Document:

EX-10.1

 Exhibit 10.1 

FORWARD SHARE PURCHASE AGREEMENT 

This Forward Share Purchase Agreement (this “Agreement”) is entered into as of October 14, 2021, by and among
(i) GigCapital4, Inc., a Delaware corporation (“GigCapital4”), and (ii) the investors signatory hereto (each individually an “Investor” and collectively, the “Investors”). GigCapital4 and each
Investor is individually referred to herein as a “Party” and collectively as the “Parties”. 
 Recitals

 WHEREAS, GigCapital4 is a Private-to-Public Equity
(PPE)TM company, also known as a blank check company or special purpose acquisition company, formed for the purpose of effecting a merger, capital stock exchange, asset acquisition, stock
purchase, reorganization or similar business combination with one or more businesses; 
 WHEREAS, GigCapital4 has entered into an agreement
and plan of merger (as amended from time to time, the “Merger Agreement”) with BigBear.ai Holdings, LLC, a Delaware limited liability company (“BigBear”), pursuant to which a wholly-owned merger subsidiary of
GigCapital4 will merge with and into BigBear, and then BigBear as the surviving company of that merger will merge with and into GigCapital4 (such transactions, the “Business Combination”), which will be renamed BigBear.ai Holdings,
Inc. upon the consummation of that second merger (GigCapital4, as the post-combination company shall be referred to herein as the “Company”), and GigCapital4 has filed a preliminary proxy statement with the U.S. Securities and
Exchange Commission (the “Commission”) that will seek, among other things, stockholder approval of the Business Combination; and 

WHEREAS, the Parties wish to enter into this Agreement, pursuant to which the Company shall purchase from the Investors, and the Investors
shall sell and transfer to the Company, in each case, subject to the conditions set forth herein, certain shares of common stock, par value $0.0001 per share of GigCapital4 held by the Investors (the “Shares”) on the terms set forth
herein. 
 NOW, THEREFORE, in consideration of the premises, representations, warranties and the mutual covenants contained in this
Agreement, and for other good and valuable consideration, the receipt, sufficiency and adequacy of which are hereby acknowledged, the Parties agree as follows: 

Agreement 
 1.
Sale of Shares; Shares Purchase and Sale; Closing. 
 (a) Forward Share Purchase. Subject to the conditions set forth in
Section 4, on the three (3) month anniversary of the date of the closing of the Business Combination (the “Business Combination Closing Date”), the Investors may each individually elect to sell
and transfer to the Company, and the Company shall purchase from each Investor, up to that number of Shares (including any Additional Shares) that are then held by such Investor, and have been continuously held by such Investor since the Business
Combination Closing Date, but not to exceed 2,500,000 Shares (including any Additional Shares) in the aggregate between the Investors, unless otherwise agreed in writing by all Parties, at a price per Share equal to $10.15 per Share (the
“Shares Purchase Price”). Each Investor shall notify the Company and the Escrow Agent in writing five (5) Business Days (as defined below) prior to the three (3) month anniversary of the Business Combination Closing
Date whether or not such Investor is exercising such Investor’s right to sell any of the Shares (including any Additional Shares) held by such Investor to the Company pursuant to this Agreement (each, a “Shares Sale Notice”).
Any Investor that fails to timely deliver a Shares Sales Notice in accordance with the immediately preceding sentence shall be deemed to have forfeited its right to sell any Shares (including any Additional Shares) to the Company pursuant to this
Agreement. 

 (b) Shares Closing. If a Shares Sale Notice is timely delivered by any Investor to
the Company and Escrow Agent, the closing of the sale of the Shares contemplated in each such timely delivered Share Sales Notice (the “Shares Closing”) shall occur no later than the three (3) month anniversary of the Business
Combination Closing Date (the “Shares Closing Date”). On the Shares Closing Date, each selling Investor shall deliver, or cause to be delivered, the Shares (including any Additional Shares) subject to the applicable Shares Sale
Notice free and clear of all liens and encumbrances to the Escrow Agent, and in exchange therefor, the Escrow Agent shall deliver to each such selling Investor(s) an amount equal to (i) the Shares Purchase Price multiplied by
(ii) the number of Shares being sold by such selling Investor (with respect to any particular selling Investor, the “Investor Shares Purchase Price”), which shall be paid by wire transfer of immediately available funds from the
Escrow Account. The Escrow Agent shall, (i) without delay, release from the Escrow Account to each selling Investor on the Shares Closing Date, for such selling Investor’s use without restriction, an amount equal to such Investor’s
Investor Shares Purchase Price, and (ii) promptly deliver such sold Shares to the Company. 
 2. Representations and Warranties of the
Investors. Each Investor represents and warrants to GigCapital4, severally and not jointly, as follows, as of the date hereof: 
 (a)
Organization and Power. Such Investor is duly organized, validly existing, and in good standing under the laws of the jurisdiction of its formation and has all requisite power and authority to carry on its business as presently conducted and
as proposed to be conducted. 
 (b) Authorization. Each Investor has full power and authority to enter into this Agreement. This
Agreement, when executed and delivered by each Investor will constitute the valid and legally binding obligation of each Investor enforceable against it in accordance with its terms, except (i) as limited by applicable bankruptcy, insolvency,
reorganization, moratorium, fraudulent conveyance and any other laws of general application affecting enforcement of creditors’ rights generally, or (ii) as limited by laws relating to the availability of specific performance, injunctive
relief or other equitable remedies ((i) and (ii) collectively, the “Enforceability Exceptions”). 
 (c)
Governmental Consents and Filings. No consent, approval, order or authorization of, or registration, qualification, designation, declaration or filing with, any federal, state or local governmental authority is required on the part of such
Investor in connection with the consummation of the transactions contemplated by this Agreement (collectively, the “Transactions”) other than disclosure reports regarding such transactions that such Investor is required to file in
accordance with the terms of the Exchange Act (as defined below). 
 (d) Compliance with Other Instruments. The execution, delivery
and performance by each Investor of this Agreement and the consummation each Investor of the Transactions will not result in any violation or default (i) of any provisions of its organizational documents, (ii) of any instrument, judgment,
order, writ or decree to which it is a party or by which it is bound, (iii) under any note, indenture or mortgage to which it is a party or by which it is bound, (iv) under any lease, agreement, contract or purchase order to which it is a
party or by which it is bound, or (v) of any provision of federal or state statute, rule or regulation applicable to it, in each case (other than clause (i)), which would have a material adverse effect on such Investor or its ability to
consummate the Transactions. 
 (e) Share-Holdings. As of the date of this Agreement, neither Investor holds any Shares. 

(f) Disclosure of Information. Each Investor has had an opportunity to discuss GigCapital4’s and the Company’s business,
management and financial affairs, and the terms and conditions of this Agreement, as well as the terms of the Business Combination, with GigCapital4’s management. 

  
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 (g) No Other Representations and Warranties;
Non-Reliance. Except for the specific representations and warranties contained in this Section 2 and in any certificate or written agreement delivered pursuant hereto, neither the
Investor or any person acting on behalf of either Investor nor any of the Investors’ respective affiliates (collectively, the “Investor Parties”) has made, makes or shall be deemed to make any other express or implied
representation or warranty with respect to either Investor, and the Investor Parties disclaim any such representation or warranty. Except for the specific representations and warranties expressly made by GigCapital4 in
Section 3 of this Agreement, in any certificate or written agreement delivered pursuant hereto and in any public filings, the Investor Parties specifically disclaim that they are relying upon any other representations or
warranties that may have been made by the GigCapital4 Parties (as defined below). 
 3. Representations and Warranties of
GigCapital4. GigCapital4 represents and warrants to each Investor as follows: 
 (a) Organization and Corporate Power.
GigCapital4 is a corporation duly incorporated, validly existing and in good standing as a corporation under the laws of the State of Delaware and has all requisite corporate power and authority to carry on its business as presently conducted and as
proposed to be conducted. GigCapital4 has no subsidiaries other than the merger subsidiary referenced in the recitals hereto that was formed for the purpose of effecting the Business Combination. 

