EX-10.2




 Exhibit 10.2 

BACKSTOP SUBSCRIPTION AGREEMENT 

GigCapital4, Inc. 
 1731 Embarcadero Road, Suite 200 

Palo Alto, CA 94303 
 Ladies and Gentlemen: 

In connection with the proposed business combination (the “Transaction”) between GigCapital4, Inc., a Delaware corporation
(the “Company”), and BigBear.ai Holdings, LLC, a Delaware limited liability company (formerly known as Lake Intermediate, LLC) (“BigBear”), pursuant to an Agreement and Plan of Merger (as amended, the
“Merger Agreement”) entered into among the Company, GigCapital4 Merger Sub Corporation, a Delaware corporation and wholly owned subsidiary of the Company (“Merger Sub”), BigBear and BBAI Ultimate Holdings, LLC, a
Delaware limited liability company (formerly known as PCISM Ultimate Holdings, LLC) (“BBAI”), whereby, among other things, (a) Merger Sub will merge with and into BigBear (the “First Merger”), with BigBear as
the surviving company in the First Merger and (b) immediately following the First Merger, BigBear will merge with and into the Company (the “Second Merger”), with the Company as the surviving company in the Second Merger. The
Company is seeking, and AE BBAI Aggregator, LP, a Delaware limited partnership (the “Investor”) desires to make, a commitment to purchase, prior to the closing of the Transaction, shares of the Company’s common stock, par value
$0.0001 per share (the “Shares”), in a private placement for a purchase price of $10.00 per share. Capitalized terms used but not otherwise defined herein shall have the meaning ascribed to them in the Merger Agreement. 

In connection therewith, and in consideration of the foregoing and the mutual representations, warranties and covenants, and subject to the
conditions, set forth herein, and intending to be legally bound hereby, the Investor and the Company agree as follows: 
 1.
Subscription. The Investor hereby irrevocably subscribes for and agrees to purchase from the Company, on the terms provided for herein, an aggregate number of Shares equal to the result of (a) the difference between (i) $75,000,000,
minus (ii) Available Closing Company Cash, divided by (b) $10.00, rounded up to the next whole number of Shares (the “Subscribed Shares”). The aggregate purchase price to be paid by the Investor for the Subscribed
Shares shall be an amount equal to the product of (x) the number of Subscribed Shares, multiplied by (y) $10.00 (the “Subscription Amount”). For the avoidance of doubt, in no event shall the Subscription Amount exceed
$75,000,000 or be less than $0. For purposes hereof, “Available Closing Company Cash” means an amount equal to (i) all amounts in the Trust Account (after reduction for the aggregate amount of payments required to be made in
connection with the Acquiror Stockholder Redemption and excluding, for the avoidance of doubt, the total amount allocated to satisfy the Company’s obligations pursuant to those certain Forward Share Purchase Agreements, by and between the
Company and each of (1) Glazer Capital, LLC and Meteora Capital LLC, on behalf of itself and its affiliated investment funds, (2) Highbridge Tactical Credit Master Fund, L.P. and Highbridge SPAC Opportunity Fund, L.P., and (3) Tenor
Opportunity Master Fund, Ltd. (in each case, whether such amount is in escrow or otherwise), plus (ii) $200,000,000 (representing the aggregate amount required to be funded to the Company pursuant to the Note Subscription Agreements),
minus (iii) the aggregate amount of Indebtedness of BigBear and its Subsidiaries required to be repaid upon the consummation of the Transaction, minus (iv) the aggregate amount of Company Transaction Expenses and Acquiror
Transaction Expenses (including any deferred underwriting fees) that are required to be paid upon the consummation of the Transaction, minus (v) the Cash Merger Consideration, plus (vi) the aggregate amount of cash and cash
equivalents of Big Bear and its Subsidiaries as of immediately prior to the consummation of the Transaction. 
 2. Closing. The
closing of the sale of the Shares contemplated hereby (the “Closing” and the date on which the Closing occurs, the “Closing Date”) shall occur on the date of, and is contingent upon the substantially concurrent
consummation of, the Transaction and the satisfaction or waiver of the conditions set forth in Section 3 below. On the Closing Date, the Investor shall deliver to the Company the Subscription Amount by wire transfer of
immediately available funds. On the Closing Date, the Company shall issue the Shares to the Investor and subsequently cause the Shares to be registered in book entry form in the name of the Investor on the Company’s share register; provided,
however, that the Company’s obligation to issue the Shares to the Investor is contingent upon the Company having received the Subscription Amount in full in accordance with this Section 2. 











 3. Closing Conditions. 

a. The obligation of the parties hereto to consummate the purchase and sale of the Shares pursuant to this Backstop Subscription Agreement
shall be subject to the following conditions: 
 (i) no applicable governmental authority shall have enacted, issued,
promulgated, enforced or entered any judgment, order, law, rule or regulation (whether temporary, preliminary or permanent) which is then in effect and has the effect of making consummation of the transactions contemplated hereby illegal or
otherwise restraining or prohibiting consummation of the transactions contemplated hereby (except in the case of a governmental authority located outside the United States where such judgment, order, law, rule or regulation would not be reasonably
expected to have a Company Material Adverse Effect (as defined below)), and no such governmental authority shall have instituted a proceeding seeking to impose any such restraint or prohibition (except in the case of a governmental authority located
outside the United States where such restraint or prohibition would not be reasonably expected to have a Company Material Adverse Effect); 

(ii) all conditions precedent to the closing of the Transaction under the Merger Agreement shall have been satisfied (as
determined by the parties to the Merger Agreement and other than those conditions which, by their nature, are to be satisfied at the closing of the Transaction, including to the extent that any such condition is dependent upon the consummation of
the purchase and sale of the Shares pursuant to this Backstop Subscription Agreement) or waived by the party entitled to the benefit thereof under the Merger Agreement, and the closing of the Transaction shall be scheduled to occur substantially
concurrently with the Closing; and 
 (iii) the Shares shall have been approved for listing on a national securities exchange
(an “Exchange”), subject to official notice of issuance. 
 b. The obligation of the Company to consummate the issuance and
sale of the Shares at the Closing pursuant to this Backstop Subscription Agreement shall be subject to the satisfaction or valid waiver by the Company of the additional conditions that: 

(i) all representations and warranties of the Investor contained in this Backstop Subscription Agreement are true and correct
in all material respects (other than representations and warranties that are qualified as to materiality or Investor Material Adverse Effect, which representations and warranties shall be true and correct in all respects) at and as of the Closing
Date, and consummation of the Closing shall constitute a reaffirmation by the Investor of each of the representations, warranties, covenants and agreements of the Investor contained in this Backstop Subscription Agreement as of the Closing; and 

(ii) the Investor shall have performed, satisfied and complied in all material respects with all covenants, agreements and
conditions required by this Backstop Subscription Agreement to be performed, satisfied or complied with by it at or prior to the Closing, except where the failure of such performance, satisfaction or compliance has not had or would not reasonably be
expected to have an Investor Material Adverse Effect. 
 c. The obligation of the Investor to consummate the purchase of the Shares at the
Closing pursuant to this Backstop Subscription Agreement shall be subject to the satisfaction or valid waiver by the Investor of the additional conditions that: 

(i) all representations and warranties of the Company contained in this Backstop Subscription Agreement shall be true and
correct in all material respects (other than representations and warranties that are qualified as to materiality or Company Material Adverse Effect, which representations and warranties shall be true and correct in all respects) at and as of the
Closing Date, and consummation of the Closing shall constitute a reaffirmation by the Company of each of the representations, warranties, covenants and agreements of the Company contained in this Backstop Subscription Agreement as of the Closing
Date; 
  

  
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 (ii) the Company shall have performed, satisfied and complied in all
material respects with all covenants, agreements and conditions required by this Backstop Subscription Agreement to be performed, satisfied or complied with by it at or prior to the Closing, except where the failure of such performance or compliance
would not or would not reasonably be expected to prevent, materially delay, or materially impair the ability of the Company to consummate the Closing; and 

(iii) Each counterparty to any Note Subscription Agreement shall have fully funded its obligations thereunder when required to
do so pursuant to the terms thereof. 
 4. Further Assurances. After the date hereof, the Company and the Investor shall execute and
deliver such additional documents and take such additional actions as the parties reasonably may deem to be practical and necessary in order to consummate the subscription as contemplated by this Backstop Subscription Agreement. 

