Subscription Agreement Liability	3 Months Ended	6 Months Ended	9 Months Ended
Dec. 31, 2023	Mar. 31, 2024	Jun. 30, 2024
Armada Acquisition Corp I [Member]
Subscription Liability [Line Items]
Subscription Agreement Liability	Note 4 — Subscription Agreement Liability Effective December 12, 2023, the Company and the Sponsor, entered into a subscription agreement (the “Subscription Agreement”) with Polar Multi-Strategy Master Fund (“Polar”), an unaffiliated third party of the Company, pursuant to which Polar agreed to make certain capital contributions (the “Investor Capital Contribution”) from time to time, at the request of the Sponsor, subject to the terms and conditions of the Subscription Agreement, to the Sponsor to meet the Sponsor’s commitment to fund the Company’s working capital needs and extension payments. In exchange for the commitment of Polar to provide the Investor Capital Contribution, (i) the Sponsor will transfer shares of common stock, par value $0.0001 per share, to Polar at the closing of its initial business combination, as further described below; and (ii) the Company and the Sponsor have agreed jointly and severally to return the Investor Capital Contribution to the Investor at the closing of an initial business combination. The maximum aggregate Investor Capital Contribution is $440,000, with an initial Investor Capital Contribution of $110,000 available for drawdown within five (5) business days of the Subscription Agreement and the remaining amount to be available for drawdown in three equal tranches of $110,000 during January, February and March 2024. The initial Investor Capital Contribution of $110,000 has been funded to the Sponsor, on January 16, 2024, the second Investor Capital Contribution of $110,000 was funded to the Sponsor, and on February 13, 2024, the third Investor Capital Contribution of $110,000 was funded to the Sponsor. In exchange for the foregoing commitment of Polar to make the Investor Capital Contributions to the Sponsor, the Company agrees to, or cause the surviving entity following the closing of the Company’s initial business combination to, issue 880,000 shares of Company common stock currently held by the Sponsor in consideration for the amount that has been funded by Polar as of or prior to the closing of an initial business combination (the “Subscription Shares”). The Company or the surviving entity of the business combination shall promptly file a registration statement for resale to register the Subscription Shares after the closing of an initial business combination, but no later than 45 calendar days after the closing of business combination, and cause the registration statement to be declared effective by 150 calendar days after the closing of an initial business combination. The Subscription Shares shall be free from the lockup provisions currently applicable to these shares (for a period of 180 days following the closing of the business combination), provided that the stockholders of the Company shall have approved a proposal to such effect at the stockholders meeting held to approve the initial business combination. In the event that Sponsor or the Company defaults in its obligations under the terms of the Subscription Agreement and in the event that such default continues for a period of five (5) business days following written notice to the Sponsor and Company (the “Default Date”), the Company (or the surviving entity following the De-SPAC Closing) shall immediately issue to Investor 220,000 shares of Company’s Common Stock (the “Default Shares” and together with the Subscription Shares, the “Investor Shares”) on the Default Date and shall issue an additional 220,000 Default Shares on each monthly anniversary of the Default Date thereafter, until the default is cured. If the Company liquidates without consummating an initial business combination, neither the Company nor the Sponsor shall have any further obligation under the Subscription Agreement other than distributing to the Investor any available cash balances in their operating accounts up to the amount of the Investor Capital Contribution (subject to applicable law) excluding any funds held in the Trust Account. The Company accounts for the subscription agreement liability as a bundled transaction with allocation of individual items based on their relative fair values. The fair value of shares issuable under the Subscription Agreement is considered cost of borrowing of the funds lent by the Sponsor upon receipt of the Contributions from the Investor and the net amount is recorded as subscription agreement liability in the Company’s balance sheet. The Company recognized $108,634 of cost of borrowing attributable to the draw under the Subscription Agreement in December 2023. Such cost of borrowing is amortized over the term of the Subscription Agreement and is included in the Company’s statement of operations as interest expense. For the three months ended December 31, 2023, the Company recorded $5,384 of interest expense attributable to the previously recognized cost of borrowing. The net amount of subscription liability is presented as a separate line item in the Company’s balance sheet as of December 31, 2023.	