Warrants (Details) - $ / shares	9 Months Ended
Warrants (Details) - $ / shares	Sep. 30, 2025	Dec. 31, 2024	Feb. 12, 2024
Warrants [Line Items]
Warrants exercisable	30 days
Warrant expire term	5 years
Newly issued price	$ 10
Redemption trigger price	18
Redemption warrants price	$ 10
Founder Warrants [Member]
Warrants [Line Items]
Warrants outstanding	2,354,166	2,354,166
Warrants exercise price			$ 0.1
Warrants issued	2,354,166
Private Placement Warrants [Member]
Warrants [Line Items]
Warrants outstanding	288,333	288,333
Warrants exercise price	$ 0.178	$ 0.18
Private placement units transferable	30 days
Warrants issued	288,334
Public Warrants [Member]
Warrants [Line Items]
Warrants outstanding	9,416,666	9,416,666
Warrants exercise price	$ 0.17	$ 0.18
Warrants issued	9,416,666
Warrant [Member]
Warrants [Line Items]
Warrants exercise price	$ 11.5
Share Trigger Price One [Member] \| Public Warrants [Member]
Warrants [Line Items]
Price per warrant	$ 0.01
Notice of redemption	30 days
Trading days	20 days
Trading day period ending	30 days
Share Trigger Price Two [Member] \| Public Warrants [Member]
Warrants [Line Items]
Warrant redemption condition minimum share price	$ 10
Price per warrant	$ 0.1
Notice of redemption	30 days
Redemption period	30 days
As a Percentage of Market Value [Member]
Warrants [Line Items]
Percentage of exercise price of warrants will be adjusted of market value	115.00%
As a Percentage of Newly Issued Price [Member]
Warrants [Line Items]
Percentage of exercise price of warrants will be adjusted of market value	115.00%
Minimum [Member] \| Share Trigger Price One [Member] \| Public Warrants [Member]
Warrants [Line Items]
Warrant redemption condition minimum share price	$ 18
Minimum [Member] \| Share Trigger Price One [Member] \| Reference Value [Member]
Warrants [Line Items]
Warrant redemption condition minimum share price	18
Minimum [Member] \| Share Trigger Price Two [Member] \| Public Warrants [Member]
Warrants [Line Items]
Warrant redemption condition minimum share price	$ 10
Maximum [Member] \| Public Warrants [Member]
Warrants [Line Items]
Percentage of outstanding ordinary shares	65.00%
Class A Ordinary Shares [Member]
Warrants [Line Items]
Number of business days	20 days
Effective business days	60 days
Trading days	20 days
Trading day period ending	30 days
Issued price per share	$ 12
Volume-weighted average trading price	10 days
Class A Ordinary Shares [Member] \| Warrant [Member]
Warrants [Line Items]
Issued price per share	$ 9.2
Class A Ordinary Shares [Member] \| Warrants and Rights Subject to Mandatory Redemption [Member]
Warrants [Line Items]
Warrant redemption condition minimum share price	18
Class A Ordinary Shares [Member] \| Share Trigger Price Two [Member] \| Public Warrants [Member]
Warrants [Line Items]
Price per warrant	$ 0.1
Notice of redemption	30 days
Trading day period ending	10 days
Redemption period	30 days
Trading day period	10 days
Class A Ordinary Shares [Member] \| Maximum [Member]
Warrants [Line Items]
Issued price per share	$ 9.2
Newly Issued Price [Member]
Warrants [Line Items]
Percentage of total equity proceeds	60.00%
Event Triggering Adjustment to Exercise Price of Warrants [Member] \| As a Percentage of Market Value [Member] \| Warrants and Rights Subject to Mandatory Redemption One [Member]
Warrants [Line Items]
Percentage of market value and newly issued price	100.00%
Event Triggering Adjustment to Exercise Price of Warrants [Member] \| As a Percentage of Newly Issued Price [Member] \| Warrants and Rights Subject to Mandatory Redemption Two [Member]
Warrants [Line Items]
Percentage of market value and newly issued price	180.00%
IPO [Member] \| Warrant [Member]
Warrants [Line Items]
Warrants issued	9,705,000

Plum Acquisition Corp. III 10-Q