(b) Authorization. All corporate action required to be taken by GigCapital4’s Board of Directors in order to authorize GigCapital4
to enter into this Agreement has been taken. This Agreement, when executed and delivered by GigCapital4, shall constitute the valid and legally binding obligation of GigCapital4, enforceable against GigCapital4 in accordance with its term, subject
to the effect of the Enforceability Exceptions. 
 (c) Disclosure. GigCapital4 has not disclosed to the Investors material non-public information with respect to GigCapital4 or the Business Combination, other than any such information that shall be publicly disclosed by GigCapital4 either by the issuance of a press release or the filing
with the Commission a Current Report on Form 8-K, in each case, by 9:00 a.m., Eastern Time on the first Business Day immediately following the date that the Parties enter into this Agreement. Such public
disclosure shall disclose the name of the Investors as having entered into the Agreement. 
 (d) Governmental Consents and Filings.
No consent, approval, order or authorization of, or registration, qualification, designation, declaration or filing with, any federal, state or local governmental authority is required on the part of GigCapital4 in connection with the consummation
of the Transactions, other than disclosure reports regarding such transactions GigCapital4 is required to file in accordance with the terms of the Exchange Act. 

(e) Compliance with Other Instruments. The execution, delivery and performance by GigCapital4 of this Agreement and the consummation by
GigCapital4 of the Transactions will not result in any violation or default (i) of any provisions of its organizational documents, (ii) of any instrument, judgment, order, writ or decree to which it is a party or by which it is bound,
(iii) under any note, indenture or mortgage to which it is a party or by which it is bound, (iv) under any lease, agreement, contract or purchase order to which it is a party or by which it is bound, or (v) of any provision of federal
or state statute, rule or regulation applicable to it, in each case (other than clause (i)), which would have a material adverse effect on GigCapital4 or its ability to consummate the Transactions. 

(f) Adequacy of Financing. The Company will have available to it sufficient funds to satisfy its obligations under this Agreement. 

  
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 (g) SEC Filings. To the knowledge of GigCapital4, none of GigCapital4’s reports
and other filings with the Commission, as of their respective dates, contained any untrue statement of a material fact or omitted to state a material fact required to be stated therein or necessary to make the statements therein, in light of the
circumstances under which they were made, not misleading. 
 (h) Most Favored Nation. Subject to the exception provided for in
Section 4(g) with regard to what constitutes a Company Material Adverse Effect for the purposes of Section 6(c), the material terms of any Additional Investor Agreements (as such term is defined
below) already entered into by GigCapital4 are no more favorable to such Additional Investors (as such term is defined below) thereunder than the terms of this Agreement are in respect of the Investors hereunder. 

(i) No Other Representations and Warranties; Non-Reliance. Except for the specific
representations and warranties contained in this Section 3 and in any certificate or written agreement delivered pursuant hereto or in any public filings, neither GigCapital4 or any person on behalf of GigCapital4 nor any
of GigCapital4’s affiliates (collectively, the “GigCapital4 Parties”) has made, makes or shall be deemed to make any other express or implied representation or warranty with respect to GigCapital4, the Company, the Transactions
or the Business Combination, and the GigCapital4 Parties disclaim any such representation or warranty. Except for the specific representations and warranties expressly made by each Investor in Section 2 of this Agreement
and in any certificate or agreement delivered pursuant hereto, the GigCapital4 Parties specifically disclaim that they are relying upon any other representations or warranties that may have been made by the Investor Parties. 

4. Additional Agreements. 

(a) No Short Sales. Each Investor agrees not to engage in any transactions involving any Short Sales involving any securities of
GigCapital4 or the Company prior to the Share Closing Date. For purposes hereof, “Short Sales” include, without limitation, all “short sales” as defined in Rule 200 promulgated under Regulation SHO under the Securities and
Exchange Act of 1934 (as amended, the “Exchange Act”). 
 (b) No Redemptions; No Tenders. Each Investor further
agrees not to (i) request redemption of any of the Shares (including any Additional Shares) in conjunction with GigCapital4’s stockholders’ approval of the Business Combination, or (ii) tender the Shares (including any Additional
Shares) to GigCapital4 in response to any redemption or tender offer that GigCapital4 may commence for its shares of common stock; provided that (x) all of the Additional Investors shall be bound by a substantially similar restriction as
set forth in this Section 4(b) in the Additional Investor Agreements (as defined below), and (y) the Shares subject to this Section 4(b) shall not represent more than twenty-five percent (25%)
of the aggregate number of shares of common stock of GigCapital4 subject to such restriction (or a substantially similar restriction) pursuant to this Agreement and the Additional Investor Agreements (and in the event that fewer than an aggregate of
10,000,000 shares of common stock of GigCapital4 are subject to such a restriction (or a substantially similar restriction) pursuant to this Agreement and the Additional Investor Agreements, the number of Shares set forth in
Section 1(a) (solely for the purposes of this Section 4(b)) shall be reduced ratably such that the aggregate number of Shares subject to such restrictions shall be no more than twenty-five percent
(25%) of the total number of shares of common stock of GigCapital4 that are subject to such restrictions pursuant to the Agreement and the Additional Investor Agreements, unless otherwise mutually agreed upon in writing). 

(c) Option to Purchase Additional Shares and Certain Derivatives. GigCapital4 hereby acknowledges that nothing in this Agreement shall
prohibit either Investor from purchasing from third parties prior to the Business Combination Closing Date additional shares of common stock of GigCapital4, including shares that have previously been tendered by third parties for redemption in
conjunction with GigCapital4’s stockholders’ approval of the Business Combination, to the extent such third parties unwind 

  
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such tenders for redemption (the “Additional Shares”), or any warrants, convertible notes or options (including puts or calls) of GigCapital4; provided, the aggregate
number of Shares and Additional Shares owned by the Investors and subject to Sections 1, 4(b) (including after application of any ratable reduction as provided for in Section 4(b)) and 4(c) shall not exceed 2,500,000 shares
of common stock of GigCapital4, in the aggregate among the Investors, unless otherwise agreed in writing by all Parties. For the avoidance of doubt, all Additional Shares shall be deemed Shares for all purposes hereunder and shall be purchased by
the Company in accordance with Section 1. 
 (d) Open Market Sale. Notwithstanding anything to the contrary
herein, the Parties agree that each Investor shall, commencing on the day after the date by which shares of common stock of GigCapital4 must be tendered for redemption in conjunction with GigCapital4’s stockholders’ approval of the
Business Combination (the “Redemption Date”), have the right, but not the obligation, to sell any or all of the Shares (including any Additional Shares) in the open market if the sale price exceeds $10.00 per Share prior to payment
of any commissions due by the Investors for such sale. Each Investor shall give written notice to the Company and Escrow Agent of any sale of the Shares (including any Additional Shares) pursuant to Section 4(d) within
three (3) Business Days following the date of such sale (each, an “Open Market Sale Notice”), and each Open Market Sale Notice shall include the date of the sale, the number of Shares sold, and confirmation that the sale price
per Share was greater than $10.00 per Share prior to the payment of any commissions due by the Investor for the sale. If the Investors sell any Shares (including any Additional Shares) in the open market after the Redemption Date and prior to the
one (1) month anniversary of the Business Combination Closing Date at a sales price per Share that is greater than $10.05 (such sale, the “Early Sale” and such shares, the “Early Sale Shares”), then,
within five (5) Business Days of the Company’s and the Escrow Agent’s receipt of such Open Market Sale Notice, the Escrow Agent shall release from the Escrow Account (x) to each selling Investor an amount equal to $0.05 per Early
Sale Share sold by such Investor (the “Early Sale Premium”) and (y) to the Company an amount equal to $10.10 per Early Sale Share sold in such Early Sale. 

