Exhibit 10.4

PRIVATE PLACEMENT UNIT SUBSCRIPTION AGREEMENT

This PRIVATE PLACEMENT UNIT SUBSCRIPTION AGREEMENT (this “Agreement”) is made as of the [x] day of [x] 2026, by and between Armada Acquisition Corp. III, a Cayman Islands exempted company (the “Company”), having its principal place of business at 1760 Market Street, Suite 602, Philadelphia, Pennsylvania 19103, and Cohen & Company Capital Markets, a division of Cohen & Company Securities, LLC (the “Purchaser”).

WHEREAS, the Company desires to sell to the Purchaser on a private placement basis (the “Offering”) an aggregate of [x] units (the “Initial Units”) of the Company, each Initial Unit comprised of one Class A ordinary share of the Company, par value $0.0001 per share, and one-half of one redeemable warrant (the “Warrants”), each whole Warrant entitling the holder thereof to purchase one Class A ordinary share (the “Warrant Shares”) at a price of $11.50 per share, to be governed by the Warrant Agreement (as defined herein), for an aggregate purchase price of $[x], or $10.00 per Initial Unit, and up to [x] additional units (“the Additional Units” and together with the Initial Units, the “Units”), each Additional Unit comprised of one Class A ordinary share and one-half of one Warrant, for an aggregate purchase price of $[x], or $10.00 per Additional Unit. As provided in the Registration Statement (as defined below), the Warrants are exercisable during the period commencing on the later of the consummation of the Company’s initial Business Combination (as defined below) and 12 months after the closing of the IPO (as defined below) and will expire on the fifth anniversary of the consummation of the Business Combination (provided that so long as the Private Warrants are held by the Purchaser or its designees, the Purchaser or its designees will not be permitted to exercise such Warrants after the five year anniversary of the commencement of sales in the IPO in accordance with FINRA Rule 5110(g)(8)).

WHEREAS, the Purchaser desires to purchase the Units on the terms and conditions set forth herein and the Company wishes to accept such subscription.

NOW, THEREFORE, in consideration of the promises and the mutual covenants hereinafter set forth and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Company and the Purchaser hereby agree as follows:

1 Agreement to Subscribe

1.1 Purchase and Issuance of the Initial Units. For the aggregate sum of $[x] (the “Purchase Price”), upon the terms and subject to the conditions of this Agreement, the Purchaser hereby agrees to purchase from the Company, and the Company hereby agrees to sell to the Purchaser, on the Closing Date (as defined in Section 1.2) [x] Initial Units at $10.00 per Initial Unit.

In addition to the foregoing, the Purchaser hereby agrees to purchase up to an additional [x] Additional Units at $10.00 per Additional Unit for an aggregate purchase price of $[x] (the “Additional Purchase Price” and together with the Initial Purchase Price, the “Purchase Price”). The purchase and issuance of the Additional Units shall occur only in the event that the underwriters’ 45-day over-allotment option (“Over-Allotment Option”) in the IPO is exercised in full or part. The total number of Additional Units to be purchased hereunder shall be in the same proportion as the amount of the Over-Allotment Option that is exercised. Each purchase of Additional Units shall occur simultaneously with the consummation of any portion of the Over-Allotment Option.

1.2 Closing. The closing (the “Closing”) of the Offering shall take place by electronic exchange of executed documents simultaneously with the consummation of the Company’s initial public offering (“IPO”) and the consummation of the exercise of all or any portion of the Over-Allotment Option, as applicable (each a “Closing Date”).

1.3 Delivery of the Purchase Price. The Initial Purchase Price or the Additional Purchase Price, as applicable, shall be paid by wire transfer of immediately available funds or by such other method as may be reasonably acceptable to the Company, to the trust account (the “Trust Account”) at a financial institution chosen by the Company, maintained by Continental Stock Transfer & Trust Company, a New York corporation (“Continental”), as trustee, on or prior to each Closing Date.

1.4 Delivery of the Units. Upon the applicable Closing Date after delivery of the Purchase Price in accordance with Section 1.3, the Purchaser shall become irrevocably entitled to receive the Units purchased hereunder.