5. Company Representations and Warranties. The Company represents and warrants to the Investor that: 

a. The Company (i) is duly organized, validly existing and in good standing under the laws of the State of Delaware, (ii) has the
requisite corporate power and authority to own, lease and operate its properties, to carry on its business as it is now being conducted and to enter into and perform its obligations under this Backstop Subscription Agreement, and (iii) is duly
licensed or qualified to conduct its business and, if applicable, is in good standing under the laws of each jurisdiction (other than its jurisdiction of incorporation) in which the conduct of its business or the ownership of its properties or
assets requires such license or qualification, except, with respect to the foregoing clause (iii), where the failure to be in good standing would not reasonably be expected to have a Company Material Adverse Effect. For purposes of this Backstop
Subscription Agreement, a “Company Material Adverse Effect” means any event, circumstance, change, development, effect or occurrence (collectively “Effect”) that, individually or in the aggregate with all other
Effects, (a) is or would reasonably be expected to be materially adverse to the business, financial condition or results of operations of the Company and its subsidiaries taken as a whole; or (b) would prevent, materially delay or
materially impede the performance by the Company or its subsidiaries of their respective obligations under this Backstop Subscription Agreement, the Merger Agreement or the consummation of the Transaction; provided, however, that, in the case of
clause (a), none of the following shall be deemed to constitute, alone or in combination, or be taken into account in the determination of whether, there has been or will be a Company Material Adverse Effect: (i) any change or proposed change
in or change in applicable law or GAAP (including, in each case, the interpretation thereof) after the date of this Backstop Subscription Agreement; (ii) events or conditions generally affecting the industries or geographic areas in which the
Company operates; (iii) any downturn in general economic conditions, including changes in the credit, debt, securities, financial or capital markets (including changes in interest or exchange rates, prices of any security or market index or
commodity or any disruption of such markets); (iv) acts of war, sabotage, civil unrest or terrorism, or any escalation or worsening of any such acts of war, sabotage, civil unrest or terrorism, or changes in global, national, regional, state or
local political or social conditions; (v) any hurricane, tornado, flood, earthquake, mudslide, wildfire, natural disaster, epidemic, disease outbreak, pandemic (including, for the avoidance of doubt, the novel coronavirus, SARS-CoV-2 or COVID-19 and all related strains and sequences) or other acts of God, (vi) any actions taken or not taken by the
Company as required by this Backstop Subscription Agreement, the Merger Agreement or any other agreement executed and delivered in connection with the Transaction and specifically contemplated by the Merger Agreement or (vii) any Effect
attributable to the announcement or execution, pendency, negotiation or consummation of the Transaction, except in the cases of clauses (i) through (iii), to the extent that the Company is materially and disproportionately affected thereby as
compared with other participants in the industry in which the Company operates. 
 b. As of the Closing Date, the Shares will be duly
authorized and, when issued and delivered to the Investor against full payment therefor in accordance with the terms of this Backstop Subscription Agreement, the Shares will be validly issued, fully paid and
non-assessable and will not have been issued in violation of or subject to any preemptive or similar rights created under the Company’s certificate of incorporation (as amended to the Closing Date) or
under the General Corporation Law of the State of Delaware. 

  
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 c. This Backstop Subscription Agreement has been duly authorized, executed and delivered by
the Company and, assuming that this Backstop Subscription Agreement constitutes the valid and binding agreement of the Investor, this Backstop Subscription Agreement is enforceable against the Company in accordance with its terms, except as may be
limited or otherwise affected by bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium or other laws relating to or affecting the rights of creditors generally. 

d. The execution and delivery of this Backstop Subscription Agreement, the issuance and sale of the Shares and the compliance by the Company
with all of the provisions of this Backstop Subscription Agreement and the consummation of the transactions contemplated herein will not conflict with or result in a breach or violation of any of the terms or provisions of, or constitute a default
under, or result in the creation or imposition of any lien, charge or encumbrance upon any of the property or assets of the Company pursuant to the terms of (i) any indenture, mortgage, deed of trust, loan agreement, lease, license or other
agreement or instrument to which the Company is a party or by which the Company is bound or to which any of the property or assets of the Company is subject, (ii) the organizational documents of the Company, or (iii) any statute or any
judgment, order, rule or regulation of any court or governmental agency or body, domestic or foreign, having jurisdiction over the Company or any of its properties that, in each case of clauses (i) and (iii), would reasonably be expected to
have a Company Material Adverse Effect or have a material adverse effect on the Company’s ability to consummate the transactions contemplated hereby, including the issuance and sale of the Subscribed Shares. 

e. Assuming the accuracy of the representations and warranties of the Investor set forth herein, the Company is not required to obtain any
consent, waiver, authorization or order of, give any notice to, or make any filing or registration with, any court or other federal, state, local or other governmental authority, self-regulatory organization or other person in connection with the
issuance of the Shares pursuant to this Backstop Subscription Agreement, other than (i) filings with the U.S. Securities and Exchange Commission (the “SEC”), (ii) filings required by applicable state securities laws,
(iii) the filings required in accordance with Section 13 of this Backstop Subscription Agreement; (iv) filings required by the Exchange, including with respect to obtaining approval of the Company’s
stockholders, (v) those required to consummate the Transaction as provided under the Merger Agreement, (vi) those that will be obtained on or prior to the Closing; and (vi) consents, waivers, authorizations, orders, notices or
filings, the failure of which to obtain or make, would not reasonably be expected to have, individually or in the aggregate, a Company Material Adverse Effect. 

f. As of their respective dates, all reports required to be filed by the Company with the SEC (the “SEC Reports”) complied in
all material respects with the applicable requirements of the Securities Act and the Securities Exchange Act of 1934, as amended (the “Exchange Act”), and the rules and regulations of the SEC promulgated thereunder, and none of the
SEC Reports, when filed, contained any untrue statement of a material fact or omitted to state a material fact required to be stated therein or necessary in order to make the statements therein, in the light of the circumstances under which they
were made, not misleading. The financial statements of the Company included in the SEC Reports comply in all material respects with applicable accounting requirements and the rules and regulations of the SEC with respect thereto as in effect at the
time of filing and fairly present in all material respects the financial position of the Company as of and for the dates thereof and the results of operations and cash flows for the periods then ended, subject, in the case of unaudited statements,
to normal, year-end audit adjustments. 
 g. As of the date hereof, the issued and outstanding Shares
are registered pursuant to Section 12(b) of the Exchange Act, and are listed for trading on Nasdaq under the symbol “GIG” (it being understood that the trading symbol will be changed in connection with the Transaction). There is no
suit, action, proceeding or investigation pending or, to the knowledge of the Company, threatened against the Company by Nasdaq or the SEC, respectively, to prohibit or terminate the listing of the Company’s Shares on the Exchange or to
deregister the Shares under the Exchange Act. The Company has taken no action that is designed to terminate the registration of the Shares under the Exchange Act. 

h. Assuming the accuracy of the Investor’s representations and warranties set forth in Section 6 of this
Backstop Subscription Agreement, no registration under the Securities Act is required for the offer and sale of the Shares by the Company to the Investor. 

