfeitures related to outstanding unvested stock options that are expected to vest was $8.3 million, which is expected to be recognized over a weighted-average period of 2.4 years. Restricted stock units (RSUs) Prior to the IPO, RSUs granted under the award plan generally vested upon the satisfaction of both a service condition and a liquidity-event related performance condition. Both the service and liquidity-event related performance conditions needed to be met for the expense to be recognized. RSUs granted after the IPO generally vest solely based on the satisfaction of a service condition. We record stock-based compensation expense for service-based RSUs on a straight-line basis over the requisite service period, which is generally the vesting period. Prior to the IPO, we had not recognized stock-based compensation expense related to certain RSU awards as the qualifying liquidity-event related performance condition had not yet occurred and was not considered probable of occurring. As the performance condition related to these awards was met upon commencement of trading of the Company's Class A common stock on the NYSE, the Company recognized stock-based compensation expense of $423.8 million, net of $62.7 million of capitalized costs related to internally developed software, associated with the vesting of RSUs for which the service-based condition had also been met. Stock-based compensation expense related to remaining service-based awards after the IPO is recorded over the remaining requisite service period. A summary of RSUs activities for the six months ended June 30, 2026 and 2025 is as follows:
As of June 30, 2026, unrecognized stock-based compensation cost net of estimated forfeitures related to outstanding unvested RSUs that are expected to vest was $408.7 million, which is expected to be recognized over a weighted-average period of 3.2 years. Shares issued for business combinations The Company has issued the following common shares for the purchase of common shares subject to forfeiture based on certain service conditions in connection with its acquisitions. These shares were issued to the employees of the acquired businesses and are valued based on the fair value of the Company’s common shares at the acquisition date. The Company records stock-based compensation expenses over the requisite service period, with an increase to additional paid-in capital. The shares issued for business combinations are subject to forfeiture based on service conditions through various dates over a four-year period from their respective acquisition dates.
As of June 30, 2026 unrecognized stock-based compensation cost net of estimated forfeitures related to outstanding unvested shares and warrants issued for business combinations that are expected to vest was $25.8 million, which is expected to be recognized over a weighted-average period of 1.5 years. ESPP The Company's ESPP became effective on June 4, 2025, with the grant date of the initial offering period beginning on March 5, 2026. Refer to Note 2 for additional details regarding the Company's ESPP. As of June 30, 2026, $4.5 million has been withheld on behalf of employees for future purchases under the ESPP due to the timing of payroll deductions. As of June 30, 2026, there was approximately $0.8 million of unrecognized stock-based compensation cost net of estimated forfeitures related to the ESPP, which is expected to be recognized over a remaining period of 0.2 years. The Company estimated the fair value of ESPP purchase rights using a Black-Scholes option-pricing model. The weighted average assumptions utilized in the valuation of ESPP purchase rights are presented below:
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