2 Representations and Warranties of the Purchaser

The Purchaser hereby represents and warrants to the Company that:

2.1 No Government Recommendation or Approval. It understands that no United States federal or state agency or similar agency of any other country has passed upon or made any recommendation or endorsement of the Company, the Offering, the Units, the Warrants, the Warrant Shares, or the Class A ordinary shares underlying the Units (excluding the Warrant Shares, the “Unit Shares” and, collectively with the Units, the Warrants, and the Warrant Shares, the “Securities”).

2.2 Organization. It is a company, validly existing and in good standing under the laws of its jurisdiction and possesses all requisite power and authority necessary to carry out the transactions contemplated by this Agreement.

2.3 Private Offering. It is an “accredited investor” as such term is defined in Rule 501(a) of Regulation D under the Securities Act of 1933, as amended (the “Securities Act”) or it is not a “U.S. Person” as defined in Rule 902 of Regulation S (“Regulation S”) under the Securities Act. It acknowledges that the sale contemplated hereby is being made in reliance on a private placement exemption to “Accredited Investors” within the meaning of Section 501(a) of Regulation D under the Securities Act and similar exemptions under state law or a non-U.S. Person under Regulation S.

2.4 Authority. This Agreement has been validly authorized, executed and delivered by the Purchaser and is a valid and binding agreement enforceable in accordance with its terms, except as such enforceability may be limited by applicable bankruptcy, insolvency, fraudulent conveyance or similar laws affecting the enforcement of creditors’ rights generally and subject to general principles of equity (regardless of whether enforcement is sought in a proceeding at law or in equity).

2.5 No Conflicts. The execution, delivery and performance of this Agreement and the consummation by the Purchaser of the transactions contemplated hereby do not violate, conflict with or constitute a default under (i) the Purchaser’s organizational documents, (ii) any agreement, indenture or instrument to which the Purchaser is a party or (iii) any law, statute, rule or regulation to which the Purchaser is subject, or any agreement, order, judgment or decree to which the Purchaser is subject.

2.6 No Legal Advice from Company. It acknowledges it has had the opportunity to review this Agreement and the transactions contemplated by this Agreement and the other agreements entered into between the parties hereto with its own legal counsel and investment and tax advisors. Except for any statements or representations of the Company made in this Agreement and the other agreements entered into between the parties hereto, it is relying solely on such counsel and advisors and not on any statements or representations of the Company or any of its representatives or agents for legal, tax or investment advice with respect to this investment, the transactions contemplated by this Agreement or the securities laws of any jurisdiction.

2.7 Access to Information; Independent Investigation. Prior to the execution of this Agreement, it has had the opportunity to ask questions of and receive answers from representatives of the Company concerning an investment in the Company, as well as the finances, operations, business and prospects of the Company, and the opportunity to obtain additional information to verify the accuracy of all information so obtained. In determining whether to make this investment, it has relied solely on its own knowledge and understanding of the Company and its business based upon its own due diligence investigation and the information furnished pursuant to this paragraph. It understands that no person has been authorized to give any information or to make any representations which were not furnished pursuant to this Section 2 and it has not relied on any other representations or information in making its investment decision, whether written or oral, relating to the Company, its operations and/or its prospects.

2.8 Reliance on Representations and Warranties. It understands the Units are being offered and sold to it in reliance on exemptions from the registration requirements under the Securities Act, and analogous provisions in the laws and regulations of various states, and that the Company is relying upon the truth and accuracy of the representations, warranties, agreements, acknowledgments and understandings of the Purchaser set forth in this Agreement in order to determine the applicability of such provisions.

2.9 No Advertisements. It is not subscribing for the Units as a result of or subsequent to any advertisement, article, notice or other communication published in any newspaper, magazine, or similar media or broadcast over television or radio, or presented at any seminar or meeting.

2.10 Legend. It acknowledges and agrees the certificates evidencing the Securities shall bear a restrictive legend (the “Legend”), in form and substance as set forth in Section 4 hereof, prohibiting the offer, sale, pledge or transfer of the securities, except (i) pursuant to an effective registration statement covering these securities under the Securities Act or (ii) pursuant to any other exemptions from the registration requirements under the Securities Act and such laws which, in the opinion of counsel for the Company, is available.