  
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 i. Neither the Company nor any person acting on its behalf has engaged or will engage in any
form of general solicitation or general advertising (within the meaning of Regulation D) in violation of the Securities Act in connection with any offer or sale of the Subscribed Shares. 

j. Except for each Placement Agent (as defined below), no broker or finder is entitled to any brokerage or finder’s fee or commission from
the Company solely in connection with the sale of the Subscribed Shares to the Investor. 
 k. As of the date hereof, except for such matters
as have not had a Company Material Adverse Effect, the Company is in compliance with all state and federal laws applicable to the conduct of its business. The Company has not received any written, or to its knowledge, other communication from a
governmental entity that alleges that the Company is not in compliance with or is in default or violation of any applicable law, except where such non-compliance, default or violation would not be reasonably
likely to have, individually or in the aggregate, a Company Material Adverse Effect. Except for such matters as have not had and would not be reasonably likely to have, individually or in the aggregate, a Company Material Adverse Effect, as of the
date hereof there is no (i) action, lawsuit, claim or other proceeding, in each case by or before any governmental authority pending, or, to the knowledge of the Company, threatened against the Company or (ii) judgment, decree, injunction,
ruling or order of any governmental entity or arbitrator outstanding against the Company. 
 6. Investor Representations and
Warranties. The Investor represents and warrants to the Company that: 
 a. The Investor (i) is duly organized, validly existing and
in good standing under the laws of its jurisdiction of incorporation, and (ii) has the requisite limited partnership power and authority to enter into and perform its obligations under this Backstop Subscription Agreement. 

b. This Backstop Subscription Agreement has been duly executed and delivered by the Investor, and assuming the due authorization, execution and
delivery of the same by the Company, this Backstop Subscription Agreement shall constitute the valid and legally binding obligation of the Investor, enforceable against the Investor in accordance with its terms, except as such enforceability may be
limited by bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other laws affecting creditors generally and by the availability of equitable remedies. 

c. The execution and delivery of this Backstop Subscription Agreement, the purchase of the Subscribed Shares and the compliance by the Investor
with all of the provisions of this Backstop Subscription Agreement and the consummation of the transactions contemplated herein will not conflict with or result in a breach or violation of any of the terms or provisions of, or constitute a default
under, or result in the creation or imposition of any lien, charge or encumbrance upon any of the property or assets of the Investor pursuant to the terms of (i) any indenture, mortgage, deed of trust, loan agreement, lease, license or other
agreement or instrument to which the Investor is a party or by which the Investor is bound or to which any of the property or assets of the Investor is subject; (ii) the organizational documents of the Investor; or (iii) any statute or any
judgment, order, rule or regulation of any court or governmental agency or body, domestic or foreign, having jurisdiction over the Investor or any of its properties that, in the case of clauses (i) and (iii), would reasonably be expected to
have an Investor Material Adverse Effect. For purposes of this Backstop Subscription Agreement, an “Investor Material Adverse Effect” means an event, change, development, occurrence, condition or effect with respect to the Investor
that would reasonably be expected to have a material adverse effect on the Investor’s ability to consummate the transactions contemplated hereby, including the purchase of the Subscribed Shares. 

d. The Investor (i) is a “qualified institutional buyer” (as defined in Rule 144A under the Securities Act) or an institutional
“accredited investor” (within the meaning of Rule 501(a)(1), (2), (3) or (7) under the Securities Act), in either case, satisfying the applicable requirements set forth on Annex A hereto, and an “institutional
account” as defined in FINRA Rule 4512(c), (ii) is acquiring the Subscribed Shares only for its own account and not for the account of others, or if the Investor is subscribing for the Subscribed Shares as a fiduciary or agent for one or more
investor accounts, each owner of such account is a qualified institutional buyer and the Investor has full investment discretion with respect to each such account, and the full power and authority to make the acknowledgements, representations and
agreements herein on behalf of each owner of each such account, and (iii) is not acquiring the Subscribed Shares with a view to, or for offer or sale in connection with, any distribution thereof in violation of the Securities Act (and has
provided the Company with the requested information on Annex A). The Investor is not an entity formed for the specific purpose of acquiring the Subscribed Shares. 
  

  
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 e. The Investor understands that the Subscribed Shares are being offered in a transaction
not involving any public offering within the meaning of the Securities Act and that the Subscribed Shares have not been registered under the Securities Act. The Investor understands that the Subscribed Shares may not be offered, resold, transferred,
pledged or otherwise disposed of by the Investor absent an effective registration statement under the Securities Act, except (i) to the Company or a subsidiary thereof, (ii) to non-U.S. persons
pursuant to offers and sales that occur outside the United States within the meaning of Regulation S under the Securities Act or (iii) pursuant to another applicable exemption from the registration requirements of the Securities Act, and, in
the case of each of clauses (i) and (iii), in accordance with any applicable securities laws of the states and other jurisdictions of the United States, and that any book-entry positions or certificates representing the Subscribed Shares shall
contain a restrictive legend to such effect. The Investor acknowledges that the Subscribed Shares will not be eligible for resale pursuant to Rule 144A promulgated under the Securities Act. The Investor understands and agrees that the Subscribed
Shares will be subject to transfer restrictions under applicable securities laws and, as a result of these transfer restrictions, the Investor may not be able to readily offer, resell, transfer, pledge or otherwise dispose of the Subscribed Shares
and may be required to bear the financial risk of an investment in the Subscribed Shares for an indefinite period of time. The Investor understands that it has been advised to consult legal counsel and tax and accounting advisors prior to making any
offer, resale, pledge, transfer or disposition of any of the Subscribed Shares. 
 Each book entry for the Subscribed Shares shall contain a notation, and
each certificate (if any) evidencing the Shares shall be stamped or otherwise imprinted with a legend, in substantially the following form: 
 THE
SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED UNDER THE UNITED STATES SECURITIES ACT OF 1933, AS AMENDED, OR THE SECURITIES LAWS OF ANY STATE OR OTHER JURISDICTION, AND MAY NOT BE OFFERED OR TRANSFERRED BY SALE, ASSIGNMENT, PLEDGE OR
OTHERWISE UNLESS (I) A REGISTRATION STATEMENT FOR THESE SECURITIES UNDER THE SECURITIES ACT AND APPLICABLE STATE SECURITIES LAWS IS IN EFFECT OR (II) THE COMPANY HAS RECEIVED AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY TO THE EFFECT
THAT SUCH REGISTRATION IS NOT REQUIRED. 
 f. The Investor understands and agrees that the Investor is purchasing the Subscribed Shares
directly from the Company. The Investor further acknowledges that there have not been, and the Investor hereby expressly and irrevocably acknowledges and agrees that it is not relying on, any representations, warranties, covenants, agreements or
statements made to the Investor by or on behalf of the Company, BigBear or the Company or BigBear’s respective affiliates or any of the respective subsidiaries, control persons, officers, directors, employees, partners, agents or
representatives, or any other party to the Transaction or any other person or entity (including the Placement Agents), expressly or by implication (including by omission), other than those representations, warranties, covenants, agreements and
statements of the Company expressly set forth in this Backstop Subscription Agreement, and all other purported representations, warranties, covenants, agreements or statements (including by omission) are hereby disclaimed by the Investor. The
Investor acknowledges that certain information provided by the Company was based on projections, and such projections were prepared based on assumptions and estimates that are inherently uncertain and are subject to a wide variety of significant
business, economic and competitive risks and uncertainties that could cause actual results to differ materially from those contained in the projections. 

