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Related Party Transactions (Details Narrative)																																							1 Months Ended	3 Months Ended						6 Months Ended				9 Months Ended		12 Months Ended
Related Party Transactions (Details Narrative)	Jul. 17, 2024 USD ($)	Jul. 16, 2024 USD ($)	Jul. 05, 2024 USD ($)	Jun. 22, 2024 USD ($)	Jun. 21, 2024 USD ($)	Jun. 17, 2024 USD ($)	Jun. 15, 2024 USD ($)	Jun. 06, 2024 USD ($)	May 15, 2024 USD ($)	Apr. 25, 2024 USD ($)	Apr. 16, 2024 USD ($)	Mar. 13, 2024 USD ($)	Feb. 17, 2024 USD ($)	Feb. 16, 2024 USD ($)	Feb. 13, 2024 USD ($)	Jan. 16, 2024 USD ($)	Dec. 19, 2023 USD ($)	Nov. 09, 2023 USD ($)	Oct. 11, 2023 USD ($)	Oct. 10, 2023 USD ($)	Sep. 12, 2023 USD ($)	Sep. 08, 2023 USD ($)	Aug. 08, 2023 USD ($)	Aug. 02, 2023 USD ($) $ / shares	Jul. 28, 2023 USD ($)	Jun. 26, 2023 shares	Feb. 17, 2023 USD ($)	Feb. 02, 2023 USD ($)	Nov. 10, 2022 USD ($)	Oct. 02, 2021 shares	Aug. 17, 2021 USD ($) Investor $ / shares shares	Jul. 23, 2021 USD ($) $ / shares shares	Jun. 16, 2021 $ / shares shares	Jun. 16, 2021 USD ($) Director $ / shares shares	May 29, 2021 shares	Feb. 08, 2021 USD ($) $ / shares shares	Feb. 08, 2021 $ / shares shares	Feb. 03, 2021 USD ($) $ / shares shares	Jul. 31, 2022 USD ($)	Jun. 30, 2024 USD ($) $ / shares	Mar. 31, 2024 USD ($) $ / shares	Dec. 31, 2023 USD ($) Director $ / shares shares	Jun. 30, 2023 USD ($)	Mar. 31, 2023 USD ($)	Dec. 31, 2022 USD ($)	Jun. 30, 2024 USD ($) $ / shares	Mar. 31, 2024 USD ($) Director $ / shares shares	Jun. 30, 2023 USD ($)	Mar. 31, 2023 USD ($)	Jun. 30, 2024 USD ($) Director $ / shares shares	Jun. 30, 2023 USD ($)	Dec. 31, 2023 USD ($) $ / shares	Sep. 30, 2023 USD ($) Director $ / shares	Sep. 30, 2022 USD ($) $ / shares shares	Aug. 14, 2024 USD ($)	Jul. 30, 2024 USD ($)	Apr. 22, 2024 USD ($)	Feb. 15, 2024 USD ($)	Feb. 09, 2024 USD ($)	Nov. 20, 2023 USD ($)	Dec. 31, 2022 £ / shares	Dec. 31, 2022 $ / shares	May 09, 2022 USD ($)	Oct. 01, 2021 shares	Sep. 30, 2021 shares
Related Party Transaction [Line Items]
Common stock issued, value																																														$ 25,146
Common stock, par value \| (per share)																																																													£ 0.0001	$ 0.0001
Issuance of representative																																																$ 199,974
Proceeds from sale of restricted investments													$ 49,619
Proceeds from related party debt																																														$ 222,306
Sponsor [Member] \| Subsequent Event [Member]
Related Party Transaction [Line Items]
Aggregate loaned amount														$ 60,381
Related Party [Member]
Related Party Transaction [Line Items]
Common stock issued, value																																																				$ 199,974
Armada Acquisition Corp I [Member]
Related Party Transaction [Line Items]
Common stock issued, value																																						$ 25,000
Common stock, par value \| $ / shares																																								$ 0.0001	$ 0.0001	$ 0.0001				$ 0.0001	$ 0.0001			$ 0.0001		$ 0.0001	$ 0.0001	$ 0.0001
Underwriters over-allotment option expired \| shares																																										1,125,000					1,125,000			1,125,000				1,125,000
Issuance of representative shares, shares \| shares																																				162,500
Aggregate loaned amount																						$ 79,099	$ 20,840		$ 125,245
Payment for administrative fees																																															$ 10,000			$ 60,000			$ 0
Amount deposited into trust account													248,095											$ 354,502
Debt instrument, interest rate, stated percentage																																																										0.00%
Proceeds from sale of restricted investments													49,619											70,900				$ 117,079,879														$ 117,079,879					117,079,879			117,079,879			130,246,958	$ 182,069
Payment to acquire restricted investments																$ 70,900
Administrative fees expense																																								$ 30,000	$ 30,000	30,000	$ 30,000		$ 30,000		60,000			90,000	$ 90,000			120,000
Proceeds from related party debt																											$ 450,000		$ 1,500,000
Armada Acquisition Corp I [Member] \| Extension Note [Member]
Related Party Transaction [Line Items]
Aggregate loaned amount																	$ 70,900
Proceeds from sale of restricted investments																					$ 70,900		70,900
Armada Acquisition Corp I [Member] \| Tranche Two [Member]
Related Party Transaction [Line Items]
Payment to acquire restricted investments							$ 49,619		$ 49,619		$ 49,619	$ 49,619		49,619		70,900
Armada Acquisition Corp I [Member] \| Tranche Two [Member] \| Extension Note [Member]
Related Party Transaction [Line Items]
Proceeds from sale of restricted investments																					70,900
Payment to acquire restricted investments												49,619									$ 70,900	70,900
Armada Acquisition Corp I [Member] \| Tranche Four [Member] \| Extension Note [Member]
Related Party Transaction [Line Items]
Proceeds from sale of restricted investments																				$ 70,900
Payment to acquire restricted investments						$ 49,619													$ 70,900	70,900