(e) Escrow. 
 (i)
Simultaneously with the closing of the Business Combination, GigCapital4 shall deposit, for good and valuable consideration, the receipt, sufficiency and adequacy of which GigCapital4 hereby acknowledges, into an escrow account (the “Escrow
Account”) with Continental Stock Transfer & Trust Company (the “Escrow Agent”), subject to the terms of a written escrow agreement (the “Escrow Agreement”) substantially in the form attached as
Exhibit A hereto and to be entered into prior to the Redemption Date, an amount equal to the lesser of (x) $25,375,000 and (y) $10.15 multiplied by the number of Shares and Additional Shares held by the Investors as of the
closing of the Business Combination. Concurrently with the execution of the Escrow Agreement, the Company shall provide irrevocable written instructions to the Escrow Agent to release from the Escrow Account the aggregate Shares Purchase Price in
accordance with Section 1 and the aggregate Early Sales Premium in accordance Section 4(d). The payments to be made by the Company to each Investor in accordance with
Section 1 or Section 4(d), if applicable, will be made solely with funds from the Escrow Account. 

(ii) In the event that any Investor sells any Shares (including any Additional Shares) as provided in Section 4(d),
upon receipt by the Company and the Escrow Agent of an Open Market Sale Notice, the Escrow Agent shall release from the Escrow Account to the Company for the Company’s use without restriction an aggregate amount equal to the number of Shares
(including any Additional Shares) sold multiplied by $10.15; provided that if an Investor sold any Early Sale Shares, within five (5) Business Days of the Company’s and the Escrow Agent’s receipt of the applicable Open
Market Sale Notice, the Escrow Agent shall release from the Escrow Account (a) for the selling Investor’s use without restriction an amount equal to the Early Sale Premium with respect to the Early Sale Shares sold by such Investor, and
(b) for the Company’s use without restriction an amount equal to the number of Early Sale Shares sold in the Early Sale multiplied by $10.10. 

  
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 (iii) In the event that any Investor elects not to sell to the Company any Shares
(including any Additional Shares) held by such Investor by either (A) delivering a written notice to the Escrow Agent stating such Investor’s intention not to sell any Shares (or any Additional Shares) to the Escrow Agent, or (B) such
Investor failing to timely deliver a Shares Sale Notice to the Company pursuant to Section 1(a) for all of its Shares, the Escrow Agent shall release from the Escrow Account to the Company for the Company’s use without
restriction an amount equal to (x) $10.15 multiplied by (y) the number of Shares held by such Investor. 
 (f)
Notification. The Company shall notify each Investor of the occurrence of any event that would make any of the representations and warranties of GigCapital4 set forth in Section 3 untrue or incorrect at any time
between the date of this Agreement and the Shares Closing Date, except where the failure of a representation and warranty to be true and correct would not have a material adverse effect on GigCapital4 or the Company’s ability to consummate the
Transactions. 
 (g) Most Favored Nation. Shortly before the execution of this Agreement, GigCapital4 may have entered into, or
concurrently with, or shortly after, the execution of this Agreement, GigCapital4 may enter into, separate agreements with other investors (the “Additional Investors”) for the purchase and sale of GigCapital4 common stock imposing
restrictions on dispositions of GigCapital4 common stock by the Additional Investors similar to those herein ((i) and (ii) collectively, the “Additional Investor Agreements”). GigCapital4 agrees not to provide the Additional
Investors material terms in the Additional Investor Agreements that are more favorable to such Additional Investors than the terms provided to the Investors in this Agreement, except that (i) the Additional Investor Agreements for Additional
Investors (including with such Additional Investors’ affiliates) who are not parties to a Note Subscription Agreement (as defined in the Merger Agreement) will, solely for the purposes of the Additional Investor Agreements to which such
Additional Investors are a party, have an expanded definition of what constitutes a Company Material Adverse Effect for the purposes of Section 6(c), and this shall not constitute a breach of this
Section 4(g) or provide any rights to either Investor notwithstanding the subsequent sentence and (ii) the Additional Investor Agreements may provide that the ratable reduction in the number of Shares contemplated in
Section 4(b) applies for purposes beyond Section 4(b), including by ratably reducing the number of Shares subject to Section 1(a) (or, in each case in this clause (ii),
the section(s) of such Additional Investor Agreements containing the provisions analogous to those set forth in Section 1(a) or Section 4(b) hereof, as applicable). In the event that GigCapital4
provides the Additional Investors with material terms in the Additional Investor Agreements that are more favorable than the terms provided to the Investors in this Agreement at any time prior to the Business Combination Closing Date, GigCapital4
shall promptly inform each Investor of such more favorable terms, and each Investor shall have the mutual right to elect to have such more favorable terms included herein, in which case the Parties shall promptly amend this Agreement to effect the
same. 
 (h) Security Agreement in Escrow Account. To secure the obligations of GigCapital4 and the Company under this Agreement,
GigCapital4 and the Company each grant to each Investor a security interest in, and lien on, all right, title, and interest of GigCapital4 and the Company in and to the Escrow Account in respect of all funds required to satisfy GigCapital4’s
and the Company’s obligations hereunder, the Escrow Agreement, all rights related thereto, and all proceeds, products, and profits of the foregoing. In the event of a default by GigCapital4 or the Company under this Agreement or the Escrow
Agreement, then, in addition to any other rights each Investor may have under this Agreement, the Escrow Agreement, and applicable law, each Investor shall also have the rights and remedies of a secured party under the Uniform Commercial Code as
enacted in the State of New York. GigCapital4 and the Company shall use commercially reasonable efforts to prepare and file such UCC financing statements or other documents as reasonably directed by each Investor with respect to their security
interests. 
 (i) Indemnification. GigCapital4 (referred to as the “Indemnitor”) agrees to indemnify each Investor
and their respective officers, directors, employees, agents and shareholders (collectively referred to as the “Indemnitees”) against, and hold them harmless of and from, any and all loss, liability, cost, damage and expense,
including without limitation, reasonable and documented out-of-pocket outside counsel fees, which the Indemnitees may suffer or incur by reason of any action, claim or proceeding, in each case, brought by a third party creditor of GigCapital4, the
Company or any of their respective subsidiaries asserting that the Investors are not entitled to receive the aggregate Share Purchase Price or such portion thereof as they are entitled to receive pursuant to Section 1(a) and Section 4(d)
of this Agreement, in each case unless such action, claim or proceeding is the result of the fraud, bad faith, willful misconduct or gross negligence of any Indemnitee. 

  
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 5. Closing Conditions. The obligation of the Company to purchase the Shares at the
Shares Closing under this Agreement shall be subject in all respects to the consummation of the Business Combination, such Shares being free and clear of all liens and other encumbrances as of the Shares Closing and such Shares being continuously
held by the Investors from the closing of the Business Combination through the three (3) month anniversary of the Business Combination Closing Date. 

6. Termination. This Agreement may be terminated as follows: 

(a) at any time by mutual written consent of all Parties; 

(b) automatically if the stockholders of GigCapital4 fail to approve the Business Combination; and 

(c) prior to the closing of the Business Combination by mutual agreement of each Investor if there occurs a Company Material Adverse Effect
(as defined in the Merger Agreement). 
 In the event of termination in accordance with Section 6(a), 6(b)
or 6(c), this Agreement shall forthwith become null and void and have no effect, without any liability on the part of either Investor, GigCapital4, or the Company and their respective directors, officers, employees, partners, managers,
members, or stockholders and all rights and obligations of each Party shall cease; provided, however, that nothing contained in this Section 6 shall relieve any Party from liabilities or damages arising out of any
actual fraud or willful breach by such party of any of its representations, warranties, covenants or agreements contained in this Agreement prior to termination of this Agreement. 

7. General Provisions. 

(a) Notices. All notices and other communications given or made pursuant to this Agreement shall be in writing and shall be deemed
effectively given upon the earlier of actual receipt, or (i) personal delivery to the Party to be notified, (ii) when sent, if sent by electronic mail during normal business hours of the recipient, and if not sent during normal business
hours, then on the recipient’s next Business Day, (iii) five (5) Business Days after having been sent by registered or certified mail, return receipt requested, postage prepaid, or (iv) one (1) Business Day after deposit with a
nationally recognized overnight courier, freight prepaid, specifying next Business Day delivery, with written verification of receipt. All notices and other communications sent to a Party shall be sent to the
e-mail address or address as set forth on the signature page of such Party hereto, or to such e-mail address or address as subsequently modified by written notice given
by such Party in accordance with this Section 7(a). 
 (b) No Finder’s Fees. Each Party represents
that it neither is nor will be obligated for any finder’s fee or commission in connection with the Transactions. Each Investor agrees to indemnify and to hold harmless GigCapital4 from any liability for any commission or compensation in the
nature of a finder’s or broker’s fee arising out of the Transactions (and the costs and expenses of defending against such liability or asserted liability) for which the Investors, or any of their respective officers, employees or
representatives is responsible or arising out of any agreement entered into by any such person or entity. GigCapital4 agrees to indemnify and hold harmless each Investor from any liability for any commission or compensation in the nature of a
finder’s or broker’s fee arising out of the Transactions (and the costs and expenses of defending against such liability or asserted liability) for which GigCapital4 or any of its officers, employees or representatives is responsible or
arising out of any agreement entered into by any such person or entity. 
 (c) Survival of Representations and Warranties. All of the
representations and warranties contained herein shall survive the Shares Closing. 