g. In making its decision to purchase the Subscribed Shares, the Investor has relied solely upon independent investigation made by the Investor
and upon the representations, warranties and covenants of the Company expressly set forth herein (and no other representations and warranties). The Investor acknowledges and agrees that the Investor has received such information as the Investor
deems necessary in order to make an investment decision with respect to the Subscribed Shares, including with respect to the Company, the Transaction and the business of BigBear and each of its subsidiaries (collectively, the “Acquired
Companies”). Without limiting the generality of the foregoing, the Investor acknowledges that the Investor has reviewed the Company’s filings with the SEC. The Investor represents and agrees that the Investor and the Investor’s
professional advisor(s), if any, have had the full opportunity to ask such questions, receive such answers and obtain such information as the Investor and such undersigned’s professional advisor(s), if any, have deemed necessary to make an
investment decision with respect to the Subscribed Shares. The Investor acknowledges and agrees that none of William Blair & Company, L.L.C., 

  
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Oppenheimer & Co. Inc. or BMO Capital Markets Corp., each acting as a placement agent to the Company (each, a “Placement Agent” and together, the “Placement
Agents”), nor any affiliate of any Placement Agent, has provided the Investor with any information or advice with respect to the Subscribed Shares nor is such information or advice necessary or desired. No Placement Agent nor any of its
affiliates has made or makes any representation or warranty, whether express or implied, of any kind or character as to the Company or the Acquired Companies or the quality or value of the Subscribed Shares and each Placement Agent and any of its
respective affiliates may have acquired non-public information with respect to the Company or the Acquired Companies which the Investor agrees need not be provided to it. In connection with the issuance of the
Subscribed Shares to the Investor, no Placement Agent nor any of its affiliates has acted as a financial advisor or fiduciary to the Investor and no Placement Agent has provided any advice or recommendation in connection with the Transaction. 

h. The Investor became aware of this offering of the Subscribed Shares solely by means of direct contact between the Investor and the Company
or by means of contact from one or more Placement Agents, BigBear or its subsidiaries and/or their respective advisors (including, without limitation, attorneys, accountants, bankers, consultants and financial advisors), agents, control persons,
representatives, affiliates, directors, officers, managers, members, and/or employees, and/or the representatives of such persons (such parties referred to collectively as “Representatives”). The Subscribed Shares were offered to
the Investor solely by direct contact between the Investor and the Company, one or more Placement Agents, BigBear or its subsidiaries and/or their respective Representatives. The Investor acknowledges that it is not relying upon, and has not relied
upon, any statement, representation or warranty made by any person or entity (including, without limitation, the Company, each Placement Agent, BigBear and/or their respective Representatives), other than the representations and warranties expressly
set forth in this Backstop Subscription Agreement, in making its investment or decision to invest in the Company. The Investor did not become aware of this offering of the Subscribed Shares, nor were the Subscribed Shares offered to the Investor, by
any other means, and none of the Company, any Placement Agent, BigBear or its subsidiaries or their respective Representatives acted as investment advisor, broker or dealer to the Investor. The Investor acknowledges that the Company represents and
warrants that the Subscribed Shares (i) were not offered by any form of general solicitation or general advertising, and (ii) are not being offered in a manner involving a public offering under, or in a distribution in violation of, the
Securities Act, or any state securities laws. 
 i. The Investor acknowledges that it is aware that there are substantial risks incident to
the purchase and ownership of the Subscribed Shares, including those set forth in the Company’s filings with the Commission. The Investor has such knowledge and experience in financial and business matters as to be capable of evaluating the
merits and risks of an investment in the Subscribed Shares, and the Investor has had an opportunity to seek, and has sought, such accounting, legal, business and tax advice as the Investor has considered necessary to make an informed investment
decision. The Investor acknowledges that it (i) is a sophisticated investor, experienced in investing in private equity transactions and capable of evaluating investment risks independently, both in general and with regard to all transactions
and investment strategies involving a security or securities, and (ii) has exercised independent judgment in evaluating its purchase of the Subscribed Shares. 

j. Alone, or together with any professional advisor(s), the Investor represents and acknowledges that the Investor has adequately analyzed and
fully considered the risks of an investment in the Subscribed Shares and determined that the Subscribed Shares are a suitable investment for the Investor and that the Investor is able at this time and in the foreseeable future to bear the economic
risk of a total loss of the Investor’s investment in the Company. The Investor acknowledges specifically that a possibility of total loss exists. 

k. The Investor understands and agrees that no federal or state agency has passed upon or endorsed the merits of the offering of the Subscribed
Shares or made any findings or determination as to the fairness of this investment. 
 l. The Investor is not (i) a person or entity
named on the List of Specially Designated Nationals and Blocked Persons administered by the U.S. Treasury Department’s Office of Foreign Assets Control (“OFAC”) or in any Executive Order issued by the President of the United
States and administered by OFAC, or any other list of prohibited or restricted parties promulgated by OFAC, the Department of Commerce, or the Department of State (“Consolidated Sanctions Lists”), or a person or entity prohibited or
restricted by any OFAC sanctions program, or a person or entity whose property and interests in property subject to U.S. jurisdiction are otherwise blocked under any U.S. laws, Executive Orders or regulations, (ii) a person or entity listed on
the Sectoral Sanctions 

  
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Identifications (“SSI”) List maintained by OFAC or otherwise determined by OFAC to be subject to one or more of the Directives issued under Executive Order 13662 of
March 20, 2014, or on any other of the Consolidated Sanctions Lists, (iii) an entity owned, directly or indirectly, individually or in the aggregate, 50 percent or more by, acting on behalf of, or controlled by, one or more persons
described in subsections (i) or (ii), (iv) organized, incorporated, established, located, resident or born in, or a citizen, national or the government, including any political subdivision, agency or instrumentality thereof, of, Cuba,
Iran, North Korea, Myanmar, Venezuela, Syria, the Crimea region of Ukraine or any other country or territory embargoed or subject to substantial trade restrictions by the United States, (v) a person or entity named on the U.S. Department of
Commerce, Bureau of Industry and Security (“BIS”) Denied Persons List, Entity List, or Unverified List (“BIS Lists”), (vi) a Designated National as defined in the Cuban Assets Control Regulations, 31 C.F.R.
Part 515, or (vii) a non-U.S. shell bank or providing banking services indirectly to a non-U.S. shell bank (collectively, (i) through (vii), a
“Restricted Person”). The Investor agrees to provide law enforcement agencies, if requested thereby, such records as required by applicable law, provided that the Investor is permitted to do so under applicable law. the Investor
represents that if it is a financial institution subject to the Bank Secrecy Act (31 U.S.C. Section 5311 et seq.), as amended by the USA PATRIOT Act of 2001 and its implementing regulations (collectively, the “BSA/PATRIOT
Act”), that the Investor maintains policies and procedures reasonably designed to comply with applicable obligations under the BSA/PATRIOT Act. The Investor also represents that the Investor maintains policies and procedures reasonably
designed for the screening of its investors against the OFAC and BIS sanctions programs, including for Restricted Persons, and otherwise to ensure compliance with all applicable sanctions and embargo laws, statutes, and regulations. The Investor
further represents and warrants that it maintains policies and procedures reasonably designed to ensure that the funds held by the Investor and used to purchase the Subscribed Shares were legally derived and were not obtained, directly or
indirectly, from a Restricted Person. The Investor is not a “foreign person,” “foreign government,” or a “foreign entity,” in each case, as defined in Section 721 of the Defense Production Act of 1950, as amended,
including, without limitation, all implementing regulations thereof (the “DPA”). The Investor is not controlled, in whole or in part, by a “foreign person,” as defined in the DPA. 

