Fair Value Measurements - Contingent Consideration and Contingent Founder Shares (Successor) (Details) - USD ($) $ in Thousands			2 Months Ended	3 Months Ended	9 Months Ended
	Jul. 21, 2023	Apr. 27, 2023	Sep. 30, 2023	Sep. 30, 2024	Sep. 30, 2024	Dec. 31, 2023
Class of Stock [Line Items]
Number of additional shares to be issued		16,000,000
Threshold increase in Episodic Migraine Contingent Consideration Shares		11,000,000
Number of Chronic Migraine Contingent Consideration Shares by increase in Episodic Migraine Contingent Consideration Shares		0
Number of Contingent Consideration Shares to be issued upon Threshold Increase in Episodic Migraine Contingent Consideration Shares		0
Reduction in number of Chronic Migraine Contingent Consideration Shares		1,000,000
Minimum number of Chronic Migraine Contingent Consideration Shares after Reduction		0
Contingent consideration liability				$ 6,886	$ 6,886	$ 104,350
Income related to the change in fair value of contingent consideration			$ (75,939)	$ 0	$ (97,464)
Maximum
Class of Stock [Line Items]
Number of additional shares to be issued		16,000,000
Reduction in Episodic Migraine Contingent Consideration Shares		1,000,000
Founder Shares
Class of Stock [Line Items]
Number of founder shares subject to vesting and forfeiture conditions.	3,450,000	3,450,000
Percentage of shares unvested and subject to the restrictions and forfeiture provisions		50.00%
Percentage of shares not subject to restrictions and forfeiture provisions		50.00%
Percentage of warrants not subject to restrictions and forfeiture provisions		100.00%
Migraine Phase 3 Contingent Founder Shares | Upon the achievement of the conditions for the issuance of the Migraine Phase 3 Contingent Consideration Shares on or prior to the Migraine Phase 3 Outside Date
Class of Stock [Line Items]
Number of additional shares to be issued		1,000,000
Number of founder shares subject to vesting and forfeiture conditions.		1,000,000
Migraine Phase 3 Contingent Founder Shares | Upon the achievement of the conditions for the issuance of the CD BLA Contingent Consideration Shares on or prior to the CD BLA Outside Date
Class of Stock [Line Items]
Number of founder shares subject to vesting and forfeiture conditions.		1,000,000
Migraine Phase 3 Contingent Founder Shares | Upon the earlier of (x) the achievement of the conditions for the issuance of the Episodic Migraine Contingent Consideration Shares on or before the Episodic Migraine Outside Date and (y) the achievement of the conditions for the issuance of the Chronic Migraine Contingent Consideration Shares on or before the Chronic Migraine Outside Date
Class of Stock [Line Items]
Number of founder shares subject to vesting and forfeiture conditions.		1,450,000
CD BLA Contingent Founder Shares
Class of Stock [Line Items]
Number of additional shares to be issued		4,000,000
Episodic/Chronic Migraine Contingent Founder Shares
Class of Stock [Line Items]
Number of additional shares to be issued		11,000,000
Number of common shares become due and payable		2,000,000
Episodic/Chronic Migraine Contingent Founder Shares | Maximum
Class of Stock [Line Items]
Reduction in Episodic Migraine Contingent Consideration Shares		2,000,000
Episodic Migraine Contingent Consideration Shares
Class of Stock [Line Items]
Number of additional shares to be issued		4,000,000
Chronic Migraine Contingent Consideration Shares
Class of Stock [Line Items]
Number of additional shares to be issued		7,000,000