Note 4 — Subscription Agreement Liability Effective December 12, 2023, the Company and the Sponsor entered into a subscription agreement (the “Subscription Agreement”) with Polar Multi-Strategy Master Fund (“Polar”), an unaffiliated third party of the Company, pursuant to which Polar agreed to make certain capital contributions (the “Investor Capital Contribution”) from time to time, at the request of the Sponsor, subject to the terms and conditions of the Subscription Agreement, to the Sponsor to meet the Sponsor’s commitment to fund the Company’s working capital needs and extension payments. In exchange for the commitment of Polar to provide the Investor Capital Contribution, (i) the Sponsor will transfer shares of common stock, par value $0.0001 per share, to Polar at the closing of its initial business combination, as further described below; and (ii) the Company and the Sponsor have agreed jointly and severally to return the Investor Capital Contribution to the Investor at the closing of an initial business combination. The maximum aggregate Investor Capital Contribution is $440,000, with an initial Investor Capital Contribution of $110,000 available for drawdown within five (5) business days of the Subscription Agreement and the remaining amount to be available for drawdown in three equal tranches of $110,000 during January, February and March 2024. On December 19, 2023, the initial Investor Capital Contribution of $110,000 was funded to the Sponsor, on January 16, 2024, the second Investor Capital Contribution of $110,000 was funded to the Sponsor, on February 13, 2024, the third Investor Capital Contribution of $110,000 was funded to the Sponsor, and on March 13, 2024, the fourth and final Investor Capital Contribution of $110,000 was funded to the Sponsor. In exchange for the foregoing commitment of Polar to make the Investor Capital Contributions to the Sponsor, the Company agrees to, or cause the surviving entity following the closing of the Company’s initial business combination to, issue 880,000 shares of Company’s common stock. currently held by the Sponsor in consideration for the amount that has been funded by Polar as of or prior to the closing of an initial business combination (the “Subscription Shares”). The Company or the surviving entity of the business combination shall promptly file a registration statement for resale to register the Subscription Shares after the closing of an initial business combination, but no later than 45 calendar days after the closing of business combination, and cause the registration statement to be declared effective by 150 calendar days after the closing of an initial business combination. The Subscription Shares shall be free from the lockup provisions currently applicable to these shares (for a period of 180 days following the closing of the business combination), provided that the stockholders of the Company shall have approved a proposal to such effect at the stockholders meeting held to approve the initial business combination. In the event that Sponsor or the Company defaults in its obligations under the terms of the Subscription Agreement and in the event that such default continues for a period of five (5) business days following written notice to the Sponsor and Company (the “Default Date”), the Company (or the surviving entity following the De-SPAC Closing) shall immediately issue to Investor 220,000 shares of Company’s Common Stock (the “Default Shares” and together with the Subscription Shares, the “Investor Shares”) on the Default Date and shall issue an additional 220,000 Default Shares on each monthly anniversary of the Default Date thereafter, until the default is cured. If the Company liquidates without consummating an initial business combination, neither the Company nor the Sponsor shall have any further obligation under the Subscription Agreement other than distributing to the Investor any available cash balances in their operating accounts up to the amount of the Investor Capital Contribution (subject to applicable law) excluding any funds held in the Trust Account. The Company accounts for the subscription agreement liability as a bundled transaction with allocation of individual items based on their relative fair values. The fair value of shares issuable under the Subscription Agreement is considered cost of borrowing of the funds lent by the Sponsor upon receipt of the Contributions from the Investor and the net amount is recorded as subscription agreement liability in the Company’s condensed balance sheet. The Company recognized $434,460 of cost of borrowing attributable to the draws under the Subscription Agreement. Such cost of borrowing is amortized over the term of the Subscription Agreement and is included in the Company’s statement of operations as interest expense. For the six months ended March 31, 2024, the Company recorded $124,198 of interest expense attributable to the previously recognized cost of borrowing. The net amount of subscription liability of $129,738 is presented as a separate line item in the Company’s condensed balance sheet as of March 31, 2024.	