2.11 Experience, Financial Capability and Suitability. It is (i) sophisticated in financial matters and is able to evaluate the risks and benefits of the investment in the Securities and (ii) able to bear the economic risk of his investment in the Securities for an indefinite period of time because the Securities have not been registered under the Securities Act and therefore cannot be sold unless subsequently registered under the Securities Act or an exemption from such registration is available. It has substantial experience in evaluating and investing in transactions of securities in companies similar to the Company so that it is capable of evaluating the merits and risks of its investment in the Company and has the capacity to protect its own interests. It has substantial experience in evaluating and investing in transactions of securities in companies similar to the Company so that it is capable of evaluating the merits and risks of its investment in the Company and has the capacity to protect its own interests.

2.12 Investment Purposes. It is purchasing the Securities solely for investment purposes, for its own account and not for the account or benefit of any other person, and not with a view towards the distribution or dissemination thereof and it has no present arrangement to sell the interest in the Securities to or through any person or entity. It shall not engage in hedging transactions with regard to the Securities unless in compliance with the Securities Act.

2.13 Restrictions on Transfer. It acknowledges and understands the Units are being offered in a transaction not involving a public offering in the United States within the meaning of the Securities Act. The Securities have not been registered under the Securities Act, and, if in the future, it decides to offer, resell, pledge or otherwise transfer the Securities, such Securities may be offered, resold, pledged or otherwise transferred only (A) pursuant to an effective registration statement filed under the Securities Act, (B) pursuant to an exemption from registration under Rule 144 promulgated under the Securities Act (“Rule 144”), if available, or (C) pursuant to any other available exemption from the registration requirements of the Securities Act, and in each case in accordance with any applicable securities laws of any state or any other jurisdiction. It agrees that if any transfer of its Securities or any interest therein is proposed to be made, as a condition precedent to any such transfer, it may be required to deliver to the Company an opinion of counsel satisfactory to the Company. Absent registration or another available exemption from registration, it agrees it will not resell the Securities. It further acknowledges that because the Company is a shell company, Rule 144 may not be available to it for the resale of the Securities until the one-year anniversary following consummation of the initial Business Combination of the Company, despite technical compliance with the requirements of Rule 144 and the release or waiver of any contractual transfer restrictions.

3 Representations and Warranties of the Company

The Company represents and warrants to the Purchaser that:

3.1 Valid Issuance of Share Capital. The total number of all classes of share capital which the Company has authority to issue is 200,000,000 Class A ordinary shares of a par value of US$0.0001 each, 20,000,000 Class B ordinary shares of a par value of US$0.0001 each and 1,000,000 preference shares of a par value of US$0.0001 each. As of the date hereof, the Company has issued 8,852,917 Class B ordinary shares (of which 1,136,250 Class B ordinary shares are subject to forfeiture as described in the Registration Statement relating to the IPO (the “Registration Statement”)) to the Company’s sponsor. As of the date hereof, no preferred shares are issued and outstanding. All of the issued share capital of the Company has been duly authorized, validly issued, and are fully paid and non-assessable.

3.2 Title to Securities. Upon issuance in accordance with, and payment pursuant to, the terms hereof and the warrant agreement to be entered into with Continental on or prior to the closing of the IPO (the “Warrant Agreement”) and the amended and restated memorandum and articles of association of the Company (as applicable), as the case may be, each of the Securities will be duly and validly issued, fully paid and non-assessable. On the date of issuance of the Units, the Warrant Shares shall have been reserved for issuance. Upon issuance in accordance with, and the payment pursuant to, the terms hereof, and the Warrant Agreement, the Purchaser will have or receive good title to the Warrant Shares, free and clear of all liens, claims and encumbrances of any kind other than transfer restrictions under federal and state securities laws.

3.3 Organization and Qualification. The Company has been duly incorporated and is validly existing as a Cayman Islands exempted company and has the requisite corporate power to own its properties and assets and to carry on its business as now being conducted.