  
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 (d) Entire Agreement. This Agreement, together with any documents, instruments and
writings that are delivered pursuant hereto or referenced herein, constitute the entire agreement and understanding of the Parties in respect of its subject matter and supersedes all prior understandings, agreements, or representations by or among
the Parties, written or oral, to the extent they relate in any way to the subject matter hereof or to the Transactions. 
 (e)
Successors. All of the terms, agreements, covenants, representations, warranties, and conditions of this Agreement are binding upon, and inure to the benefit of and are enforceable by, the Parties and their respective successors. Nothing in
this Agreement, express or implied, is intended to confer upon any party other than the Parties or their respective successors and assigns any rights, remedies, obligations or liabilities under or by reason of this Agreement, except as expressly
provided in this Agreement. 
 (f) Assignments. Except as otherwise specifically provided herein, no Party may assign either this
Agreement or any of its rights, interests, or obligations hereunder without the prior written approval of the each of the other Parties. 

(g) Counterparts. This Agreement may be executed in two or more counterparts, each of which will be deemed an original but all of which
together will constitute one and the same instrument. Signatures sent by facsimile transmission or in PDF format shall be deemed to be originals for all purposes of this Agreement. 

(h) Headings. The section headings contained in this Agreement are inserted for convenience only and will not affect in any way the
meaning or interpretation of this Agreement. 
 (i) Governing Law; Jurisdiction. This Agreement, the entire relationship of the
Parties, and any litigation among the Parties (whether grounded in contract, tort, statute, law or equity) shall be governed by, construed in accordance with, and interpreted pursuant to the laws of the State of Delaware, without giving effect to
its choice of laws or conflict of law provision or rule (whether of the State of Delaware or any other jurisdiction) that would cause the application of the laws of any jurisdiction other than the State of Delaware. Any dispute arising from or
relating to the relative rights of the parties hereto and all other questions concerning the construction, validity and interpretation of this Agreement, shall be brought exclusively in the Court of Chancery of the State of Delaware (the
“Court of Chancery”) or, to the extent the Court of Chancery does not have subject matter jurisdiction, the United States District Court for the District of Delaware and the appellate courts having jurisdiction of appeals in such
courts (the “Delaware Federal Court”) or, to the extent neither the Court of Chancery nor the Delaware Federal Court has subject matter jurisdiction, the Superior Court of the State of Delaware (the “Chosen
Courts”), and, solely with respect to any such action (i) irrevocably submits to the exclusive jurisdiction of the Chosen Courts, (ii) waives any objection to laying venue in any such action in the Chosen Courts, and
(iii) waives any objection that the Chosen Courts are an inconvenient forum or do not have jurisdiction over any party hereto. 
 (j)
MUTUAL WAIVER OF JURY TRIAL. EACH PARTY TO THIS AGREEMENT HEREBY WAIVES ALL RIGHTS TO TRIAL BY JURY IN ANY ACTION, SUIT, OR PROCEEDING BROUGHT TO RESOLVE ANY DISPUTE BETWEEN OR AMONG ANY OF THE PARTIES HERETO, WHETHER ARISING IN CONTRACT,
TORT, OR OTHERWISE, ARISING OUT OF, CONNECTED WITH, RELATED OR INCIDENTAL TO THIS AGREEMENT AND/OR THE TRANSACTIONS CONTEMPLATED HEREBY. 

(k) Amendments. This Agreement may not be amended, modified or waived as to any particular provision, except with the prior written
consent of all Parties. 

  
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 (l) Severability. The provisions of this Agreement will be deemed severable and the
invalidity or unenforceability of any provision will not affect the validity or enforceability of the other provisions hereof; provided that if any provision of this Agreement, as applied to any Party or to any circumstance, is adjudged by a
governmental authority, arbitrator, or mediator not to be enforceable in accordance with its terms, the Parties agree that the governmental authority, arbitrator, or mediator making such determination will have the power to modify the provision in a
manner consistent with its objectives such that it is enforceable, and/or to delete specific words or phrases, and in its reduced form, such provision will then be enforceable and will be enforced. 

(m) Expenses. At the Business Combination Closing Date, GigCapital4 shall pay the reasonable and documented out-of-pocket fees and expenses of legal counsel to the Investors, in an amount not to exceed, the product of (A) $2,000 multiplied by (B) (i) the number of Shares
subject to the Investors’ collective obligations not to redeem divided by (ii) 1,000,000. 
 (n) Construction. The
Parties 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 and no presumption or burden
of proof will arise favoring or disfavoring any Party because of the authorship of any provision of this Agreement. For purposes of this Agreement, “Business Day” means any day other than Saturday, Sunday, or a day on which
commercial banks in New York are obligated by any applicable law to close. Any reference to any federal, state, local, or foreign law will be deemed also to refer to law as amended and all rules and regulations promulgated thereunder, unless the
context requires otherwise. 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 intend that each representation, warranty, and covenant contained herein will have independent significance. If a Party 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 has not breached will not detract from or mitigate the fact that such party is in breach of the
first representation, warranty, or covenant. 
 (o) Waiver. No waiver by a Party of any default, misrepresentation, or breach of
warranty or covenant hereunder, whether intentional or not, may be deemed to extend to any prior or subsequent default, misrepresentation, or breach of warranty or covenant hereunder or affect in any way any rights arising because of any prior or
subsequent occurrence. 
 (p) Specific Performance. Each Party agrees that irreparable damage may occur in the event any provision of
this Agreement was not performed by any other Party in accordance with the terms hereof and that the other Parties shall be entitled to seek specific performance of the terms hereof, in addition to any other remedy at law or equity. 

[Signature page follows] 
  

  
 9 

 IN WITNESS WHEREOF, the undersigned have executed this Agreement to be effective as
of the date first set forth above. 
  

	
	Investors:
	
	HIGHBRIDGE TACTICAL CREDIT MASTER FUND, L.P.
	By: Highbridge Capital Management, LLC, as Trading Manager
	
	By: /s Jonathan Segal
	Name: Jonathan Segal
	Title: Managing Director, Co-Chief Investment Officer
	
	HIGHBRIDGE SPAC OPPORTUNITY FUND, L.P.
	By: Highbridge Capital Management, LLC, as Trading Manager
	
	By: /s Jonathan Segal
	Name: Jonathan Segal
	Title: Managing Director, Co-Chief Investment Officer
	
	Address for Notices to each Investor:
	
	 Highbridge Capital Management, LLC
 277 Park
Ave. 23rd Floor

	New York, NY 10172
	E-mail: 
	Phone: 
	Attention: 
	
	GigCapital4:
	
	GIGCAPITAL4, INC.
	