Armada Acquisition Corp I [Member] \| Tranche Five [Member] \| Extension Note [Member]
Related Party Transaction [Line Items]
Proceeds from sale of restricted investments																		$ 70,900
Payment to acquire restricted investments																		70,900
Armada Acquisition Corp I [Member] \| Tranche One [Member]
Related Party Transaction [Line Items]
Proceeds from sale of restricted investments																	70,900
Payment to acquire restricted investments																	70,900
Armada Acquisition Corp I [Member] \| Tranche One [Member] \| Extension Note [Member]
Related Party Transaction [Line Items]
Proceeds from sale of restricted investments																							70,900
Payment to acquire restricted investments															$ 49,619								70,900
Armada Acquisition Corp I [Member] \| Subsequent Event [Member]
Related Party Transaction [Line Items]
Aggregate loaned amount																																																							$ 7,500,000	$ 5,141,250				$ 12,510
Amount deposited into trust account													248,095
Debt instrument, interest rate, stated percentage																																																											0.00%
Proceeds from sale of restricted investments													49,619
Armada Acquisition Corp I [Member] \| Subsequent Event [Member] \| Tranche Two [Member]
Related Party Transaction [Line Items]
Proceeds from sale of restricted investments																70,900
Armada Acquisition Corp I [Member] \| Subsequent Event [Member] \| Tranche Four [Member] \| Extension Note [Member]
Related Party Transaction [Line Items]
Payment to acquire restricted investments																			$ 70,900
Armada Acquisition Corp I [Member] \| Subsequent Event [Member] \| Tranche Five [Member] \| Extension Note [Member]
Related Party Transaction [Line Items]
Payment to acquire restricted investments		$ 49,619																$ 70,900
Armada Acquisition Corp I [Member] \| Sponsor [Member]
Related Party Transaction [Line Items]
Promissory Notes-Related Party																																								247,454	247,454	247,454				$ 247,454	247,454			247,454		$ 247,454	247,454	251,754
Aggregate loaned amount											53,388						39,100							425,402	$ 125,245																																$ 40,939	$ 297,714					$ 483,034
Repayments of debt																																							$ 187,034
Payment for services																																								0	0	0	$ 4,300	$ 4,300			0		$ 4,300	0	$ 4,300		4,300	44,246
Notes Issued				$ 32,000	$ 1,364			$ 5,150	$ 12,381	$ 19,054
Promissory note outstanding																																								125,245	125,245	125,245				125,245	125,245			125,245		125,245
Proceeds from sale of restricted investments													49,619														$ 49,619
Debt conversion converted instrument amount																								$ 425,402
Debt instrument interest rate during period																									0.00%				0.00%
Line of Credit Facility, Maximum Amount Outstanding During Period																																																		248,095			141,800
Armada Acquisition Corp I [Member] \| Sponsor [Member] \| Promissory Notes [Member]
Related Party Transaction [Line Items]
Promissory Notes-Related Party																																								3,056,726	2,776,600					3,056,726	2,776,600			3,056,726			2,564,439
Armada Acquisition Corp I [Member] \| Sponsor [Member] \| Extension Note [Member]
Related Party Transaction [Line Items]
Loan conversion price \| $ / shares																								$ 10
Debt conversion converted instrument amount																								$ 425,402
Line of Credit Facility, Maximum Amount Outstanding During Period																																															354,502			354,502
Armada Acquisition Corp I [Member] \| Sponsor [Member] \| Working Capital Loan [Member]
Related Party Transaction [Line Items]
Aggregate loaned amount												$ 60,381		$ 60,381		39,100
Armada Acquisition Corp I [Member] \| Sponsor [Member] \| Working Capital Loan Tranche August Two Thousand And Twenty Three [Member]
Related Party Transaction [Line Items]
Promissory Notes-Related Party																																								20,840	20,840	20,840				20,840	20,840			20,840		20,840
Aggregate loaned amount																							$ 20,840
Armada Acquisition Corp I [Member] \| Sponsor [Member] \| Working Capital Loan Tranche September Two Thousand And Twenty Three [Member]
Related Party Transaction [Line Items]
Promissory Notes-Related Party																																								79,099	79,099	79,099				79,099	79,099			79,099		79,099
Aggregate loaned amount																						$ 79,099
Armada Acquisition Corp I [Member] \| Sponsor [Member] \| Working Capital Loan Tranche October Two Thousand And Twenty Three [Member]
Related Party Transaction [Line Items]
Promissory Notes-Related Party																																								59,099	59,099	59,099				59,099	59,099			59,099		59,099
Aggregate loaned amount																				$ 59,099
Armada Acquisition Corp I [Member] \| Sponsor [Member] \| Working Capital Loan Tranche November Two Thousand And Twenty Three [Member]
Related Party Transaction [Line Items]
Promissory Notes-Related Party																																								12,510	12,510	12,510				12,510	12,510			12,510		12,510