m. The Investor does not have, as of the date hereof, and during the 30-day period immediately prior to
the date hereof, the Investor has not entered into, any “put equivalent position” as such term is defined in Rule 16a-1 under the Exchange Act or short sale positions with respect to the securities
of the Company. Notwithstanding the foregoing, in the case of a the Investor that is a multi-managed investment vehicle whereby separate portfolio managers manage separate portions of the Investor’s assets and the portfolio managers have no
direct knowledge of the investment decisions made by the portfolio managers managing other portions of the Investor’s assets, the representation set forth above shall only apply with respect to the portion of assets managed by the portfolio
manager that made the investment decision to purchase the Subscribed Shares covered by this Backstop Subscription Agreement. 
 n. If the
Investor is an employee benefit plan that is subject to Title I of ERISA, a plan, an individual retirement account or other arrangement that is subject to Section 4975 of the Code or an employee benefit plan that is a governmental plan (as
defined in Section 3(32) of ERISA), a church plan (as defined in Section 3(33) of ERISA), a non-U.S. plan (as described in Section 4(b)(4) of ERISA) or other plan that is not subject to the
foregoing but may be subject to provisions under any other federal, state, local, non-U.S. or other laws or regulations that are similar to such provisions of ERISA or the Internal Revenue Code of 1986, as
amended, or an entity whose underlying assets are considered to include “plan assets” of any such plan, account or arrangement (each, a “Plan”) subject to the fiduciary or prohibited transaction provisions of ERISA or
Section 4975 of the Code, the Investor represents and warrants that neither the Company, nor any of its respective affiliates (the “Transaction Parties”) has acted as the Plan’s fiduciary, or has been relied on for advice,
with respect to its decision to acquire and hold the Subscribed Shares, and none of the Transaction Parties shall at any time be relied upon as the Plan’s fiduciary with respect to any decision to acquire, continue to hold or transfer the
Subscribed Shares. 
 o. The Investor has, and at the Closing the Investor will have, sufficient immediately available funds (or commitments
therefor) to pay the Purchase Price pursuant to Section 2 of this Backstop Subscription Agreement. 
 p. No
disclosure or offering document has been prepared by any Placement Agent in connection with the offer and sale of the Subscribed Shares. Each Placement Agent and each of its Representatives have made no independent investigation with respect to the
Company, BigBear or its subsidiaries, or the Subscribed Shares or the accuracy, completeness or adequacy of any information supplied to the Investor by the Company. 

  
 8 












 q. The Investor agrees that, notwithstanding Section 10k of this
Backstop Subscription Agreement, each Placement Agent and BigBear may rely upon the representations and warranties made by the Investor to the Company in this Backstop Subscription Agreement. 

r. No foreign person (as defined in 31 C.F.R. Part 800.224) in which the national or subnational governments of a single foreign state have a
substantial interest (as defined in 31 C.F.R. Part 800.244) will acquire a substantial interest in the Company as a result of the purchase and sale of securities hereunder such that a declaration to the Committee on Foreign Investment in the United
States would be mandatory under 31 C.F.R. Part 800.401, and no foreign person will have control (as defined in 31 C.F.R. Part 800.208) over the Company from and after the Closing as a result of the purchase and sale of Securities hereunder. 

7. Investor Rights Agreement. Investor, as a Permitted Transferee (as defined in that certain Investor Rights Agreement, dated as
of June 4, 2021, by and among the Company, BBAI, and the other parties thereto (the “Investor Rights Agreement”) of BBAI, shall be bound by and subject to the terms of the Investor Rights Agreement as a “Partner”
thereunder with respect to the Investor’s ownership of the Subscribed Shares. 
 8. Termination. Subject to the last sentence of
Section 1, this Backstop Subscription Agreement shall terminate and be void and of no further force and effect, and all rights and obligations of the parties hereunder shall terminate without any further liability on the
part of any party in respect thereof, upon the earlier to occur of (a) such date and time as the Merger Agreement is validly terminated in accordance with its terms or (b) upon the mutual written agreement of each of the parties hereto and
BigBear to terminate this Backstop Subscription Agreement; provided that nothing herein will relieve any party from liability for any willful breach hereof prior to the time of termination, and each party will be entitled to any remedies at law or
in equity to recover losses, liabilities or damages arising from any such willful breach. The Company shall notify the Investor of the termination of the Merger Agreement promptly after the termination of such agreement. 

9. Trust Account Waiver. The Investor acknowledges that the Company is a blank check company with the powers and privileges to effect a
merger, asset acquisition, reorganization or similar business combination involving the Company and one or more businesses or assets. The Investor further acknowledges that, as described in the Company’s prospectus relating to its initial
public offering dated February 10, 2021 (the “Prospectus”) available at www.sec.gov, substantially all of the Company’s assets consist of the cash proceeds of the Company’s initial public offering and private
placement of its securities, and substantially all of those proceeds have been deposited in a trust account (the “Trust Account”) for the benefit of the Company, its public shareholders and the underwriter of the Company’s
initial public offering. Except with respect to interest earned on the funds held in the Trust Account that may be released to the Company to pay its tax obligations, if any, the cash in the Trust Account may be disbursed only for the purposes set
forth in the Prospectus. For and in consideration of the Company entering into this Backstop Subscription Agreement, the receipt and sufficiency of which are hereby acknowledged, the Investor hereby irrevocably waives any and all right, title and
interest, or any claim of any kind it has or may have in the future, in or to any monies held in the Trust Account, and agrees not to seek recourse against the Trust Account as a result of, or arising out of, this Backstop Subscription Agreement;
provided, however, that nothing in this Section 9 shall be deemed to limit the Investor’s right, title, interest or claim to any monies held in the Trust Account by virtue of its record or beneficial
ownership of shares of Common Stock of the Company currently outstanding on the date hereof, pursuant to a validly exercised redemption right with respect to any such shares of Common Stock, except to the extent that the Investor has otherwise
agreed with the Company to not exercise such redemption right. 
 10. Miscellaneous. 

a. Neither this Backstop Subscription Agreement nor any rights that may accrue to any party hereunder (other than the Shares acquired
hereunder, if any) may be transferred or assigned by a party without the prior written consent of the other party hereto; provided that (i) this Backstop Subscription Agreement and any of the Investor’s rights and obligations hereunder may
be assigned to any fund or account managed by the same investment manager as the Investor or by an affiliate (as defined in Rule 12b-2 of the Exchange Act) of such investment manager without the prior consent
of, but with prior written notice to, the Company and (ii) the Investor’s rights under Section 7 may be assigned to an assignee or transferee of the Shares acquired by the Investor pursuant to this Backstop
Subscription Agreement; provided, further, that prior to such assignment any such assignee shall agree in writing to be bound by the terms hereof. Notwithstanding the foregoing, no assignment pursuant to clause (i) of this
Section 10 

