EX-10.1





 Exhibit 10.1 

June 4, 2021 
 GigCapital4, Inc. 

1731 Embarcadero Rd., Suite 200 
 Palo Alto, CA 94303 

Oppenheimer & Co. Inc. 
 85 Broad Street 

New York, New York 10004 
 Nomura Securities International, Inc.

 Worldwide Plaza 
 309 West 49th Street 

New York, New York 
 10019-7316 

Re: Acknowledgement of Satisfaction of Certain Payments under Insider Letter 

Ladies and Gentlemen: 
 Reference is made to that certain Letter
Agreement between GigAcquisitions4, LLC, a Delaware limited liability company (“Sponsor”), Oppenheimer & Co. Inc. (“Oppenheimer”), Nomura Securities International, Inc.
(“Nomura” and together with Oppenheimer, the “Underwriters”) and GigCapital4, Inc., a Delaware corporation (“Acquiror”), dated as of February 8, 2021 (the
“Insider Letter), relating to an underwritten initial public offering of certain units of the Acquiror (the “IPO”). Capitalized terms used and not otherwise defined herein have the meanings ascribed to them
in the Insider Letter. 
 Section 4 of the Insider Letter permits the Acquiror to make certain payments to the Sponsor, the
Underwriters and their Affiliates. This letter agreement (this “Letter Agreement”), which constitutes the “Sponsor Agreement” contemplated by, and is being delivered to you in accordance with, the Agreement and Plan
of Merger (the “Merger Agreement”), dated as of the date hereof, entered into by and among Acquiror, GigCapital4 Merger Sub Corporation, a Delaware corporation, BigBear.ai Holdings, LLC, a Delaware limited liability company
(the “Company”), and BBAI Ultimate Holdings, LLC, a Delaware limited liability company (“Holdings”), addresses, among other things, the status of such payments in connection with the consummation of
the Transactions (as defined in the Merger Agreement). 
 In order to induce the Company and Holdings to enter into the Merger Agreement,
and to proceed with the Transactions, and in recognition of the benefit that such Transactions will confer upon the undersigned, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged,
notwithstanding anything to the contrary set forth in the Insider Letter, Sponsor hereby agrees with each of Acquiror, Oppenheimer and Nomura as follows: 

1. Sponsor acknowledges and agrees that by its own terms, that certain Administrative Services Agreement, dated as of February 1, 2021
(the “Administrative Services Agreement”), between Acquiror and Sponsor’s Affiliate GigManagement, LLC (the “Management Company”), terminates upon the consummation of the Transactions, and as
such, upon such termination and the payment on the Closing Date (as defined in the Merger Agreement) of all amounts then owed to the Management Company by Acquiror pursuant to the Administrative Services Agreement, neither the Management Company nor
any other Affiliate of Sponsor shall continue to be entitled to receive payments pursuant to the Administrative Services Agreement following the consummation of the Transactions. 

2. The promissory note referred to in paragraph 4(b) of the Insider Letter was repaid in full and extinguished upon the consummation of the
IPO, and Acquiror has no further obligation or other liabilities thereunder. 












 3. Upon payment to Sponsor on the Closing Date of any amounts owed to Sponsor by Acquiror
for the reimbursement of out-of-pocket expenses incurred by Sponsor in connection with certain activities on behalf of Acquiror, such as (a) identifying and
investigating possible business targets and business combinations, (b) advisory fees paid to directors on behalf of Acquiror pertaining to board committee service and extraordinary administrative and analytical services (it being acknowledged
and agreed by the parties hereto, for the avoidance of doubt, that any such fees that are owed to such directors by Acquiror shall remain outstanding until paid by Acquiror in accordance with their terms), and (c) any amounts owed in respect of
obligations pursuant to loans made by Sponsor or its Affiliates to finance transaction costs in connection with an intended Business Combination (collectively, the “Sponsor Expenses”), Acquiror shall owe no further Sponsor
Expenses to Sponsor following the consummation of the Transactions. 
 4. Notwithstanding anything to the contrary set forth in
Section 4(c) of the Insider Letter, Sponsor acknowledges and agrees that no portion of the Sponsor Expenses or any other loan made by Sponsor or any of its Affiliates to the Acquiror will be converted into equity securities of the Ultimate
Surviving Corporation (as defined in the Merger Agreement). 
 5. Sponsor acknowledges and agrees that the Underwriters exercised the
Over-Allotment Option in full, and as such, there was no forfeiture by Sponsor of any of its Founder Shares. Furthermore, Sponsor acknowledges that the size of the IPO was increased, and that as a result, the Acquiror effected a stock dividend
immediately prior to the consummation of the IPO in such amounts as to maintain the ownership of the stockholders of Acquiror prior to the IPO at 20.0% of Acquiror’s total issued and outstanding shares of Common Stock. 