	By: /s Dr. Raluca Dinu
	Name: Dr. Raluca Dinu
	Title: President & CEO
	
	Address for Notices:
	
	 GigCapital4, Inc.
 1731 Embarcadero Road, Suite
200

	Palo Alto, CA 94303
	Attention: Chief Executive Office

 Signature Page to Forward Share Purchase Agreement 

 Exhibit A 

Escrow Agreement 

(attached hereto)EX-10.2

 Exhibit 10.2 

FORWARD SHARE PURCHASE AGREEMENT 

This Forward Share Purchase Agreement (this “Agreement”) is entered into as of October 14, 2021, by and among
(i) GigCapital4, Inc., a Delaware corporation (“GigCapital4”), (ii) Glazer Capital, LLC, a Delaware limited liability company (“Glazer”), and (iii) Meteora Capital, LLC, a Delaware limited liability
company (“Meteora”), on behalf of itself and its affiliated investment funds (together with Glazer and Meteora, each individually an “Investor” and collectively, the “Investors”). Each of
GigCapital4, Glazer and Meteora is individually referred to herein as a “Party” and collectively as the “Parties”. Each of Glazer and Meteora is individually referred to herein as a “Principal
Investor” and together, the “Principal Investors”. Each Investor (other than the Principal Investors) is individually referred to herein as a “Non-Principal Investor”
and together, the “Non-Principal Investors”). 
 Recitals 

WHEREAS, GigCapital4 is a Private-to-Public Equity (PPE)TM company, also known as a blank check company or special purpose acquisition company, formed for the purpose of effecting a merger, capital stock exchange, asset acquisition, stock purchase,
reorganization or similar business combination with one or more businesses; 
 WHEREAS, GigCapital4 has entered into an agreement and plan
of merger (as amended from time to time, the “Merger Agreement”) with BigBear.ai Holdings, LLC, a Delaware limited liability company (“BigBear”), pursuant to which a wholly-owned merger subsidiary of GigCapital4
will merge with and into BigBear, and then BigBear as the surviving company of that merger will merge with and into GigCapital4 (such transactions, the “Business Combination”), which will be renamed BigBear.ai Holdings, Inc. upon
the consummation of that second merger (BigBear.ai Holdings, Inc., as the post-combination company shall be referred to herein as the “Company”), and GigCapital4 has filed a preliminary proxy statement with the U.S. Securities and
Exchange Commission (the “Commission”) that will seek, among other things, stockholder approval of the Business Combination; and 

WHEREAS, the Parties wish to enter into this Agreement, pursuant to which the Company shall purchase from the Investors, and the Investors may
sell and transfer to the Company, in each case, subject to the conditions set forth herein, certain shares of common stock, par value $0.0001 per share of GigCapital4 held by the Investors (the “Shares”) on the terms set forth
herein. 
 NOW, THEREFORE, in consideration of the premises, representations, warranties and the mutual covenants contained in this
Agreement, and for other good and valuable consideration, the receipt, sufficiency and adequacy of which are hereby acknowledged, the Parties agree as follows: 

Agreement 

	 	1.	 Sale of Shares; Shares Purchase and Sale; Closing. 

(a) Forward Share Purchase. Subject to the conditions set forth in Section 4, on the three (3) month
anniversary of the date of the closing of the Business Combination (the “Business Combination Closing Date”), the Investors may elect to sell and transfer to the Company, and the Company shall purchase from the Investors, up to that
number of Shares (including any Additional Shares) that are then held by the Investors, and have been continuously held by the Investors since the Business Combination Closing Date, but not to exceed 5,000,000 Shares (including any Additional
Shares) in the aggregate unless otherwise agreed in writing by all Parties, at a price per Share equal to $10.15 per Share (the “Shares Purchase Price”). Each Principal Investor shall, and the Principal Investors shall cause the Non-Principal Investors to, notify the Company and the Escrow Agent in writing five (5) Business Days (as defined below) prior to the three 

 
(3) month anniversary of the Business Combination Closing Date whether or not such Investor is exercising such Investor’s right to sell any of the Shares (including any Additional Shares)
held by such Investor to the Company pursuant to this Agreement (each, a “Shares Sale Notice”). Any Investor that fails to timely deliver a Shares Sales Notice in accordance with the immediately preceding sentence shall be deemed to
have forfeited its right to sell any Shares (including any Additional Shares) to the Company pursuant to this Agreement. 
 (b) Shares
Closing. If a Shares Sale Notice is timely delivered by any Investor to the Company and Escrow Agent, the closing of the sale of the Shares contemplated in each such timely delivered Share Sales Notice (the “Shares Closing”)
shall occur no later than the three (3) month anniversary of the Business Combination Closing Date (the “Shares Closing Date”). On the Shares Closing Date, each selling Investor shall deliver, or cause to be delivered, the
Shares (including any Additional Shares) subject to the applicable Shares Sale Notice free and clear of all liens and encumbrances to Escrow Agent and, in exchange therefor, the Escrow Agent shall deliver to each such selling Investor(s) an amount
equal to (i) the Shares Purchase Price multiplied by (ii) the number of Shares being sold by such selling Investor (with respect to any particular selling Investor, the “Investor Shares Purchase Price”), which shall
be paid by wire transfer of immediately available funds from the Escrow Account. The Escrow Agent shall, (i) without delay, release from the Escrow Account to each selling Investor on the Shares Closing Date, for such selling Investor’s
use without restriction, an amount equal to such Investor’s Investor Shares Purchase Price, and (ii) promptly deliver such sold Shares to the Company. 

2. Representations and Warranties of the Principal Investors. Each Principal Investor represents and warrants to GigCapital4,
severally and not jointly, and Meteora (and not Glazer) represents and warrants to GigCapital4 on behalf of the Non-Principal Investors as follows, as of the date hereof: 

(a) Organization and Power. Such Investor is duly organized, validly existing, and in good standing under the laws of the jurisdiction
of its formation and has all requisite power and authority to carry on its business as presently conducted and as proposed to be conducted. 

(b) Authorization. Such Principal Investor has full power and authority to enter into this Agreement. This Agreement, when executed and
delivered by such Principal Investor will constitute the valid and legally binding obligation of such Principal Investor enforceable against it in accordance with its terms, except (i) as limited by applicable bankruptcy, insolvency,
reorganization, moratorium, fraudulent conveyance and any other laws of general application affecting enforcement of creditors’ rights generally, or (ii) as limited by laws relating to the availability of specific performance, injunctive
relief or other equitable remedies ((i) and (ii) collectively, the “Enforceability Exceptions”). 
 (c)
Governmental Consents and Filings. No consent, approval, order or authorization of, or registration, qualification, designation, declaration or filing with, any federal, state or local governmental authority is required on the part of such
Investor in connection with the consummation of the transactions contemplated by this Agreement (collectively, the “Transactions”) other than disclosure reports regarding such transactions that such Investor is required to file in
accordance with the terms of the Exchange Act (as defined below). 
 (d) Compliance with Other Instruments. The execution, delivery
and performance by such Principal Investor of this Agreement and the consummation by such Principal Investor and the other Investors of the Transactions will not result in any violation or default (i) of any provisions of its organizational
documents, (ii) of any instrument, judgment, order, writ or decree to which it is a party or by which it is bound, (iii) under any note, indenture or mortgage to which it is a party or by which it is bound, (iv) under any lease,
agreement, contract or purchase order to which it is a party or by which it is bound, or (v) of any provision of federal or state statute, rule or regulation applicable to it, in each case (other than clause (i)), which would have a material
adverse effect on such Principal Investor or any of the other Investors or its or their ability to consummate the Transactions. 

  
 2 

 (e) Share-Holdings. As of the date of this Agreement, the Investors collectively hold
6,416 Shares, with the per Investor holdings of Shares set forth on Appendix A hereto. 
 (f) Disclosure of Information. Such
Principal Investor has had an opportunity to discuss GigCapital4’s and the Company’s business, management and financial affairs, and the terms and conditions of this Agreement, as well as the terms of the Business Combination, with
GigCapital4’s management. 
 (g) No Other Representations and Warranties; Non-Reliance.
Except for the specific representations and warranties contained in this Section 2 and in any certificate or written agreement delivered pursuant hereto, neither any Principal Investor or any person acting on behalf of such
Principal Investor nor any of such Principal Investor’s affiliates (collectively, the “Principal Investor Parties”) has made, makes or shall be deemed to make any other express or implied representation or warranty with respect
to such Principal Investor or the other Investors, and the Principal Investor Parties disclaim any such representation or warranty. Except for the specific representations and warranties expressly made by GigCapital4 in
Section 3 of this Agreement, in any certificate or written agreement delivered pursuant hereto and in any public filings, the Principal Investor Parties specifically disclaim that they are relying upon any other
representations or warranties that may have been made by the GigCapital4 Parties (as defined below). 
 3. Representations and
Warranties of GigCapital4. GigCapital4 represents and warrants to each Principal Investor as follows: 
 (a) Organization and
Corporate Power. GigCapital4 is a corporation duly incorporated, validly existing and in good standing as a corporation under the laws of the State of Delaware and has all requisite corporate power and authority to carry on its business as
presently conducted and as proposed to be conducted. GigCapital4 has no subsidiaries other than the merger subsidiary referenced in the recitals hereto that was formed for the purpose of effecting the Business Combination. 