3.4 Authorization; Enforcement. (i) The Company has the requisite corporate power and authority to enter into and perform its obligations under this Agreement and to issue the Securities in accordance with the terms hereof, (ii) the execution, delivery and performance of this Agreement by the Company and the consummation by it of the transactions contemplated hereby have been duly authorized by all necessary corporate action and no further consent or authorization of the Company or its Board of Directors or shareholders is required, and (iii) this Agreement constitutes, and upon the execution and delivery thereof, the Warrants and Warrant Agreement, will constitute, valid and binding obligations of the Company enforceable against the Company in accordance with their respective terms, except as such enforceability may be limited by applicable bankruptcy, insolvency, fraudulent conveyance, moratorium, reorganization, or similar laws relating to, or affecting generally the enforcement of, creditors’ rights and remedies or by equitable principles of general application and except as enforcement of rights to indemnity and contribution may be limited by federal and state securities laws or principles of public policy.

3.5 No Conflicts. The execution, delivery and performance of this Agreement and the consummation by the Company of the transactions contemplated hereby do not (i) result in a violation of the Company’s amended and restated memorandum and articles of association, (ii) conflict with, or constitute a default under any agreement, indenture or instrument to which the Company is a party or (iii) conflict with any law statute, rule or regulation to which the Company is subject or any agreement, order, judgment or decree to which the Company is subject. Other than any federal, state or foreign securities filings which may be required to be made by the Company subsequent to the Closing, and any registration statement which may be filed pursuant thereto, the Company is not required under federal, state or local law, rule or regulation to obtain any consent, authorization or order of, or make any filing or registration with, any court or governmental agency or self-regulatory entity in order for it to perform any of its obligations under this Agreement or issue the Securities in accordance with the terms hereof.

4 Legends

4.1 Legend. The Company will issue the Units, the Warrants and the Unit Shares, and when issued, the Warrant Shares purchased by the Purchaser, in the name of the Purchaser. The Securities will bear the following Legend and appropriate “stop transfer” instructions:

THESE SECURITIES (i) HAVE NOT BEEN REGISTERED UNDER THE UNITED STATES SECURITIES ACT OF 1933, AS AMENDED (THE “SECURITIES ACT”), AND THESE SECURITIES MAY NOT BE OFFERED, SOLD, PLEDGED OR OTHERWISE TRANSFERRED EXCEPT (A) PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT FILED UNDER THE SECURITIES ACT, (B) TO A NON-U.S. PERSON IN AN OFFSHORE TRANSACTION IN ACCORDANCE WITH RULE 903 OR RULE 904 OF REGULATION S UNDER THE SECURITIES ACT, (C) PURSUANT TO THE RESALE LIMITATIONS SET FORTH IN RULE 905 OF REGULATION S UNDER THE SECURITIES ACT, (D) PURSUANT TO AN EXEMPTION FROM REGISTRATION PROVIDED BY RULE 144 UNDER THE SECURITIES ACT (IF AVAILABLE) OR (E) PURSUANT TO ANY OTHER EXEMPTION FROM THE REGISTRATION REQUIREMENTS OF THE SECURITIES ACT, IN EACH CASE IN ACCORDANCE WITH ANY APPLICABLE SECURITIES LAWS OF ANY STATE OF THE UNITED STATES OR ANY OTHER JURISDICTION. HEDGING TRANSACTIONS INVOLVING THESE SECURITIES MAY NOT BE CONDUCTED UNLESS IN COMPLIANCE WITH THE SECURITIES ACT. THESE SECURITIES ARE DEEMED UNDERWRITERS’ COMPENSATION BY THE FINANCIAL INDUSTRY REGULATORY AUTHORITY (“FINRA”) AND ARE SUBJECT TO LIMITATIONS IN ACCORDANCE WITH FINRA RULE 5110.

“THE SECURITIES REPRESENTED BY THIS CERTIFICATE ARE SUBJECT TO AN AGREEMENT BETWEEN ARMADA ACQUISITION CORP. III AND COHEN & COMPANY CAPITAL MARKETS, A DIVISION OF COHEN & COMPANY SECURITIES, LLC, AND MAY ONLY BE OFFERED, SOLD, TRANSFERRED, PLEDGED OR OTHERWISE DISPOSED OF DURING THE TERM OF THE LOCKUP PURSUANT TO THE TERMS SET FORTH THEREIN.”

4.2 Purchaser’s Compliance. Nothing in this Section 4 shall affect in any way the Purchaser’s obligations and agreements to comply with all applicable securities laws upon resale of the Securities.

