Significant Accounting Policies (Tables) - Armada Acquisition Corp I [Member]

3 Months Ended

6 Months Ended

9 Months Ended

12 Months Ended

Dec. 31, 2023

Mar. 31, 2024

Jun. 30, 2024

Sep. 30, 2023

Summary of common stock reflected in the balance sheets are reconciled

At December 31, 2023 and September 30, 2023, the common stock reflected in the balance sheets are reconciled in the following table:

Gross Proceeds	$	150,000,000
Proceeds allocated to Public Warrants		(11,700,000	)
Issuance costs related to common stock		(3,261,589	)
Remeasurement of carrying value to redemption value		14,961,589
Subsequent remeasurement of carrying value to redemption    value – Trust interest income (excluding the amount that    can be withdrawn from Trust Account for taxes)		548,862
Common stock subject to possible redemption –    September 30, 2022		150,548,862
Redemptions		(129,175,094	)
Remeasurement of carrying value to redemption value		3,943,038
Common stock subject to possible redemption –    September 30, 2023	$	25,316,806
Remeasurement of carrying value to redemption value		467,884
Common stock subject to possible redemption –    December 31, 2023	$	25,784,690

At March 31, 2024 and September 30, 2023, the common stock reflected in the balance sheets are reconciled in the following table:

Gross Proceeds	$	150,000,000
Proceeds allocated to Public Warrants		(11,700,000	)
Issuance costs related to common stock		(3,261,589	)
Remeasurement of carrying value to redemption value		14,961,589
Subsequent remeasurement of carrying value to redemption    value – Trust interest income (excluding the amount that    can be withdrawn from Trust Account for taxes)		548,862
Common stock subject to possible redemption –    September 30, 2022	$	150,548,862
Redemptions		(129,175,094	)
Remeasurement of carrying value to redemption value		3,943,038
Common stock subject to possible redemption –    September 30, 2023	$	25,316,806
Remeasurement of carrying value to redemption value		467,884
Common stock subject to possible redemption –    December 31, 2023	$	25,784,690
Redemptions		(10,384,496	)
Remeasurement of carrying value to redemption value		347,252
Common stock subject to possible redemption –    March 31, 2024	$	15,747,446

At June 30, 2024 and September 30, 2023, the common stock reflected in the balance sheets are reconciled in the following table:

Gross Proceeds	$	150,000,000
Proceeds allocated to Public Warrants		(11,700,000	)
Issuance costs related to common stock		(3,261,589	)
Remeasurement of carrying value to redemption value		14,961,589
Subsequent remeasurement of carrying value to redemption value –    Trust interest income (excluding the amount that can be withdrawn    from Trust Account for taxes)		548,862
Common stock subject to possible redemption – September 30, 2022	$	150,548,862
Redemptions		(129,175,094	)
Remeasurement of carrying value to redemption value		3,943,038
Common stock subject to possible redemption – September 30, 2023	$	25,316,806
Redemptions		(10,384,496	)
Remeasurement of carrying value to redemption value		1,108,476
Common stock subject to possible redemption – June 30, 2024	$	16,040,786

At September 30, 2023 and 2022, the common stock reflected in the balance sheets are reconciled in the following table:

Gross Proceeds	$	150,000,000
Proceeds allocated to Public Warrants		(11,700,000	)
Issuance costs related to common stock		(3,261,589	)
Remeasurement of carrying value to redemption value		14,961,589
Subsequent remeasurement of carrying value to redemption    value – Trust interest income (excluding the amount    that can be withdrawn from Trust Account for taxes)		548,862
Common stock subject to possible redemption –    September 30, 2022		150,548,862
Redemptions		(129,175,094	)
Remeasurement of carrying value to redemption value		3,943,038
Common stock subject to possible redemption –    September 30, 2023	$	25,316,806

Schedule of basic and diluted net loss per share

Accretion of the carrying value of common stock subject to redemption value is excluded from net (loss) income per common stock because the redemption value approximates fair value.

	For the Three Months Ended December 31,
	2023						2022
	Common Stock Subject to Possible Redemption			Non-Redeemable Common Stock			Common Stock Subject to Possible Redemption		Non-Redeemable Common Stock
Basic and diluted net (loss) income per share
Numerator:
Allocation of net (loss) income	$	(105,483	)	$	(254,831	)	$	439,673	$	167,354
Denominator
Weighted-average shares outstanding		2,363,349			5,709,500			15,000,000		5,709,500
Basic and diluted net (loss) income per share	$	(0.04	)	$	(0.04	)	$	0.03	$	0.03

Accretion of the carrying value of common stock subject to redemption value is excluded from net (loss) income per common stock because the redemption value approximates fair value.

	For the Three Months Ended March 31,
	2024						2023
	Common stock subject to possible redemption			Common stock			Common stock subject to possible redemption			Common stock
Basic and diluted net (loss) income per share
Numerator:
Allocation of net (loss) income	$	(94,932	)	$	(285,914	)	$	(15,605	)	$	(11,538	)
Denominator
Weighted-average shares outstanding		1,895,714			5,709,500			7,722,273			5,709,500
Basic and diluted net (loss) income per share	$	(0.05	)	$	(0.05	)	$	(0.00	)	$	(0.00	)

	For the Six Months Ended March 31,
	2024						2023
	Common stock subject to possible redemption			Common stock			Common stock subject to possible redemption		Common stock
Basic and diluted net (loss) income per share
Numerator:
Allocation of net (loss) income	$	(201,430	)	$	(539,730	)	$	386,387	$	193,497
Denominator
Weighted-average shares outstanding		2,130,809			5,709,500			11,401,124		5,709,500
Basic and diluted net (loss) income per share	$	(0.09	)	$	(0.09	)	$	0.03	$	0.03

Accretion of the carrying value of common stock subject to redemption value is excluded from net (loss) income per common stock because the redemption value approximates fair value.

	For the Three Months Ended June 30,												For the Nine Months Ended June 30,
	2024						2023						2024						2023
	Common stock subject to possible redemption			Common stock			Common stock subject to possible redemption			Common stock			Common stock subject to possible redemption			Common stock			Common stock subject to possible redemption		Common stock
Basic and diluted net (loss) income    per share
Numerator: Allocation of net (loss)    income, as adjusted	$	(283,071	)	$	(1,140,024	)	$	(212,999	)	$	(346,585	)	$	(539,100	)	$	(1,625,155	)	$	12,296	$	8,004
Denominator:
Basic and diluted weighted average    shares outstanding		1,417,687			5,709,500			3,508,852			5,709,500			1,893,969			5,709,500			8,770,367		5,709,500
Basic and diluted net (loss) income    per share	$	(0.20	)	$	(0.20	)	$	(0.06	)	$	(0.06	)	$	(0.28	)	$	(0.28	)	$	0.00	$	0.00

Accretion of the carrying value of common stock subject to redemption value is excluded from net loss per common stock because the redemption value approximates fair value.

	For The Year Ended September 30,
	2023						2022
	Common stock subject to redemption			Common stock			Common stock subject to redemption			Common stock
Basic and diluted net loss per share
Numerator:
Allocation of net loss	$	(179,201	)	$	(140,949	)	$	(2,624,009	)	$	(998,785	)
Denominator
Weighted-average shares outstanding		7,259,013			5,709,500			15,000,000			5,709,500
Basic and diluted net loss per share	$	(0.02	)	$	(0.02	)	$	(0.17	)	$	(0.17	)