Aggregate loaned amount																																																												$ 12,510
Armada Acquisition Corp I [Member] \| Sponsor [Member] \| Subscription Agreement With Polar [Member]
Related Party Transaction [Line Items]
Promissory Notes-Related Party																																									39,100	2,776,600					39,100					2,776,600	2,564,439
Aggregate loaned amount																	$ 39,100
Armada Acquisition Corp I [Member] \| Sponsor [Member] \| Subsequent Event [Member]
Related Party Transaction [Line Items]
Aggregate loaned amount											$ 53,388																																														$ 40,939		$ 297,714
Notes Issued	$ 381		$ 5,150							$ 19,054
Amount deposited into trust account													248,095
Proceeds from sale of restricted investments													49,619
Armada Acquisition Corp I [Member] \| Sponsor [Member] \| Subsequent Event [Member] \| Working Capital Loan [Member]
Related Party Transaction [Line Items]
Aggregate loaned amount																$ 39,100
Armada Acquisition Corp I [Member] \| Related Party [Member]
Related Party Transaction [Line Items]
Promissory Notes-Related Party																																								$ 3,056,726	$ 2,776,600	2,776,600				$ 3,056,726	2,776,600			3,056,726		$ 2,776,600	2,564,439	$ 251,754									$ 483,034
Monthly fee																																										$ 10,000					$ 10,000			$ 10,000			$ 10,000
Amount deposited into trust account													$ 248,095
Armada Acquisition Corp I [Member] \| President [Member]
Related Party Transaction [Line Items]
Conversion of Stock, Shares Converted \| shares																																		50,000
Armada Acquisition Corp I [Member] \| Director [Member]
Related Party Transaction [Line Items]
Conversion of Stock, Shares Converted \| shares																										90,000								35,000
Number of independent directors \| Director																																		3								3					3			3			3
Armada Acquisition Corp I [Member] \| Chief Executive Officer [Member]
Related Party Transaction [Line Items]
Shares subject to forfeiture \| shares																																6,007,500
Armada Acquisition Corp I [Member] \| Founder Shares [Member]
Related Party Transaction [Line Items]
Common stock issued, value																																						$ 25,000
Price per share \| $ / shares																															$ 0.006	$ 0.006	$ 0.006	$ 0.006				$ 0.006
Common stock issued \| shares																																1,200,000	700,000	700,000				4,312,500
Common stock, par value \| $ / shares																																						$ 0.0001
Aggregate purchase price																																$ 6,975		$ 4,070
Period after business combination for transfer of shares																																										180 days					180 days			180 days			180 days
Stock allocated to each anchor investor, shares \| shares																															131,250
Stock allocated to anchor investors, shares \| shares																															1,312,500
Stock allocated to each anchor investor, value																															$ 424,491
Stock allocated to each anchor investor, value per share \| $ / shares																															$ 3.23
Armada Acquisition Corp I [Member] \| Founder Shares [Member] \| Over-Allotment Option [Member]
Related Party Transaction [Line Items]
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Number \| shares																																																																1,125,000	1,125,000
Underwriters over-allotment option expired \| shares																														1,125,000
Armada Acquisition Corp I [Member] \| Founder Shares [Member] \| Chief Executive Officer President and Independent Directors [Member]
Related Party Transaction [Line Items]
Shares subject to forfeiture \| shares																																205,000
Armada Acquisition Corp I [Member] \| Units [Member]
Related Party Transaction [Line Items]
Number of anchor investors \| Investor																															10
Armada Acquisition Corp I [Member] \| Units [Member] \| IPO [Member]
Related Party Transaction [Line Items]
Price per share \| $ / shares																															$ 10
Common stock issued \| shares																															15,000,000
Percentage of units purchased by anchor investors																															9.90%
Armada Acquisition Corp I [Member] \| Representative Shares [Member]
Related Party Transaction [Line Items]
Price per share \| $ / shares																																				$ 0.0001	$ 0.0001
Period after business combination for transfer of shares																																										30 days					30 days			30 days			30 days
Issuance of representative shares, shares \| shares																																			87,500	87,500	162,500
Issuance of representative																																				$ 25
Period from Initial Public Offering closing to complete acquisition for waiver of distribution rights																																																					15 months
Extended period from Initial Public Offering closing to complete acquisition for waiver of distribution rights																																																					18 months