4.3 Company’s Refusal to Register Transfer of the Securities. The Company shall refuse to register any transfer of the Securities, if in the sole judgment of the Company such purported transfer would not be made (i) pursuant to an effective registration statement filed under the Securities Act, or (ii) pursuant to an available exemption from the registration requirements of the Securities Act and applicable state securities laws and (iii) in compliance herewith.

4.4 Registration Rights. The Purchaser will be entitled to certain registration rights which will be governed by a registration rights agreement (“Registration Rights Agreement”) to be entered into with the Company on or prior to the closing of the IPO.

5 Lockup

The Purchaser acknowledges and agrees that the Securities shall not be transferable, saleable or assignable until thirty (30) days after the consummation of an acquisition, share exchange, purchase of all or substantially all of the assets of, or any other similar business combination with one or more businesses or entities (a “Business Combination”), except (a)(i) to the Company’s sponsor’s members, (ii) the directors or officers of the Company, the Company’s sponsor, the Company’s sponsor’s members or the Purchaser, (iii) any affiliates or family members of the directors or officers of the Company, the Company’s sponsor, the Company’s sponsor’s members or the Purchaser, (iv) any members or partners of the Company’s sponsor, the Company’s sponsor’s members, the Purchaser or their respective affiliates, or any affiliates of the Company’s sponsor, the Company’s sponsor’s members, the Purchaser, or any employees of such affiliates; (b) in the case of an individual, by gift to a member of the individual’s immediate family, or to a trust, the beneficiary of which is a member of the individual’s immediate family, an affiliate of such person, or to a charitable organization; (c) in the case of an individual, by virtue of laws of descent and distribution upon death of the individual; (d) in the case of an individual, pursuant to a qualified domestic relations order; (e) in the case of a trust by distribution to one or more permissible beneficiaries of such trust; (f) by private sales or transfers made in connection with any forward purchase agreement or similar arrangement or in connection with the consummation of the Company’s Business Combination at prices no greater than the price at which the securities were originally purchased; (g) to the Company for no value for cancellation in connection with the consummation of an initial Business Combination; or (h) in the event of the Company’s liquidation prior to the Company’s completion of an initial business combination; (i) by virtue of the laws of the State of Delaware, pursuant to the Company’s sponsor’s limited liability company agreement, upon dissolution of such sponsor, or the organizational documents of the Purchaser upon dissolution of the Purchaser; or (j) in the event of the Company’s completion of a liquidation, merger, share exchange, reorganization or other similar transaction which results in all of the Company’s shareholders having the right to exchange their Class A ordinary shares for cash, securities or other property subsequent to the completion of the Company’s initial Business Combination; provided, however, that in the case of clauses (a) through (f) these permitted transferees must enter into a written agreement agreeing to be bound by these transfer restrictions. The Purchaser acknowledges that the Units and the related registration rights will be deemed compensation by the Financial Industry Regulatory Authority (“FINRA”) and will therefore, pursuant to Rule 5110(e) of the FINRA Manual, be subject to lock-up for a period of 180 days immediately following the commencement of sales in the IPO, subject to certain limited exceptions to permitted transferees hereunder and in accordance with FINRA Rule 5110(e)(2)(B).

6 Securities Laws Restrictions

The Purchaser agrees not to sell, transfer, pledge, hypothecate or otherwise dispose of all or any part of the Securities unless, prior thereto (a) a registration statement on the appropriate form under the Securities Act and applicable state securities laws with respect to the Securities proposed to be transferred shall then be effective or (b) the Company shall have received an opinion from counsel reasonably satisfactory to the Company, that such registration is not required because such transaction complies with the Securities Act and the rules promulgated by the Securities and Exchange Commission thereunder and with all applicable state securities laws.

7 Waiver of Redemption Rights

In connection with the Securities purchased pursuant to this Agreement, the Purchaser hereby waives any and all redemption rights (i) in connection with the Company’s completion of the Business Combination, (ii) upon the Company’s failure to complete the Business Combination within 18 months from the completion of the IPO or the liquidation of the Company prior to the expiration of such 18 month period or (iii) if the Company seeks an amendment to its amended and restated memorandum and articles of association (x) in a manner that would affect the substance or timing of the Company’s obligation to redeem 100% of the Public Shares (as defined below) or (y) with respect to any other material provision relating to the rights of holders of the Company’s Class A ordinary shares or pre-initial business combination activity. In the event the Purchaser purchases ordinary shares in the IPO or in the aftermarket (“Public Shares”), such Purchase shall be eligible to redeem any Public Shares upon the same terms offered to all other holders of ordinary shares purchased in the IPO.