  
 9 












 
shall relieve the Investor of its obligations hereunder. The parties hereto acknowledge and agree that (i) this Backstop Subscription Agreement is being entered into in order to induce each
of the Company, BBAI and BigBear to execute and deliver that certain Amendment No. 2 to Merger Agreement (the “Merger Agreement Amendment”) and without the representations, warranties, covenants and agreements of the Company
and the Investor hereunder, each of the Company, BBAI and BigBear would not enter into the Merger Agreement Amendment, (ii) each representation, warranty, covenant and agreement of the Investor hereunder is being made also for the benefit of
BBAI and BigBear and (iii) BBAI and BigBear may directly enforce (including by an action for specific performance, injunctive relief or other equitable relief) each of the covenants and agreements in this Backstop Subscription Agreement of
(A) the Investor in respect of its obligations under Sections 1, 2, and 4 and (B) the Company in respect of its obligations under Sections 1, 2, 4, in each case pursuant to the terms and subject to
the conditions set forth in this Backstop Subscription Agreement. 
 b. The Company may request from the Investor such additional information
as the Company may deem necessary to register the resale of the Shares and evaluate the eligibility of the Investor to acquire the Shares, and the Investor shall reasonably promptly provide such information as may reasonably be requested; provided,
that the Company agrees to keep any such information provided by the Investor confidential other than as necessary to include in any registration statement the Company is required to file hereunder. The Investor acknowledges and agrees that if it
does not provide the Company with such requested information, the Company may not be able to register the Shares acquired by the Investor pursuant to this Backstop Subscription Agreement for resale pursuant to Section 7
hereof. The Investor hereby agrees that its identity and the Subscription Agreement, as well as the nature of the Investor’s obligations hereunder, may be disclosed in any public announcement or disclosure required by the SEC and in any
registration statement, proxy statement, consent solicitation statement or any other SEC filing to be filed by the Company in connection with the issuance of Shares contemplated by this Backstop Subscription Agreement and/or the Transaction. 

c. The Investor acknowledges that the Company, BBAI, BigBear, the Placement Agent and others will rely on the acknowledgments, understandings,
agreements, representations and warranties contained in this Backstop Subscription Agreement. Prior to the Closing, the Investor agrees to promptly notify the Company, BigBear and the Placement Agent if any of the acknowledgments, understandings,
agreements, representations and warranties set forth in Section 6 above are no longer accurate in any material respect (other than those acknowledgments, understandings, agreements, representations and warranties qualified
by materiality, in which case the Investor shall notify the Company, BigBear and the Placement Agent if they are no longer accurate in all respects). The Investor agrees that each purchase by the Investor of Shares from the Company will constitute a
reaffirmation of the acknowledgments, understandings, agreements, representations and warranties herein (as modified by any such notice) by the Investor as of the time of such purchase. The Placement Agent may rely on the representations, warranties
and covenants of the Company and the Investor contained in this Backstop Subscription Agreement as if such representations, warranties and covenants, as applicable, were made directly to the Placement Agent. 

d. The Company, BigBear, BBAI and the Placement Agent are each entitled to rely upon this Backstop Subscription Agreement and each is
irrevocably authorized to produce this Backstop Subscription Agreement or a copy hereof to any interested party in any administrative or legal proceeding or official inquiry with respect to the matters covered hereby; provided,
however, that the foregoing clause of this Section 10d shall not give BigBear, BBAI or the Placement Agent any rights other than those expressly set forth herein and, without limiting the generality of the foregoing
and for the avoidance of doubt, in no event shall BigBear or BBAI be entitled to rely on any of the representations and warranties of the Company set forth in this Backstop Subscription Agreement. 

e. All of the agreements, representations and warranties made by each party hereto in this Backstop Subscription Agreement shall survive the
Closing. 
 f. This Backstop Subscription Agreement may not be amended, modified, waived or terminated (other than pursuant to the terms of
Section 8 above) except by an instrument in writing, signed by each of the parties hereto and BigBear and BBAI. No failure or delay of either party in exercising any right or remedy hereunder shall operate as a waiver
thereof, nor shall any single or partial exercise of any such right or power, or any abandonment or discontinuance of steps to enforce such right or power, or any course of conduct, preclude any other or further exercise thereof or the exercise of
any other right or power. The rights and remedies of the parties hereunder are cumulative and are not exclusive of any rights or remedies that they would otherwise have hereunder. Notwithstanding anything to the contrary herein,
Section 6, Section 10c, Section 10d, this Section 10f and Section 11 may not be modified, waived or terminated in a
manner that is material and adverse to the Placement Agent without the written consent of the Placement Agent. 
  

  
 10 












 g. This Backstop Subscription Agreement (including the schedule hereto) constitutes the
entire agreement, and supersedes all other prior agreements, understandings, representations and warranties, both written and oral, among the parties, with respect to the subject matter hereof. Except as set forth in the last sentence of
Section 10a, Section 10c, Section 10d, Section 10f, this Section 10g and the third sentence of
Section 10k with respect to the persons referenced specifically referenced therein, this Backstop Subscription Agreement shall not confer any rights or remedies upon any person other than the parties hereto, and their
respective successor and assigns, and the parties hereto acknowledge that such persons so referenced are third party beneficiaries of this Backstop Subscription Agreement for the purposes of, and to the extent of, the rights granted to them, if any,
pursuant to the applicable provisions. 
 h. Except as otherwise provided herein, this Backstop Subscription Agreement shall be binding upon,
and inure to the benefit of the parties hereto and their heirs, executors, administrators, successors, legal representatives, and permitted assigns, and the agreements, representations, warranties, covenants and acknowledgments contained herein
shall be deemed to be made by, and be binding upon, such heirs, executors, administrators, successors, legal representatives and permitted assigns. 

i. If any provision of this Backstop Subscription Agreement shall be adjudicated by a court of competent jurisdiction to be invalid, illegal or
unenforceable, the validity, legality or enforceability of the remaining provisions of this Backstop Subscription Agreement shall not in any way be affected or impaired thereby and shall continue in full force and effect. 

j. This Backstop Subscription Agreement may be executed in one or more counterparts (including by facsimile or electronic mail or in .pdf) and
by different parties in separate counterparts, with the same effect as if all parties hereto had signed the same document. All counterparts so executed and delivered shall be construed together and shall constitute one and the same agreement. 

k. The parties hereto acknowledge and agree that irreparable damage would occur in the event that any of the provisions of this Backstop
Subscription Agreement were not performed in accordance with their specific terms or were otherwise breached. It is accordingly agreed that the parties shall be entitled to an injunction or injunctions to prevent breaches or threatened breaches of
this Backstop Subscription Agreement, without posting a bond or undertaking and without proof of damages, to enforce specifically the terms and provisions of this Backstop Subscription Agreement, this being in addition to any other remedy to which
such party is entitled at law, in equity, in contract, in tort or otherwise. The parties hereto acknowledge and agree that BigBear or BBAI and the Placement Agent shall be entitled to specifically enforce the Company’s obligations hereunder to
issue and sell the Subscribed Shares to Investor and the provisions of this Backstop Subscription Agreement of which BigBear or BBAI and the Placement Agent are each an express third-party beneficiary, in each case, on the terms and subject to the
conditions set forth in this Backstop Subscription Agreement. The parties hereto further agree not to assert that a remedy of specific enforcement pursuant to this Section 10k is unenforceable, invalid, contrary to
applicable law or inequitable for any reason and to waive any defenses in any action for specific performance, including the defense that a remedy at law would be adequate. The parties acknowledge and agree that this
Section 10k is an integral part of the transactions contemplated hereby and without that right, the parties hereto would not have entered into this Backstop Subscription Agreement. 