(b) Authorization. All corporate action required to be taken by GigCapital4’s Board of Directors in order to authorize GigCapital4
to enter into this Agreement has been taken. This Agreement, when executed and delivered by GigCapital4, shall constitute the valid and legally binding obligation of GigCapital4, enforceable against GigCapital4 in accordance with its term, subject
to the effect of the Enforceability Exceptions. 
 (c) Disclosure. GigCapital4 has not disclosed to either Principal Investor
material non-public information with respect to GigCapital4 or the Business Combination, other than any such information that shall be publicly disclosed by GigCapital4 either by the issuance of a press
release or the filing with the Commission a Current Report on Form 8-K, in each case, by 9:00 a.m., Eastern Time on the first Business Day immediately following the date that the Parties enter into this
Agreement. Such public disclosure shall disclose the name of the Principal Investors as having entered into the Agreement. 
 (d)
Governmental Consents and Filings. No consent, approval, order or authorization of, or registration, qualification, designation, declaration or filing with, any federal, state or local governmental authority is required on the part of
GigCapital4 in connection with the consummation of the Transactions, other than disclosure reports regarding such transactions GigCapital4 is required to file in accordance with the terms of the Exchange Act. 

  
 3 

 (e) Compliance with Other Instruments. The execution, delivery and performance by
GigCapital4 of this Agreement and the consummation by GigCapital4 of the Transactions will not result in any violation or default (i) of any provisions of its organizational documents, (ii) of any instrument, judgment, order, writ or
decree to which it is a party or by which it is bound, (iii) under any note, indenture or mortgage to which it is a party or by which it is bound, (iv) under any lease, agreement, contract or purchase order to which it is a party or by
which it is bound, or (v) of any provision of federal or state statute, rule or regulation applicable to it, in each case (other than clause (i)), which would have a material adverse effect on GigCapital4 or its ability to consummate the
Transactions. 
 (f) Adequacy of Financing. The Company will have available to it sufficient funds to satisfy its obligations under
this Agreement. 
 (g) SEC Filings. To the knowledge of GigCapital4, none of GigCapital4’s reports and other filings with the
Commission, as of their respective dates, contained any untrue statement of a material fact or omitted to state a material fact required to be stated therein or necessary to make the statements therein, in light of the circumstances under which they
were made, not misleading. 
 (h) Most Favored Nation. The material terms of any Additional Investor Agreements (as such term is
defined below) already entered into by GigCapital4 are no more favorable to such Additional Investors (as such term is defined below) thereunder than the terms of this Agreement are in respect of the Investors hereunder. 

(i) No Other Representations and Warranties; Non-Reliance. Except for the specific
representations and warranties contained in this Section 3 and in any certificate or written agreement delivered pursuant hereto or in any public filings, neither GigCapital4 or any person on behalf of GigCapital4 nor any
of GigCapital4’s affiliates (collectively, the “GigCapital4 Parties”) has made, makes or shall be deemed to make any other express or implied representation or warranty with respect to GigCapital4, the Company, the Transactions
or the Business Combination, and the GigCapital4 Parties disclaim any such representation or warranty. Except for the specific representations and warranties expressly made by the Principal Investors in Section 2 of this
Agreement and in any certificate or agreement delivered pursuant hereto, the GigCapital4 Parties specifically disclaim that they are relying upon any other representations or warranties that may have been made by the Principal Investor Parties. 

4. Additional Agreements. 

(a) No Short Sales. Each Principal Investor agrees not to, and Meteora agrees to cause the
Non-Principal Investors not to, engage in any transactions involving any Short Sales involving any securities of GigCapital4 or the Company. For purposes hereof, “Short Sales” include, without
limitation, all “short sales” as defined in Rule 200 promulgated under Regulation SHO under the Securities and Exchange Act of 1934 (as amended, the “Exchange Act”). 

(b) No Redemptions; No Tenders. Each Principal Investor further agrees not to, and Meteora will cause the Non-Principal Investors not to, (i) request redemption of any of the Shares (including any Additional Shares) in conjunction with GigCapital4’s stockholders’ approval of the Business Combination, or
(ii) tender the Shares (including any Additional Shares) to GigCapital4 in response to any redemption or tender offer that GigCapital4 may commence for its shares of common stock; provided that (x) all of the Additional Investors
shall be bound by a substantially similar restriction as set forth in this Section 4(b) in the Additional Investor Agreements (as defined below), and (y) the Shares subject to this
Section 4(b) shall not represent more than fifty percent (50%) of the aggregate number of shares of common stock of GigCapital4 subject to such restriction (or a substantially similar restriction) pursuant to this Agreement
and the Additional Investor Agreements provided, however that in the event that fewer than an aggregate 

  
 4 

 
of 10,000,000 shares of common stock of GigCapital4 are subject to such a restriction (or a substantially similar restriction) pursuant to this Agreement and the Additional Investor Agreements,
the number of Shares set forth in Section 1(a) shall be reduced ratably such that the aggregate number of Shares subject to such restrictions shall be no more than fifty percent (50%) of the total number of shares of common
stock of GigCapital4 that are subject to such restrictions pursuant to the Agreement and the Additional Investor Agreements, unless otherwise mutually agreed upon in writing. 

(c) Option to Purchase Additional Shares and Certain Derivatives. GigCapital4 hereby acknowledges that nothing in this Agreement shall
prohibit the Investors from purchasing from third parties prior to the Business Combination Closing Date additional shares of common stock of GigCapital4, including shares that have previously been tendered by third parties for redemption at their
original redemption value in conjunction with GigCapital4’s stockholders’ approval of the Business Combination, to the extent such third parties unwind such tenders for redemption (the “Additional Shares”), or any
warrants, convertible notes or options (including puts or calls) of GigCapital4; provided, the aggregate number of Shares and Additional Shares owned by the Investors and subject to Sections 1, 4(b) and 4(c) shall not
exceed 5,000,000 shares of common stock of GigCapital4, unless otherwise agreed in writing by all Parties. For the avoidance of doubt, all Additional Shares shall be deemed Shares for all purposes hereunder and shall be purchased by the Company in
accordance with Section 1. 
 (d) Open Market Sale. Notwithstanding anything to the contrary herein, the
Parties agree that the Investors shall, commencing on the day after the date by which shares of common stock of GigCapital4 must be tendered for redemption in conjunction with GigCapital4’s stockholders’ approval of the Business
Combination (the “Redemption Date”), have the right, but not the obligation, to sell any or all of the Shares (including any Additional Shares) in the open market if the sale price exceeds $10.00 per Share prior to payment of any
commissions due by the Investors for such sale. The Principal Investors shall, and Meteora shall cause all selling Non-Principal Investor to, give written notice to the Company and Escrow Agent of any sale of
the Shares (including any Additional Shares) pursuant to Section 4(d) within three (3) Business Days following the date of such sale (each, an “Open Market Sale Notice”), and each Open Market Sale
Notice shall include the date of the sale, the number of Shares sold, and confirmation that the sale price per Share was greater than $10.00 per Share prior to the payment of any commissions due by the Investor for the sale. If the Investors sell
any Shares (including any Additional Shares) in the open market after the Redemption Date and prior to the one (1) month anniversary of the Business Combination Closing Date at a sales price per Share that is greater than $10.05 (such sale, the
“Early Sale” and such shares, the “Early Sale Shares”), then, within five (5) Business Days of the Company’s and the Escrow Agent’s receipt of such Open Market Sale Notice, the Escrow Agent shall
release from the Escrow Account (x) to each selling Investor an amount equal to $0.05 per Early Sale Share sold by such Investor (the “Early Sale Premium”) and (y) to the Company an amount equal to $10.10 per Early Sale
Share sold in such Early Sale. 
 (e) Escrow. 