Note 4 — Subscription Agreements Liability Effective December 12, 2023, the Company and the Sponsor entered into a subscription agreement (the “Subscription Agreement”) with Polar Multi-Strategy Master Fund (“Polar”), an unaffiliated third party of the Company, pursuant to which Polar agreed to make certain capital contributions (the “Investor Capital Contribution”) from time to time, at the request of the Sponsor, subject to the terms and conditions of the Subscription Agreement, to the Sponsor to meet the Sponsor’s commitment to fund the Company’s working capital needs and extension payments. In exchange for the commitment of Polar to provide the Investor Capital Contribution, (i) the Sponsor will transfer shares of common stock, par value $0.0001 per share, to Polar at the closing of its initial business combination, as further described below; and (ii) the Company and the Sponsor have agreed jointly and severally to return the Investor Capital Contribution to the Investor at the closing of an initial business combination. The maximum aggregate Investor Capital Contribution is $440,000, with an initial Investor Capital Contribution of $110,000 available for drawdown within five (5) business days of the Subscription Agreement and the remaining amount to be available for drawdown in three equal tranches of $110,000 during January, February and March 2024. On December 19, 2023, the initial Investor Capital Contribution of $110,000 was funded to the Sponsor, on January 16, 2024, the second Investor Capital Contribution of $110,000 was funded to the Sponsor, on February 13, 2024, the third Investor Capital Contribution of $110,000 was funded to the Sponsor, and on March 13, 2024, the fourth and final Investor Capital Contribution of $110,000 was funded to the Sponsor. In exchange for the foregoing commitment of Polar to make the Investor Capital Contributions to the Sponsor, the Company agrees to, or cause the surviving entity following the closing of the Company’s initial business combination to, issue 880,000 shares of Company’s common stock. In the event that Sponsor or the Company defaults in its obligations under the terms of the Subscription Agreement with Polar and in the event that such default continues for a period of five (5) business days following written notice to the Sponsor and Company (the “Default Date”), the Company (or the surviving entity following the De-SPAC Closing) shall immediately issue to Investor 220,000 shares of Company’s Common Stock (the “Default Shares” and together with the Subscription Shares, the “Investor Shares”) on the Default Date and shall issue an additional 220,000 Default Shares on each monthly anniversary of the Default Date thereafter, until the default is cured. If the Company liquidates without consummating an initial business combination, neither the Company nor the Sponsor shall have any further obligation under the Subscription Agreement other than distributing to the Investor any available cash balances in their operating accounts up to the amount of the Investor Capital Contribution (subject to applicable law) excluding any funds held in the Trust Account. The shares currently held by the Sponsor in consideration for the amount that has been funded by Polar as of or prior to the closing of an initial business combination (the “Subscription Shares”). The Company or the surviving entity of the business combination shall promptly file a registration statement for resale to register the Subscription Shares after the closing of an initial business combination, but no later than 45 calendar days after the closing of business combination, and cause the registration statement to be declared effective by 150 calendar days after the closing of an initial business combination. The Subscription Shares shall be free from the lockup provisions currently applicable to these shares (for a period of 180 days following the closing of the business combination), provided that the stockholders of the Company shall have approved a proposal to such effect at the stockholders meeting held to approve the initial business combination. On April 18, 2024, the Company entered into a subscription agreement with an entity related to the Sponsor pursuant to which (i) the entity funded $33,008 to the Sponsor which is to be returned to the entity by the Sponsor promptly following the closing of the initial business combination and (ii) as an inducement for the investment, the Sponsor allocated 33,000 Founder Shares to the entity. The funds received from the entity were loaned by the Sponsor to the Company. The Company accounts for the subscription agreements liability as a bundled transaction with allocation of individual items based on their relative fair values. The fair value of shares issuable under the Subscription Agreements is considered cost of borrowing of the funds lent by the Sponsor upon receipt of the Contributions from the Investor and the net amount is recorded as subscription agreement liability in the Company’s condensed balance sheet. The Company recognized $462,716 of cost of borrowing attributable to the draws under the Subscription Agreements. Such cost of borrowing is amortized over the term of the Subscription Agreements and is included in the Company’s statement of operations as interest expense. For the nine months ended June 30, 2024, the Company recorded $344,226 of interest expense attributable to the previously recognized cost of borrowing. The net amount of subscription liability of $354,503 is presented as a separate line item in the Company’s condensed balance sheet as of June 30, 2024.