l. Any notice or communication required or permitted hereunder shall be in writing and either delivered personally, emailed or sent by
overnight mail via a reputable overnight carrier, or sent by certified or registered mail, postage prepaid, and shall be deemed to be given and received (i) when so delivered personally, (ii) when sent, with no mail undeliverable or other
rejection notice, if sent by email, or (iii) three Business Days after the date of mailing to the address below or to such other address or addresses as such person may hereafter designate by notice given hereunder: 

 

	 	(i)	 if to Investor, to such address(es) or email address(es) set forth herein; 



  
 11 













	 	(ii)	 if to, prior to the Closing, the Company, to: 



GigCapital4, Inc. 
 1731
Embarcadero Road, Suite 200 
 Palo Alto, CA 94303 

Attention:     Dr. Raluca Dinu 

Email:          
                                 

with a required copy to (which copy shall not constitute notice): 

DLA Piper LLP (US) 
 555 Mission
Street, Suite 2400 
 San Francisco, CA 94105 

Attention:     Jeffrey C. Selman 

                     John F. Maselli

 Email:
                                         
  
  

	 	(ii)	 if to BigBear or BBAI, to: 



AE BBAI Aggregator, LP 
 c/o AE
Industrial Partners, LP 
 2500 N. Military Trail, Suite 470 

Boca Raton, FL 33431 
 Attn:
Kirk Konert 
 E-mail:
                                 

with a required copy to (which shall not constitute notice): 

AE Industrial Partners, LP 

2500 N. Military Trail, Suite 470 

Boca Raton, FL 33431 
 Attn:
Kirk Konert 
 E-mail:
                                 

and 
 Kirkland & Ellis
LLP 
 300 N. LaSalle 

Chicago, IL 60654 

Attn:         Jeremy S. Liss, P.C. 

                 Matthew S. Arenson, P.C. 

                 Timothy Cruickshank, P.C. 

                 Jeffrey P. Swatzell 

E-mail:                 
                     
 m. The
Investor shall pay all of its own expenses in connection with this Backstop Subscription Agreement and the transactions contemplated herein. 
  

  
 12 












 n. THE PARTIES HERETO IRREVOCABLY SUBMIT TO THE EXCLUSIVE JURISDICTION OF THE UNITED STATES
DISTRICT COURT FOR THE SOUTHERN DISTRICT OF NEW YORK AND THE SUPREME COURT OF THE STATE OF NEW YORK SOLELY IN RESPECT OF THE INTERPRETATION AND ENFORCEMENT OF THE PROVISIONS OF THIS BACKSTOP SUBSCRIPTION AGREEMENT AND THE DOCUMENTS REFERRED TO IN
THIS BACKSTOP SUBSCRIPTION AGREEMENT AND IN RESPECT OF THE TRANSACTIONS CONTEMPLATED HEREBY, AND HEREBY WAIVE, AND AGREE NOT TO ASSERT, AS A DEFENSE IN ANY ACTION, SUIT OR PROCEEDING FOR INTERPRETATION OR ENFORCEMENT HEREOF OR ANY SUCH DOCUMENT THAT
IS NOT SUBJECT THERETO OR THAT SUCH ACTION, SUIT OR PROCEEDING MAY NOT BE BROUGHT OR IS NOT MAINTAINABLE IN SAID COURTS OR THAT VENUE THEREOF MAY NOT BE APPROPRIATE OR THAT THIS BACKSTOP SUBSCRIPTION AGREEMENT OR ANY SUCH DOCUMENT MAY NOT BE
ENFORCED IN OR BY SUCH COURTS, AND THE PARTIES HERETO IRREVOCABLY AGREE THAT ALL CLAIMS WITH RESPECT TO SUCH ACTION, SUIT OR PROCEEDING SHALL BE HEARD AND DETERMINED BY SUCH A NEW YORK STATE OR FEDERAL COURT. THE PARTIES HEREBY CONSENT TO AND GRANT
ANY SUCH COURT JURISDICTION OVER THE PERSON OF SUCH PARTIES AND OVER THE SUBJECT MATTER OF SUCH DISPUTE AND AGREE THAT MAILING OF PROCESS OR OTHER PAPERS IN CONNECTION WITH SUCH ACTION, SUIT OR PROCEEDING IN THE MANNER PROVIDED IN THIS SECTION
10n OF THIS BACKSTOP SUBSCRIPTION AGREEMENT OR IN SUCH OTHER MANNER AS MAY BE PERMITTED BY LAW SHALL BE VALID AND SUFFICIENT SERVICE THEREOF. NOTWITHSTANDING THE FOREGOING, A FINAL JUDGMENT IN ANY SUCH ACTION MAY BE ENFORCED IN OTHER
JURISDICTIONS BY SUIT ON THE JUDGMENT OR IN ANY OTHER MANNER PROVIDED BY LAW. 
 EACH PARTY ACKNOWLEDGES AND AGREES THAT ANY CONTROVERSY WHICH MAY ARISE
UNDER THIS BACKSTOP SUBSCRIPTION AGREEMENT OR THE TRANSACTIONS CONTEMPLATED HEREBY IS LIKELY TO INVOLVE COMPLICATED AND DIFFICULT ISSUES, AND THEREFORE EACH SUCH PARTY HEREBY IRREVOCABLY AND UNCONDITIONALLY WAIVES ANY RIGHT SUCH PARTY MAY HAVE TO A
TRIAL BY JURY IN RESPECT OF ANY LITIGATION DIRECTLY OR INDIRECTLY ARISING OUT OF OR RELATING TO THIS BACKSTOP SUBSCRIPTION AGREEMENT OR THE TRANSACTIONS CONTEMPLATED BY THIS BACKSTOP SUBSCRIPTION AGREEMENT. EACH PARTY CERTIFIES AND ACKNOWLEDGES THAT
(I) NO REPRESENTATIVE, AGENT OR ATTORNEY OF ANY OTHER PARTY HAS REPRESENTED, EXPRESSLY OR OTHERWISE, THAT SUCH OTHER PARTY WOULD NOT, IN THE EVENT OF LITIGATION, SEEK TO ENFORCE THE FOREGOING WAIVER; (II) SUCH PARTY UNDERSTANDS AND HAS
CONSIDERED THE IMPLICATIONS OF THE FOREGOING WAIVER; (III) SUCH PARTY MAKES THE FOREGOING WAIVER VOLUNTARILY AND (IV) SUCH PARTY HAS BEEN INDUCED TO ENTER INTO THIS BACKSTOP SUBSCRIPTION AGREEMENT BY, AMONG OTHER THINGS, THE MUTUAL WAIVER
AND CERTIFICATIONS IN THIS SECTION 10n. 
 11. Non-Reliance and Exculpation. 

