Stockholders' (Deficit) Equity and Stock-Based Compensation - IPO (Details) - USD ($) $ / shares in Units, $ in Millions			1 Months Ended			12 Months Ended
	Jul. 28, 2022	Feb. 15, 2022	Dec. 31, 2023	Nov. 30, 2023	Aug. 31, 2022	Dec. 31, 2023	Dec. 31, 2022	Sep. 30, 2024	Oct. 30, 2023	Sep. 30, 2023	Jun. 30, 2023	Mar. 31, 2023
Subsidiary, Sale of Stock [Line Items]
Preferred stock authorized (in shares)			10,000,000			10,000,000		10,000,000
Preferred stock par value (in dollar per share)			$ 0.001			$ 0.001		$ 0.001
Remainder of the principal and interest paid for the common units redemption	$ 4.0
Exercised (in shares)						2,200
Warrants outstanding							3,220,000
Warrants issued (in shares)									1,004,148
IPO
Subsidiary, Sale of Stock [Line Items]
Units issued in IPO (in shares)		2,800,000
Number of shares of common stock (in shares)		1
Number of warrants to purchase each share (in shares)		1
Warrants exercise price (in dollars per share)		$ 5.50
Warrants exercisable term (in years)		5 years
Warrants outstanding			0			0
Net proceeds from the offering		$ 10.2
Over-Allotment Option
Subsidiary, Sale of Stock [Line Items]
Purchase option - number of additional units (in shares)		140,000
Exercised (in shares)				10,500
Warrants outstanding			10,500			10,500
Term of underwriters (in days)		45 days
Exercise price of additional units (in dollars per share)		$ 6.60
Public offering price per unit sold (as percent)		120.00%
Number of units exercised				70,000
Units outstanding			70,000			70,000
Over-Allotment Option | Maximum
Subsidiary, Sale of Stock [Line Items]
Warrants issued (in shares)		420,000
Class A Common Stock
Subsidiary, Sale of Stock [Line Items]
Common stock, authorized (in shares)			160,000,000			160,000,000	160,000,000	160,000,000		160,000,000	160,000,000	160,000,000
Common stock, par value (in dollars per share)			$ 0.001			$ 0.001	$ 0.001	$ 0.001		$ 0.001	$ 0.001	$ 0.001
Class A Common Stock | Over-Allotment Option
Subsidiary, Sale of Stock [Line Items]
Purchase option - number of warrants (in shares)		21,000
Warrants exercise price (in dollars per share)		$ 0.012
Warrants outstanding			0			0
Warrants issued (in shares)		420,000
Public offering price per warrant sold (as percent)		120.00%
Class B Common Stock
Subsidiary, Sale of Stock [Line Items]
Common stock, authorized (in shares)			20,000,000			20,000,000	20,000,000	20,000,000		20,000,000	20,000,000	20,000,000
Common stock, par value (in dollars per share)			$ 0.001			$ 0.001	$ 0.001	$ 0.001		$ 0.001	$ 0.001	$ 0.001
DDM | Class A Common Stock
Subsidiary, Sale of Stock [Line Items]
Number of units exchanged (in shares)			410,000		100,000	410,000	100,000
Number of shares of common stock (in shares)			1			1
DDM | Class B Common Stock
Subsidiary, Sale of Stock [Line Items]
Number of shares of common stock (in shares)			10,868,000			10,868,000		10,868,000
DDH LLC
Subsidiary, Sale of Stock [Line Items]
Noneconomic voting rights (as percent)						100.00%
DDH LLC | IPO | Related Party | Woolford
Subsidiary, Sale of Stock [Line Items]
Aggregate purchase price of units issued		$ 14.2
Purchase price paid		$ 10.3
DDH LLC | IPO | Common Units | Related Party | Woolford
Subsidiary, Sale of Stock [Line Items]
Remaining number of units purchased		5,637
DDH LLC | IPO | Class B Preferred Units. | Related Party | Woolford
Subsidiary, Sale of Stock [Line Items]
Remaining number of units purchased		7,046