(i) Simultaneously with the closing of the Business Combination, GigCapital4 shall deposit, for good and valuable consideration, the receipt,
sufficiency and adequacy of which GigCapital4 hereby acknowledges, into an escrow account (the “Escrow Account”) with Continental Stock Transfer & Trust Company (the “Escrow Agent”), subject to the terms of
a written escrow agreement (the “Escrow Agreement”) substantially in the form attached as Exhibit A hereto and to be entered into on or prior to the Business Combination Closing Date, an amount equal to the lesser of (x)
$50,750,000 and (y) $10.15 multiplied by the number of Shares and Additional Shares held by the Investors as of the closing of the Business Combination, including after application of any ratable reduction as provided for in
Section 4(b) (the “Escrowed Funds”). The Escrow Agreement shall irrevocably cause the Escrow Agent to release from the Escrow Account the aggregate Shares Purchase Price in accordance with
Section 1 and the aggregate Early Sales Premium in accordance Section 4(d). The payments to be made by the Escrow Agent to the Investors in accordance with Section 1 or
Section 4(d), if applicable, will be made solely with the Escrowed Funds. 

  
 5 

 (ii) In the event that any Investor sells any Shares (including any Additional Shares) as
provided in Section 4(d), upon receipt by the Company of an Open Market Sale Notice, the Company may issue instructions to the Escrow Agent to release from the Escrow Account to the Company for the Company’s use
without restriction an aggregate amount equal to the number of Shares (including any Additional Shares) sold multiplied by $10.15; provided that if an Investor sold any Early Sale Shares, within five (5) Business Days of the
Company’s and the Escrow Agent’s receipt of the applicable Open Market Sale Notice, the Escrow Agent shall release from the Escrow Account (a) for the selling Investor’s use without restriction an amount equal to the Early Sale
Premium with respect to the Early Sale Shares sold by such Investor, and (b) for the Company’s use without restriction an amount equal to the number of Early Sale Shares sold in the Early Sale multiplied by $10.10. 

(iii) In the event that any Investor elects not to sell to the Company any Shares (including any Additional Shares) held by such Investor by
either (A) a Principal Investor delivering a written notice to the Company on behalf of itself (or Meteora delivering a written notice to the Company on behalf of the Non-Principal Investors) stating such
Investor’s intention not to sell any Shares (or any Additional Shares) to the Company, or (B) such Investor failing to timely deliver a Shares Sale Notice to the Company pursuant to Section 1(a) for all of its
Shares, the Company may promptly issue instructions to the Escrow Agent to release from the Escrow Account to the Company for the Company’s use without restriction an amount equal to (x) $10.15 multiplied by (y) the number of
Shares held by such Investor. 
 (f) Notification. The Company shall promptly notify the Principal Investors of the occurrence of any
event that would make any of the representations and warranties of GigCapital4 set forth in Section 3 untrue or incorrect at any time between the date of this Agreement and the Shares Closing Date, except where the failure
of a representation and warranty to be true and correct would not have a material adverse effect on GigCapital4’s or the Company’s ability to consummate the Transactions. 

(g) Most Favored Nation. Concurrently with, or shortly after, the execution of this Agreement, GigCapital4 may enter into separate
agreements with other investors (the “Additional Investors”) for the purchase and sale of GigCapital4 common stock imposing restrictions on dispositions of GigCapital4 common stock by the Additional Investors similar to those herein
((i) and (ii) collectively, the “Additional Investor Agreements”). GigCapital4 agrees not to provide the Additional Investors material terms in the Additional Investor Agreements that are more favorable to such Additional
Investors than the terms provided to the Investors in this Agreement. In the event that GigCapital4 provides the Additional Investors with material terms in the Additional Investor Agreements that are more favorable than the terms provided to the
Investors in this Agreement at any time prior to the Business Combination Closing Date, GigCapital4 shall promptly inform the Principal Investors of such more favorable terms, and the Principal Investors shall have the mutual right to elect to have
such more favorable terms included herein, in which case the Parties shall promptly amend this Agreement to effect the same. 
 (h)
Security Agreement in Escrow Account. To secure the obligations of GigCapital4 and the Company under this Agreement, GigCapital4 and the Company each grant to the Principal Investors a security interest in, and lien on, all right, title, and
interest of GigCapital4 and the Company in and to the Escrow Account in respect of all funds required to satisfy GigCapital4’s and the Company’s obligations hereunder, the Escrow Agreement, all rights related thereto, and all proceeds,
products, and profits of the foregoing. In the event of a default by GigCapital4 or the Company under this Agreement or the Escrow Agreement, then, in addition to any other rights the Principal Investors may have under this Agreement, the Escrow
Agreement, and applicable law, the Principal Investors shall also have the rights and remedies of a secured party under the Uniform Commercial Code as enacted in the State of New York. GigCapital4 and the Company shall use commercially reasonable
efforts to prepare and file such UCC financing statements or other documents as reasonably directed by the Principal Investors with respect to their security interests. 

  
 6 

 (i) Indemnification. GigCapital4 (referred to as the “Indemnitor”)
agrees to indemnify the Investors and their respective officers, directors, employees, agents and shareholders (collectively referred to as the “Indemnitees”) against, and hold them harmless of and from, any and all loss, liability,
cost, damage and expense, including without limitation, reasonable and documented out-of-pocket outside counsel fees, which the Indemnitees may suffer or incur by reason
of any action, claim or proceeding, in each case, brought by a third party creditor of GigCapital4, the Company or any of their respective subsidiaries asserting that the Investors are not entitled to receive the aggregate Share Purchase Price or
such portion thereof as they are entitled to receive pursuant to Section 1(a) and Section 4(d) of this Agreement, in each case unless such action, claim or proceeding is the result of the fraud,
bad faith, willful misconduct or gross negligence of any Indemnitee. 
 5. Closing Conditions. The obligation of the Company
to purchase the Shares at the Shares Closing under this Agreement shall be subject in all respects to the consummation of the Business Combination, such Shares being free and clear of all liens and other encumbrances as of the Shares Closing and
such Shares being continuously held by the Investors from the closing of the Business Combination through the three (3) month anniversary of the Business Combination Closing Date. 

 

	 	6.	 Termination. This Agreement may be terminated as follows: 

(a) at any time by mutual written consent of all Parties; 

(b) automatically if the stockholders of GigCapital4 fail to approve the Business Combination; and 

(c) prior to the closing of the Business Combination by mutual agreement of the Principal Investors if there occurs a Company Material Adverse
Effect (as defined in the Merger Agreement); provided that, solely for purposes of this Agreement (and not, for the avoidance of doubt, for purposes of the Merger Agreement), the failure of the counterparties to the Note Subscription
Agreements (as defined in the Merger Agreement) to fund or cause the funding of 25% or greater of the aggregate amount of the Notes (as defined in the Merger Agreement) when required to do so pursuant to the terms of the Note Subscription Agreements
shall constitute a Company Material Adverse Effect. 
 In the event of termination in accordance with
Section 6(a), 6(b) or 6(c), this Agreement shall forthwith become null and void and have no effect, without any liability on the part of Glazer, Meteora, GigCapital4, or the Company and their respective
directors, officers, employees, partners, managers, members, or stockholders and, except as otherwise provided in this Agreement, all rights and obligations of each Party shall immediately cease; provided, however, that nothing contained in
this Section 6 shall relieve any Party from liabilities or damages arising out of any actual fraud or willful breach by such party of any of its representations, warranties, covenants or agreements contained in this
Agreement prior to termination of this Agreement. 
  

	 	7.	 General Provisions. 

(a) Notices. All notices and other communications given or made pursuant to this Agreement shall be in writing and shall be deemed
effectively given upon the earlier of actual receipt, or (i) personal delivery to the Party to be notified, (ii) when sent, if sent by electronic mail during normal business hours of the recipient, and if not sent during normal business
hours, then on the recipient’s next Business Day, (iii) five (5) Business Days after having been sent by registered or certified mail, return receipt requested, 

  
 7 

 
postage prepaid, or (iv) one (1) Business Day after deposit with a nationally recognized overnight courier, freight prepaid, specifying next Business Day delivery, with written verification
of receipt. All notices and other communications sent to a Party shall be sent to the e-mail address or address as set forth on the signature page of such Party hereto, or to such e-mail address or address as subsequently modified by written notice given by such Party in accordance with this Section 7(a). 

