Related Party Transactions (Details) - USD ($)																											3 Months Ended		9 Months Ended		12 Months Ended
Related Party Transactions (Details) - USD ($)	Apr. 24, 2025	Jan. 16, 2025	Aug. 10, 2024	Jul. 31, 2024	Jun. 30, 2024	May 22, 2024	Feb. 20, 2024	Feb. 12, 2024	Feb. 01, 2024	Jan. 26, 2024	Jan. 24, 2024	Jan. 23, 2024	Jan. 17, 2024	Jan. 09, 2024	Jan. 03, 2024	Dec. 27, 2023	Nov. 09, 2023	Oct. 11, 2023	Sep. 29, 2023	Sep. 28, 2023	Sep. 06, 2023	Aug. 24, 2023	Aug. 15, 2023	Sep. 11, 2021	Aug. 05, 2021	Feb. 05, 2021	Sep. 30, 2025	Sep. 30, 2024	Sep. 30, 2025	Sep. 30, 2024	Dec. 31, 2024	Sep. 29, 2025	Jun. 04, 2025	Apr. 28, 2025	Mar. 18, 2025	Jan. 27, 2025	Jul. 30, 2021
Related Party Transactions [Line Items]
Shares issued (in Shares)								165,000			331,180	331,180	331,180
Incurred expenses
Payment for fees			$ 200,000
Working capital															$ 250,000
Subscription agreement							$ 250,000		$ 250,000
Loan amount																											$ 2,024,867		$ 2,024,867							$ 100,000
Promissory note - related party	$ 2,200,000
Loaned amount																																$ 100,000	$ 270,000	$ 100,000	$ 250,000	$ 100,000
Sponsor payments														$ 243,867
Share issued price per shares (in Dollars per share)																											$ 10		$ 10
Non-redemption agreement amount											$ 367,610	$ 367,610	$ 367,610
Percentage of fair value determined discount											10.95%	10.95%	10.95%
Percentage of redemption rights discount											5.00%	5.00%	5.00%
Founder shares valuation date per share (in Dollars per share)											$ 10.71	$ 10.71	$ 10.71
Trading price (in Dollars per share)								$ 10.5
Percentage of estimated probability of completing business combination								8.90%
Percentage of redemption ability of founder shares discount								95.00%
Estimated fair value of founder warrants								$ 17,500
Compensation expense
Sponsor Promissory Note [Member]
Related Party Transactions [Line Items]
Sponsor loan				$ 1,500,000
Conversion price per share (in Dollars per share)				$ 1.5
Private Placement Warrants [Member]
Related Party Transactions [Line Items]
Sponsor loan				$ 1,500,000
Conversion price per share (in Dollars per share)	$ 1.5
Converted value	$ 2,200,000
Promissory Note and Second Sponsor Promissory Note [Member]
Related Party Transactions [Line Items]
Outstanding balance promissory note																													$ 2,024,867
Founder Warrants [Member]
Related Party Transactions [Line Items]
Shares issued (in Shares)					175,000			175,000
Founder share (in Shares)																										1
Founder warrants (in Shares)																										2,395,833
Warrants forfeited (in Shares)																													312,500
Per warrant (in Dollars per share)								$ 0.1
Redeemable Warrant [Member]
Related Party Transactions [Line Items]
Founder share (in Shares)																1
Warrant [Member]
Related Party Transactions [Line Items]
Convertible warrant amount (in Shares)				1,500,000
Per warrant (in Dollars per share)																											11.5		$ 11.5
Transfer warrants (in Shares)						62,000																							62,000
Chief Financial Officer [Member]
Related Party Transactions [Line Items]
Payment for fees								$ 12,500
Business Combination [Member]
Related Party Transactions [Line Items]
Founder shares of value issued																$ 1
Shares issued (in Shares)					165,000
Share issued price per shares (in Dollars per share)																											$ 10		$ 10
Business Combination [Member] \| Chief Financial Officer [Member]
Related Party Transactions [Line Items]
Payment for fees								$ 6,250
Sponsor [Member]
Related Party Transactions [Line Items]
Payment for fees
Related Party [Member]
Related Party Transactions [Line Items]
Accrued expenses
Accounts payable - related party																											6,250		6,250		18,824
Promissory note - related party																											2,024,867		2,024,867		1,204,867
Sponsor [Member]
Related Party Transactions [Line Items]
Shares issued (in Shares)																3,902,648
Founder share (in Shares)											1	1	1
Amount withdrawn																	$ 280,000	$ 275,000	$ 225,126	$ 124,874	$ 225,000	$ 150,000
Extension payments															$ 1,500,000
Loan amount				$ 1,500,000							$ 1,456,000
Promissory note - related party																											1,924,867		$ 1,924,867		1,204,867
Deposits											$ 112,500			$ 112,500