6. Sponsor hereby irrevocably waives any and all rights under Section 5 of the Insider Letter and acknowledges and agrees that Sponsor has
no further rights under or pursuant to Section 5 of the Insider Letter, including any such right to purchase, receive or sell shares of Common Stock or effect or receive a stock dividend or share contribution back to capital. 

7. This Letter Agreement shall be governed by and construed and enforced in accordance with the laws of the State of New York, without giving
effect to conflicts of law principles that would result in the application of the substantive laws of another jurisdiction. Each of the undersigned hereby (a) agrees that any action, proceeding or claim against it arising out of or relating in
any way to this Letter Agreement (a “Proceeding”) shall be brought and enforced in the courts of the State of New York of the United States of America for the Southern District of New York, and irrevocably submits to such
jurisdiction, which jurisdiction shall be exclusive, (b) waives any objection to such exclusive jurisdiction and that such courts represent an inconvenient forum and (c) with respect to Sponsor only, irrevocably agrees to appoint DLA Piper
LLP (US) as agent for the service of process in the State of New York to receive, for the undersigned and on his, her or its own behalf, service of process in any Proceedings. If for any reason such agent is unable to act as such with respect to
Sponsor, Sponsor will promptly notify Acquiror and the Representatives within 30 days and nothing in this Letter Agreement will affect the right of either party to serve process in any other manner permitted by law. 

8. This Letter Agreement, the Insider Letter, the Administrative Services Agreement and the Merger Agreement constitute the entire agreement
and understanding of the parties hereto in respect of the subject matter hereof and supersede all prior understandings, agreements, or representations by or among the parties hereto, written or oral, to the extent they relate in any way to the
subject matter hereof or the transactions contemplated hereby. This Letter Agreement may not be changed, amended, modified or waived (other than to correct a typographical error) as to any particular provision, except by a written instrument
executed by all parties hereto and by Holdings. 
 9. This Letter Agreement shall be binding on the undersigned and such person’s
respective successors, heirs, personal representatives and assigns. 












 10. This Letter Agreement may be executed in counterparts, each of which when so executed
shall be deemed to be an original and all of which when taken together shall constitute one and the same instrument. The words “execution,” signed,” “signature,” and words of like import in this Letter Agreement shall
include images of manually executed signatures transmitted by facsimile or other electronic format (including, without limitation, “pdf”, “tif” or “jpg”) and other electronic signatures (including, without limitation,
DocuSign and AdobeSign). The use of electronic signatures and electronic records (including, without limitation, any contract or other record created, generated, sent, communicated, received, or stored by electronic means) shall be of the same legal
effect, validity and enforceability as a manually executed signature or use of a paper-based record-keeping system to the fullest extent permitted by applicable law, including the Federal Electronic Signatures in Global and National Commerce Act,
the New York State Electronic Signatures and Records Act and any other applicable law, including, without limitation, any state law based on the Uniform Electronic Transactions Act or the Uniform Commercial Code. 

11. The parties hereto acknowledge and agree that irreparable damage would occur in the event that any of the provisions of this Letter
Agreement were not performed in accordance with their specific terms or were otherwise breached. The parties hereto acknowledge that Holdings is an express third-party beneficiary of this Letter Agreement. It is accordingly agreed by the parties
hereto that Holdings shall be entitled to seek an injunction or injunctions to prevent breaches or threatened breaches of this Letter Agreement and to enforce specifically the terms and provisions of this Letter Agreement (including all obligations
of Sponsor hereunder), 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 further agree not to assert that a remedy of specific enforcement pursuant to
this Section 11 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 11 is an integral part of the transactions contemplated hereby and without that right, the parties hereto would not have entered into this Letter Agreement.

 [Signature Page Follows] 












 
	
	GIGACQUISITIONS4, LLC
	
	 /s/ Dr. Avi Katz 

	By: Dr. Avi Katz
	Title: President and Chief Executive Officer


  

	
	Accepted and agreed this 4th day of June, 2021.
	
	GIGCAPITAL4, INC.
	
	 /s/ Dr. Avi Katz

	By: Dr. Avi Katz
	Title: Chief Executive Officer
	
	OPPENHEIMER & CO. INC.
	
	 /s/ Peter Bennett 

	By: Peter Bennett
	Title: Managing Director, Head of ECM
	
	NOMURA SECURITIES INTERNATIONAL, INC.
	
	 /s/ James Chenard 

	By: James Chenard
	Title: Managing Director

 Signature Page to Letter Agreement