(b) No Finder’s Fees. Each Party represents that it neither is nor will be obligated for any finder’s fee or commission in
connection with the Transactions. Each Principal Investor agrees to indemnify and to hold harmless GigCapital4 from any liability for any commission or compensation in the nature of a finder’s or broker’s fee arising out of the
Transactions (and the costs and expenses of defending against such liability or asserted liability) for which the Investors, or any of their respective officers, employees or representatives is responsible or arising out of any agreement entered
into by any such person or entity. GigCapital4 agrees to indemnify and hold harmless the Principal Investors from any liability for any commission or compensation in the nature of a finder’s or broker’s fee arising out of the Transactions
(and the costs and expenses of defending against such liability or asserted liability) for which GigCapital4 or any of its officers, employees or representatives is responsible or arising out of any agreement entered into by any such person or
entity. 
 (c) Survival of Representations and Warranties. All of the representations and warranties contained herein shall survive
the Shares Closing. 
 (d) Entire Agreement. This Agreement, together with any documents, instruments and writings that are delivered
pursuant hereto or referenced herein, constitute the entire agreement and understanding of the Parties in respect of its subject matter and supersedes all prior understandings, agreements, or representations by or among the Parties, written or oral,
to the extent they relate in any way to the subject matter hereof or to the Transactions. 
 (e) Successors. All of the terms,
agreements, covenants, representations, warranties, and conditions of this Agreement are binding upon, and inure to the benefit of and are enforceable by, the Parties and their respective successors. Nothing in this Agreement, express or implied, is
intended to confer upon any party other than the Parties or their respective successors and assigns any rights, remedies, obligations or liabilities under or by reason of this Agreement, except as expressly provided in this Agreement. 

(f) Assignments. Except as otherwise specifically provided herein, no Party may assign either this Agreement or any of its rights,
interests, or obligations hereunder without the prior written approval of the each of the other Parties. 
 (g) Counterparts. This
Agreement may be executed in two or more counterparts, each of which will be deemed an original but all of which together will constitute one and the same instrument. Signatures sent by facsimile transmission or in PDF format shall be deemed to be
originals for all purposes of this Agreement. 
 (h) Headings. The section headings contained in this Agreement are inserted for
convenience only and will not affect in any way the meaning or interpretation of this Agreement. 
 (i) Governing Law; Jurisdiction.
This Agreement, the entire relationship of the Parties, and any litigation among the Parties (whether grounded in contract, tort, statute, law or equity) shall be governed by, construed in accordance with, and interpreted pursuant to the laws of the
State of Delaware, without giving effect to its choice of laws or conflict of law provision or rule (whether of the State of Delaware or any other jurisdiction) that would cause the application of the laws of any jurisdiction other than the State of
Delaware. Any dispute arising from or relating to the relative rights of the parties hereto and all other 

  
 8 

 
questions concerning the construction, validity and interpretation of this Agreement, shall be brought exclusively in the Court of Chancery of the State of Delaware (the “Court of
Chancery”) or, to the extent the Court of Chancery does not have subject matter jurisdiction, the United States District Court for the District of Delaware and the appellate courts having jurisdiction of appeals in such courts (the
“Delaware Federal Court”) or, to the extent neither the Court of Chancery nor the Delaware Federal Court has subject matter jurisdiction, the Superior Court of the State of Delaware (the “Chosen Courts”), and,
solely with respect to any such action (i) irrevocably submits to the exclusive jurisdiction of the Chosen Courts, (ii) waives any objection to laying venue in any such action in the Chosen Courts, and (iii) waives any objection that
the Chosen Courts are an inconvenient forum or do not have jurisdiction over any party hereto. 
 (j) MUTUAL WAIVER OF JURY TRIAL.
EACH PARTY TO THIS AGREEMENT HEREBY WAIVES ALL RIGHTS TO TRIAL BY JURY IN ANY ACTION, SUIT, OR PROCEEDING BROUGHT TO RESOLVE ANY DISPUTE BETWEEN OR AMONG ANY OF THE PARTIES HERETO, WHETHER ARISING IN CONTRACT, TORT, OR OTHERWISE, ARISING OUT OF,
CONNECTED WITH, RELATED OR INCIDENTAL TO THIS AGREEMENT AND/OR THE TRANSACTIONS CONTEMPLATED HEREBY. 
 (k) Amendments. This
Agreement may not be amended, modified or waived as to any particular provision, except with the prior written consent of all Parties. 

(l) Severability. The provisions of this Agreement will be deemed severable and the invalidity or unenforceability of any provision
will not affect the validity or enforceability of the other provisions hereof; provided that if any provision of this Agreement, as applied to any Party or to any circumstance, is adjudged by a governmental authority, arbitrator, or mediator
not to be enforceable in accordance with its terms, the Parties agree that the governmental authority, arbitrator, or mediator making such determination will have the power to modify the provision in a manner consistent with its objectives such that
it is enforceable, and/or to delete specific words or phrases, and in its reduced form, such provision will then be enforceable and will be enforced. 

(m) Expenses. At the Business Combination Closing Date, GigCapital4 shall pay the reasonable and documented out-of-pocket fees and expenses of legal counsel to the Principal Investors, in an amount not to exceed, in the aggregate $10,000. 

(n) Construction. The Parties 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 and no presumption or burden of proof will arise favoring or disfavoring any Party because of the authorship of any provision of this
Agreement. For purposes of this Agreement, “Business Day” means any day other than Saturday, Sunday, or a day on which commercial banks in New York are obligated by any applicable law to close. Any reference to any federal, state,
local, or foreign law will be deemed also to refer to law as amended and all rules and regulations promulgated thereunder, unless the context requires otherwise. 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 intend that each representation, warranty, and covenant contained herein will have independent significance. If a Party
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 has not breached will not detract from or mitigate the fact that such party is in breach of the first representation, warranty, or covenant. 

  
 9 

 (o) Waiver. No waiver by a Party of any default, misrepresentation, or breach of
warranty or covenant hereunder, whether intentional or not, may be deemed to extend to any prior or subsequent default, misrepresentation, or breach of warranty or covenant hereunder or affect in any way any rights arising because of any prior or
subsequent occurrence. 
 (p) Specific Performance. Each Party agrees that irreparable damage may occur in the event any provision of
this Agreement was not performed by any other Party in accordance with the terms hereof and that the other Parties shall be entitled to seek specific performance of the terms hereof, in addition to any other remedy at law or equity. 

[Signature page follows] 
  

  
 10 

 IN WITNESS WHEREOF, the undersigned have executed this Agreement to be effective as
of the date first set forth above. 
  

	
	Glazer:
	
	GLAZER CAPITAL, LLC
	
	By: /s Vik Mittal
	Name: Vik Mittal
	Title: Partner/PM
	
	Address for Notices:
	
	250 W 55th St #30A
	New York, NY 10019
	
	Meteora:
	
	METEORA CAPITAL, LLC, on behalf of itself and its affiliated investment funds
	
	By: /s Vik Mittal
	Name: Vik Mittal
	Title: CIO/Managing Partner
	
	Address for Notices:
	
	250 W 55th St #30A
	New York, NY 10019
	
	GigCapital4:
	
	GIGCAPITAL4, INC.
	
	By: /s Dr. Raluca Dinu
	Name: Dr. Raluca Dinu
	Title: President & CEO
	
	Address for Notices:
	
	GigCapital4, Inc. 1731 Embarcadero Road, Suite 200
	Palo Alto, CA 94303
	Attention: Chief Executive Officer
	Email:

 Signature Page to Forward Share Purchase Agreement 

 Appendix A 

 

					
	 Investor
	  	Number of Shares	 
	 Glazer Capital, LLC
	  	 	6,416	 
	 Meteora Capital, LLC
	  	 	0	 

 Exhibit A 

Escrow Agreement 

(attached hereto)

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