Sponsor [Member] \| Purchase Agreement [Member]
Related Party Transactions [Line Items]
Shares outstanding percentage																70.00%
Sponsor [Member] \| Chief Financial Officer [Member]
Related Party Transactions [Line Items]
Shares issued (in Shares)								365,000
Payment for fees								$ 50,000
Founder Shares [Member]
Related Party Transactions [Line Items]
Founder shares of value issued								$ 177,555
Warrants forfeited (in Shares)																								41,667	41,667
Transfer shares (in Shares)						138,000																							138,000
Administrative Support Services [Member]
Related Party Transactions [Line Items]
Principal amount
Administrative Support Services [Member] \| Sponsor [Member]
Related Party Transactions [Line Items]
Operating costs																													55,000
Sponsor Loan Commitment [Member] \| Sponsor [Member]
Related Party Transactions [Line Items]
Operating costs																							$ 1,500,000
Working capital loan upon issuance																											219,441		219,441
Working capital loan																											$ 123,500		$ 123,500
Investor [Member]
Related Party Transactions [Line Items]
Share issued price per shares (in Dollars per share)											$ 1.11	$ 1.11	$ 1.11
Class B Ordinary Shares [Member]
Related Party Transactions [Line Items]
Founder shares of value issued																										$ 25,000
Shares issued (in Shares)																										7,187,500
Founder share (in Shares)																1										1
Issuance of forfeiture (in Shares)																													937,500
Share issued price per shares (in Dollars per share)																											$ 0.85		$ 0.85
Class B Ordinary Shares [Member] \| Sponsor [Member]
Related Party Transactions [Line Items]
Founder share (in Shares)																1
Shares outstanding percentage																											20.00%		20.00%
Shares lock in period																													1 year
Class A Ordinary Shares [Member]
Related Party Transactions [Line Items]
Exercised shares (in Shares)		2,132,366
Price per shares (in Dollars per share)																											$ 12		$ 12
Trading days																													20 days
Consecutive trading days																													30 days
Class A Ordinary Shares [Member] \| Warrant [Member]
Related Party Transactions [Line Items]
Price per shares (in Dollars per share)																											9.2		$ 9.2
Class A Ordinary Shares [Member] \| Sponsor [Member]
Related Party Transactions [Line Items]
Price per shares (in Dollars per share)																											12		$ 12
Trading days																													20 days
Consecutive trading days																													30 days
Threshold period after the business combination.																													150 days
Holding period																													30 days
Share issued price per shares (in Dollars per share)											$ 0.0001	$ 0.0001	$ 0.0001
Over-Allotment Option [Member]
Related Party Transactions [Line Items]
Exercised shares (in Shares)																									3,250,000
Over-Allotment Option [Member] \| Class B Ordinary Shares [Member]
Related Party Transactions [Line Items]
Shares issued (in Shares)																								125,000	125,000
Founder Shares [Member]
Related Party Transactions [Line Items]
Shares issued (in Shares)					365,000											2,030,860
Founder share (in Shares)																1
Share issued price per shares (in Dollars per share)								$ 0.89
Founder Shares [Member] \| Purchase Agreement [Member]
Related Party Transactions [Line Items]
Founder shares of value issued																$ 1
Shares issued (in Shares)																2,030,860
Founder Shares [Member] \| Class B Ordinary Shares [Member]
Related Party Transactions [Line Items]
Shares issued (in Shares)										1,128,992						1,128,992
Private Placement [Member] \| Redeemable Warrant [Member]
Related Party Transactions [Line Items]
Founder share (in Shares)																													1
Private Placement [Member] \| Warrant [Member]
Related Party Transactions [Line Items]
Per warrant (in Dollars per share)																											$ 11.5		$ 11.5
Private Placement [Member] \| Class A Ordinary Shares [Member]
Related Party Transactions [Line Items]
Shares issued (in Shares)																665,000
Founder share (in Shares)																													1
Share issued price per shares (in Dollars per share)																																					$ 10

Plum Acquisition Corp. III 10-Q