Subscription Agreement Liability

3 Months Ended

6 Months Ended

9 Months Ended

Dec. 31, 2023

Mar. 31, 2024

Jun. 30, 2024

Armada Acquisition Corp I [Member]

Subscription Liability [Line Items]

Subscription Agreement Liability

Note 4 — Subscription Agreement Liability

Effective December 12, 2023, the Company and the Sponsor, entered into a subscription agreement (the “Subscription Agreement”) with Polar Multi-Strategy Master Fund (“Polar”), an unaffiliated third party of the Company, pursuant to which Polar agreed to make certain capital contributions (the “Investor Capital Contribution”) from time to time, at the request of the Sponsor, subject to the terms and conditions of the Subscription Agreement, to the Sponsor to meet the Sponsor’s commitment to fund the Company’s working capital needs and extension payments. In exchange for the commitment of Polar to provide the Investor Capital Contribution, (i) the Sponsor will transfer shares of common stock, par value $0.0001 per share, to Polar at the closing of its initial business combination, as further described below; and (ii) the Company and the Sponsor have agreed jointly and severally to return the Investor Capital Contribution to the Investor at the closing of an initial business combination. The maximum aggregate Investor Capital Contribution is $440,000, with an initial Investor Capital Contribution of $110,000 available for drawdown within five (5) business days of the Subscription Agreement and the remaining amount to be available for drawdown in three equal tranches of $110,000 during January, February and March 2024. The initial Investor Capital Contribution of $110,000 has been funded to the Sponsor, on January 16, 2024, the second Investor Capital Contribution of $110,000 was funded to the Sponsor, and on February 13, 2024, the third Investor Capital Contribution of $110,000 was funded to the Sponsor. In exchange for the foregoing commitment of Polar to make the Investor Capital Contributions to the Sponsor, the Company agrees to, or cause the surviving entity following the closing of the Company’s initial business combination to, issue 880,000 shares of Company common stock currently held by the Sponsor in consideration for the amount that has been funded by Polar as of or prior to the closing of an initial business combination (the “Subscription Shares”). The Company or the surviving entity of the business combination shall promptly file a registration statement for resale to register the Subscription Shares after the closing of an initial business combination, but no later than 45 calendar days after the closing of business combination, and cause the registration statement to be declared effective by 150 calendar days after the closing of an initial business combination. The Subscription Shares shall be free from the lockup provisions currently applicable to these shares (for a period of 180 days following the closing of the business combination), provided that the stockholders of the Company shall have approved a proposal to such effect at the stockholders meeting held to approve the initial business combination.

In the event that Sponsor or the Company defaults in its obligations under the terms of the Subscription Agreement and in the event that such default continues for a period of five (5) business days following written notice to the Sponsor and Company (the “Default Date”), the Company (or the surviving entity following the De-SPAC Closing) shall immediately issue to Investor 220,000 shares of Company’s Common Stock (the “Default Shares” and together with the Subscription Shares, the “Investor Shares”) on the Default Date and shall issue an additional 220,000 Default Shares on each monthly anniversary of the Default Date thereafter, until the default is cured.

If the Company liquidates without consummating an initial business combination, neither the Company nor the Sponsor shall have any further obligation under the Subscription Agreement other than distributing to the Investor any available cash balances in their operating accounts up to the amount of the Investor Capital Contribution (subject to applicable law) excluding any funds held in the Trust Account.

The Company accounts for the subscription agreement liability as a bundled transaction with allocation of individual items based on their relative fair values. The fair value of shares issuable under the Subscription Agreement is considered cost of borrowing of the funds lent by the Sponsor upon receipt of the Contributions from the Investor and the net amount is recorded as subscription agreement liability in the Company’s balance sheet. The Company recognized $108,634 of cost of borrowing attributable to the draw under the Subscription Agreement in December 2023. Such cost of borrowing is amortized over the term of the Subscription Agreement and is included in the Company’s statement of operations as interest expense. For the three months ended December 31, 2023, the Company recorded $5,384 of interest expense attributable to the previously recognized cost of borrowing. The net amount of subscription liability is presented as a separate line item in the Company’s balance sheet as of December 31, 2023.