12. The Investor acknowledges that it is not relying upon, and has not relied upon, any statement, representation or warranty made by any
person, firm or corporation (including, without limitation, the Placement Agent, any of their respective affiliates or any of its or their control persons, officers, directors, employees, partners, agents, and any representatives of any of the
foregoing), other than the statements, representations and warranties of the Company expressly contained in Section 5 of this Backstop Subscription Agreement or in the Merger Agreement, in making its investment or decision
to invest in the Company. The Investor acknowledges and agrees that none of (i) the Placement Agent, its affiliates or any of its or their control persons, officers, directors, employees or representatives, or (ii) any other party to the
Merger Agreement (other than in respect of the representations and warranties set forth in the Merger Agreement), including any such party’s representatives, affiliates or any of its or their control persons, officers, directors or employees,
that is not a party hereto shall have any liability to the Investor, or to any other investor, pursuant to, arising out of or relating to this Backstop Subscription Agreement, the negotiation hereof or thereof or its subject matter, or the
transactions contemplated hereby or thereby, including, without limitation, with respect to any action heretofore or hereafter taken or omitted to be taken by any of them in connection with the purchase of the Shares or with respect to any claim
(whether in tort, contract or otherwise) for breach of this Backstop Subscription Agreement or in respect of any written or oral representations made or alleged to be made in connection herewith, as expressly provided herein, or for any actual or
alleged inaccuracies, misstatements or omissions with respect to any information or materials of any kind furnished by the Company, BBAI, BigBear, the Placement Agent or any Non-Party Affiliates concerning the
Company, BBAI, BigBear, the Placement Agent, any of their controlled affiliates, this Backstop Subscription Agreement or the transactions contemplated hereby. For purposes of this Backstop Subscription Agreement, “Non-Party Affiliates” means each former, current or future officer, director, employee, partner, member, manager, direct or indirect equityholder or affiliate of the Company, BBAI, BigBear, the Placement
Agent or any of their controlled affiliates or any family member of the foregoing. 
  

  
 13 












 13. Disclosure. The Company shall, by 9:00 a.m., New York City time, on the first
(1st) Business Day immediately following the date of this Backstop Subscription Agreement, issue one or more press releases or file with the SEC a Current Report on Form 8-K (collectively, the
“Disclosure Document”) disclosing all material terms of the transactions contemplated hereby, the Transaction and any other material, nonpublic information that the Company has provided to the Investor at any time prior to the
filing of the Disclosure Document. Upon the issuance of the Disclosure Document, to the actual knowledge of the Company, the Investor shall not be in possession of any material, non-public information received
from the Company or any of its officers, directors, or employees or agents, and the Investor shall no longer be subject to any confidentiality or similar obligations under any current agreement, whether written or oral, with the Company or any of
their respective affiliates, relating to the transactions contemplated by this Backstop Subscription Agreement. Notwithstanding anything in this Backstop Subscription Agreement to the contrary, the Company shall not publicly disclose the name of the
Investor or any of its affiliates or advisers, or include the name of the Investor or any of its affiliates or advisers in any press release or in any filing with the SEC or any regulatory agency or trading market, without the prior written consent
of the Investor, except (i) as required by the federal securities law or pursuant to other routine proceedings of regulatory authorities, (ii) to the extent such disclosure is required by law, at the request of the staff of the SEC or
regulatory agency or under the regulations of any national securities exchange on which the Company’s securities are listed for trading, (iii) to the extent such announcements or other communications contain only information previously
disclosed in a public statement, press release or other communication previously approved in accordance with this Section 13 or (iv) as expressly contemplated by the last sentence of
Section 10b of this Backstop Subscription Agreement. 
 [SIGNATURE PAGES FOLLOW] 

  
 14 












 IN WITNESS WHEREOF, the Investor has executed or caused this Backstop Subscription
Agreement to be executed by its duly authorized representative as of the date set forth below. 
  

							
	 Name of Investor:
  

AE BBAI AGGREGATOR, LP
  

By: AE BBRED GP, LLC
 Its: General Partner
	 		  	State/Country of Formation or Domicile: Delaware
	By:	 	/s/ Kirk Konert
                                         
                       	 	        	  	
			
	Name: Kirk Konert	 		  	
			
	Title: President	 		  	
			
	Name in which Shares are to be registered (if different):	 		  	Date: November 29, 2021
			
	Investor’s EIN:                                 	 		  	
			
	Business Address-Street: 2500 N. Military Trail, Suite 470	 		  	Mailing Address-Street (if different):
			
	City, State, Zip: Boca Raton, FL 33431	 		  	City, State, Zip:
			
	Attn: Kirk Konert
                                         
                           	 		  	Attn:                                     
                                         
           
			
	Telephone No.:	 		  	Telephone No.:
			
	Facsimile No.:	 		  	Facsimile No.:

 You must pay the Subscription Amount by wire transfer of United States dollars in immediately available funds
to the account specified by the Company in the Closing Notice. To the extent the offering is oversubscribed, the number of Shares received may be less than the number of Shares subscribed for. 

  
 15 












 IN WITNESS WHEREOF, GigCapital4, Inc. has accepted this Backstop Subscription Agreement as
of the date set forth below. 
  

			
	GIGCAPITAL4, INC.
		
	By:	 	 /s/ Dr. Raluca Dinu

	Name: Dr. Raluca Dinu
	Title: Chief Executive Officer


 Date: November 29, 2021 

  
 16 












 SCHEDULE A 

ELIGIBILITY REPRESENTATIONS OF THE INVESTOR 
  

			
	A.	  	QUALIFIED INSTITUTIONAL BUYER STATUS


	
	 (Please check the applicable subparagraphs):


 ☐ We are a “qualified institutional buyer” (as defined in Rule 144A under the Securities Act).

  

			
	B.	  	INSTITUTIONAL ACCREDITED INVESTOR STATUS


	
	 (Please check the applicable subparagraphs):


  

	
	 1.  ☐ We are an “accredited investor” (within the meaning of Rule
501(a) under the Securities Act or an entity in which all of the equity holders are accredited investors within the meaning of Rule 501(a) under the Securities Act), and have marked and initialed the appropriate box on the following page indicating
the provision under which we qualify as an “accredited investor.”


  

	
	 2.  ☐ We are not a natural person.


 Rule 501(a), in relevant part, states that an “accredited investor” shall mean any person who comes within any of
the below listed categories, or who the issuer reasonably believes comes within any of the below listed categories, at the time of the sale of the securities to that person. The Investor has indicated, by marking and initialing the appropriate box
below, the provision(s) below which apply to the Investor and under which the Investor accordingly qualifies as an “accredited investor.” 

☐ Any bank, registered broker or dealer, insurance company, registered investment company, business development company, or small
business investment company; 
 ☐ Any plan established and maintained by a state, its political subdivisions, or any agency or
instrumentality of a state or its political subdivisions for the benefit of its employees, if such plan has total assets in excess of $5,000,000; 

☐ Any employee benefit plan, within the meaning of the Employee Retirement Income Security Act of 1974, if a bank, insurance
company, or registered investment adviser makes the investment decisions, or if the plan has total assets in excess of $5,000,000; 

☐ Any organization described in Section 501(c)(3) of the Internal Revenue Code, corporation, similar business trust, or
partnership, not formed for the specific purpose of acquiring the securities offered, with total assets in excess of $5,000,000; 

☐ Any trust with assets in excess of $5,000,000, not formed to acquire the securities offered, whose purchase is directed by a
sophisticated person; or 
 ☐ Any entity in which all of the equity owners are accredited investors meeting one or more of the
above tests. 
  

			
	C.	  	 FINRA INSTITUTIONAL ACCOUNT STATUS
 (Please
check the applicable subparagraphs):


  

	
	 1.  ☐ We are an “institutional account” under FINRA Rule
4512(c).


  

	
	 2.  ☐ We are not an “institutional account” under FINRA Rule
4512(c).


 This page should be completed by the Investor 

and constitutes a part of the Subscription Agreement. 

  
 17