8 Rescission Right Waiver and Indemnification

8.1 Rescission Waiver. The Purchaser understands and acknowledges that an exemption from the registration requirements of the Securities Act requires there be no general solicitation of purchasers of the Units. In this regard, if the Offering were deemed to be a general solicitation with respect to the Units, the offer and sale of such Units may not be exempt from registration and, if not, the Purchaser may have a right to rescind its purchase of the Units. In order to facilitate the completion of the Offering and in order to protect the Company, its shareholders and the Trust Account from claims that may adversely affect the Company or the interests of its shareholders, the Purchaser hereby agrees to waive, to the maximum extent permitted by applicable law, any claims, right to sue or rights in law or arbitration, as the case may be, to seek rescission of its purchase of the Units as a result of the issuance of the Units being deemed to be in violation of Section 5 of the Securities Act. The Purchaser acknowledges and agrees this waiver is being made in order to induce the Company to sell the Units to the Purchaser. The Purchaser agrees the foregoing waiver of rescission rights shall apply to any and all known or unknown actions, causes of action, suits, claims or proceedings (collectively, “Claims”) and related losses, costs, penalties, fees, liabilities and damages, whether compensatory, consequential or exemplary, and expenses in connection therewith, including reasonable attorneys’ and expert witness fees and disbursements and all other expenses reasonably incurred in investigating, preparing or defending against any Claims, whether pending or threatened, in connection with any present or future actual or asserted right to rescind the purchase of the Units hereunder or relating to the purchase of the Units and the transactions contemplated hereby.

8.2 No Recourse Against Trust Account. The Purchaser agrees not to seek recourse against the Trust Account for any reason whatsoever in connection with its purchase of the Units or any Claim that may arise now or in the future, provided that nothing herein shall preclude Purchaser from making any Claim or seeking recourse against the funds held outside of the Trust Account or seeking payment of any deferred underwriting fee due and payable pursuant to the underwriting agreement between the Company, Cohen & Company Capital Markets, a division of Cohen & Company Securities, LLC and Northland Securities, Inc. as representatives of the underwriters, in connection with the IPO.

8.3 Section 8 Waiver. The Purchaser agrees that to the extent any waiver of rights under this Section 8 is ineffective as a matter of law, the Purchaser has offered such waiver for the benefit of the Company as an equitable right that shall survive any statutory disqualification or bar that applies to a legal right. The Purchaser acknowledges the receipt and sufficiency of consideration received from the Company hereunder in this regard.

9 Terms of the Units

The Units purchased pursuant to this Agreement shall be substantially identical to the Units offered in the IPO except that the Units purchased pursuant to this Agreement (including the Class A ordinary shares and Warrants comprising such Units and the Warrant Shares) (i) will be subject to the transfer restrictions described herein; (ii) will be entitled to registration rights; (iii) with respect to the Warrants underlying the Units purchased to this Agreement, may not be exercisable more than five years from the commencement of sales in the IPO in accordance with FINRA Rule 5110(g)(8); and (iv) are being purchased pursuant to an exemption from the registration requirements of the Securities Act and will become freely tradable only after certain conditions are met or the resale of the Units is registered under the Securities Act.

10 Governing Law; Jurisdiction; Waiver of Jury Trial

This Agreement shall be governed by and construed in accordance with the laws of the State of New York for agreements made and to be wholly performed within such territory. The parties hereto hereby waive any right to a jury trial in connection with any litigation pursuant to this Agreement and the transactions contemplated hereby.

11 Assignment; Entire Agreement; Amendment

11.1 Assignment. Neither this Agreement nor any rights hereunder may be assigned by any party to any other person other than by the Purchaser, without the prior consent of the Company, to one or more persons agreeing to be bound by the terms hereof. Upon such assignment by a Purchaser, the assignee(s) shall become Purchaser hereunder and have the rights and obligations provided for herein to the extent of such assignment.

11.2 Entire Agreement. This Agreement sets forth the entire agreement and understanding between the parties as to the subject matter hereof and supersedes any and all prior discussions, agreements and understandings of any and every nature.