Note 4 — Subscription Agreement Liability

Effective December 12, 2023, the Company and the Sponsor entered into a subscription agreement (the “Subscription Agreement”) with Polar Multi-Strategy Master Fund (“Polar”), an unaffiliated third party of the Company, pursuant to which Polar agreed to make certain capital contributions (the “Investor Capital Contribution”) from time to time, at the request of the Sponsor, subject to the terms and conditions of the Subscription Agreement, to the Sponsor to meet the Sponsor’s commitment to fund the Company’s working capital needs and extension payments. In exchange for the commitment of Polar to provide the Investor Capital Contribution, (i) the Sponsor will transfer shares of common stock, par value $0.0001 per share, to Polar at the closing of its initial business combination, as further described below; and (ii) the Company and the Sponsor have agreed jointly and severally to return the Investor Capital Contribution to the Investor at the closing of an initial business combination. The maximum aggregate Investor Capital Contribution is $440,000, with an initial Investor Capital Contribution of $110,000 available for drawdown within five (5) business days of the Subscription Agreement and the remaining amount to be available for drawdown in three equal tranches of $110,000 during January, February and March 2024. On December 19, 2023, the initial Investor Capital Contribution of $110,000 was funded to the Sponsor, on January 16, 2024, the second Investor Capital Contribution of $110,000 was funded to the Sponsor, on February 13, 2024, the third Investor Capital Contribution of $110,000 was funded to the Sponsor, and on March 13, 2024, the fourth and final Investor Capital Contribution of $110,000 was funded to the Sponsor. In exchange for the foregoing commitment of Polar to make the Investor Capital Contributions to the Sponsor, the Company agrees to, or cause the surviving entity following the closing of the Company’s initial business combination to, issue 880,000 shares of Company’s common stock. currently held by the Sponsor in consideration for the amount that has been funded by Polar as of or prior to the closing of an initial business combination (the “Subscription Shares”). The Company or the surviving entity of the business combination shall promptly file a registration statement for resale to register the Subscription Shares after the closing of an initial business combination, but no later than 45 calendar days after the closing of business combination, and cause the registration statement to be declared effective by 150 calendar days after the closing of an initial business combination. The Subscription Shares shall be free from the lockup provisions currently applicable to these shares (for a period of 180 days following the closing of the business combination), provided that the stockholders of the Company shall have approved a proposal to such effect at the stockholders meeting held to approve the initial business combination.

The Company accounts for the subscription agreement liability as a bundled transaction with allocation of individual items based on their relative fair values. The fair value of shares issuable under the Subscription Agreement is considered cost of borrowing of the funds lent by the Sponsor upon receipt of the Contributions from the Investor and the net amount is recorded as subscription agreement liability in the Company’s condensed balance sheet. The Company recognized $434,460 of cost of borrowing attributable to the draws under the Subscription Agreement. Such cost of borrowing is amortized over the term of the Subscription Agreement and is included in the Company’s statement of operations as interest expense. For the six months ended March 31, 2024, the Company recorded $124,198 of interest expense attributable to the previously recognized cost of borrowing. The net amount of subscription liability of $129,738 is presented as a separate line item in the Company’s condensed balance sheet as of March 31, 2024.

Note 4 — Subscription Agreements Liability

In the event that Sponsor or the Company defaults in its obligations under the terms of the Subscription Agreement with Polar and in the event that such default continues for a period of five (5) business days following written notice to the Sponsor and Company (the “Default Date”), the Company (or the surviving entity following the De-SPAC Closing) shall immediately issue to Investor 220,000 shares of Company’s Common Stock (the “Default Shares” and together with the Subscription Shares, the “Investor Shares”) on the Default Date and shall issue an additional 220,000 Default Shares on each monthly anniversary of the Default Date thereafter, until the default is cured.

The shares currently held by the Sponsor in consideration for the amount that has been funded by Polar as of or prior to the closing of an initial business combination (the “Subscription Shares”). The Company or the surviving entity of the business combination shall promptly file a registration statement for resale to register the Subscription Shares after the closing of an initial business combination, but no later than 45 calendar days after the closing of business combination, and cause the registration statement to be declared effective by 150 calendar days after the closing of an initial business combination. The Subscription Shares shall be free from the lockup provisions currently applicable to these shares (for a period of 180 days following the closing of the business combination), provided that the stockholders of the Company shall have approved a proposal to such effect at the stockholders meeting held to approve the initial business combination.

On April 18, 2024, the Company entered into a subscription agreement with an entity related to the Sponsor pursuant to which (i) the entity funded $33,008 to the Sponsor which is to be returned to the entity by the Sponsor promptly following the closing of the initial business combination and (ii) as an inducement for the investment, the Sponsor allocated 33,000 Founder Shares to the entity. The funds received from the entity were loaned by the Sponsor to the Company.

The Company accounts for the subscription agreements liability as a bundled transaction with allocation of individual items based on their relative fair values. The fair value of shares issuable under the Subscription Agreements is considered cost of borrowing of the funds lent by the Sponsor upon receipt of the Contributions from the Investor and the net amount is recorded as subscription agreement liability in the Company’s condensed balance sheet. The Company recognized $462,716 of cost of borrowing attributable to the draws under the Subscription Agreements. Such cost of borrowing is amortized over the term of the Subscription Agreements and is included in the Company’s statement of operations as interest expense. For the nine months ended June 30, 2024, the Company recorded $344,226 of interest expense attributable to the previously recognized cost of borrowing. The net amount of subscription liability of $354,503 is presented as a separate line item in the Company’s condensed balance sheet as of June 30, 2024.