11.3 Amendment. Except as expressly provided in this Agreement, neither this Agreement nor any term hereof may be amended, waived, discharged or terminated other than by a written instrument signed by the party against whom enforcement of any such amendment, waiver, discharge or termination is sought.

11.4 Binding upon Successors. This Agreement shall be binding upon and inure to the benefit of the parties hereto and to their respective heirs, legal representatives, successors and permitted assigns.

12 Notices; Indemnity

12.1 Notices. All notices, requests, consents and other communications hereunder shall be in writing, shall be addressed to the receiving party’s address set forth on the signature page hereto or to such other address as a party may designate by notice hereunder, and shall be either (a) delivered by hand, (b) sent by overnight courier, or (c) sent by certified mail, return receipt requested, postage prepaid. All notices, requests, consents and other communications hereunder shall be deemed to have been given either (i) if by hand, at the time of the delivery thereof to the receiving party at the address of such party set forth above, (ii) if sent by overnight courier, on the next business day following the day such notice is delivered to the courier service, or (iii) if sent by certified mail, on the fifth business day following the day such mailing is made.

12.2 Indemnification. Subject to Section 8, each party shall indemnify the other party against any loss, cost or damages (including reasonable attorney’s fees and expenses) incurred as a result of such party’s breach of any representation, warranty, covenant or agreement set forth in this Agreement.

13 Counterparts

This Agreement may be executed in one or more counterparts, all of which when taken together shall be considered one and the same agreement and shall become effective when counterparts have been signed by each party and delivered to the other party, it being understood that both parties need not sign the same counterpart. In the event that any signature is delivered by facsimile transmission or any other form of electronic delivery, such signature shall create a valid and binding obligation of the party executing (or on whose behalf such signature is executed) with the same force and effect as if such signature page were an original thereof.

14 Survival; Severability

14.1 Survival. The representations, warranties, covenants and agreements of the parties hereto shall survive the Closing until one (1) year following the consummation of an initial Business Combination.

14.2 Severability. In the event that any provision of this Agreement becomes or is declared by a court of competent jurisdiction to be illegal, unenforceable or void, this Agreement shall continue in full force and effect without said provision; provided that no such severability shall be effective if it materially changes the economic benefit of this Agreement to any party.

15 Headings

The titles and subtitles used in this Agreement are used for convenience only and are not to be considered in construing or interpreting this Agreement.

16 Construction

The parties hereto have participated jointly in the negotiation and drafting of this Agreement. If an ambiguity or question of intent or interpretation arises, this Agreement will be construed as if drafted jointly by the parties hereto and no presumption or burden of proof will arise favoring or disfavoring any party hereto because of the authorship of any provision of this Agreement. The words “include,” “includes,” and “including” will be deemed to be followed by “without limitation.” Pronouns in masculine, feminine, and neuter genders will be construed to include any other gender, and words in the singular form will be construed to include the plural and vice versa, unless the context otherwise requires. The words “this Agreement,” “herein,” “hereof,” “hereby,” “hereunder,” and words of similar import refer to this Agreement as a whole and not to any particular subdivision unless expressly so limited. The parties hereto intend that each representation, warranty, and covenant contained herein will have independent significance. If any party hereto has breached any representation, warranty, or covenant contained herein in any respect, the fact that there exists another representation, warranty or covenant relating to the same subject matter (regardless of the relative levels of specificity) which such party hereto has not breached will not detract from or mitigate the fact that such party hereto is in breach of the first representation, warranty, or covenant.

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This subscription is accepted by the Company as of the date first written above.


Armada Acquisition Corp. III

By:
Name:		Stephen P. Herbert
Title:		Chief Executive Officer

Accepted and agreed this
[x] day of [x], 2026

Cohen & Company Capital Markets, a division of Cohen & Company Securities, LLC



By:
Name:		Jerry Serowik
Title:		Senior Managing Director
Address:		Cohen & Company Capital Markets,
		a division of Cohen & Company Securities, LLC
		3 Columbus Circle, 24th Floor
		New York, NY 10019

[Signature Page to Private Placement Unit Subscription Agreement (Cohen)]

Armada Acquisition Corp. III S-1/A