Third Supplemental Indenture, dated December 27, 2024 among BigBear.ai Holdings, Inc., BigBear.ai Intermediate Holdings, LLC, BigBear.ai, LLC, BigBear.ai Federal, LLC (f/k/a NuWave Solutions, L.L.C.), ProModel, LLC, Pangiam Purchaser, LLC, Pangiam Intermediate II Holdings, LLC, Pangiam Holdings, LLC, Pangiam Labs, LLC, Linkware, LLC, Pre, LLC, veriScan LLC, 214 Technologies, Inc. d/b/a Trueface and Wilmington Trust National Association, as trustee

Exhibit 4.1

Execution Version

THIRD SUPPLEMENTAL INDENTURE

BIGBEAR.AI HOLDINGS, INC.,

THE GUARANTORS PARTY HERETO

AND

WILMINGTON TRUST, NATIONAL ASSOCIATION,

as Trustee

Dated as of December 27, 2024

6.00% Convertible Senior Notes due 2026

THIS THIRD SUPPLEMENTAL INDENTURE (this “Supplemental Indenture”), entered into as of December 27, 2024, among BIGBEAR.AI HOLDINGS, INC., a Delaware corporation (the “Company”), BigBear.ai Intermediate Holdings, LLC, a Delaware limited liability company, BigBear.ai, LLC, a Delaware limited liability company, BigBear.ai Federal, LLC (f/k/a NuWave Solutions, L.L.C.), a Maryland limited liability company, ProModel LLC, a Pennsylvania limited liability company, Pangiam Purchaser, LLC, a Delaware limited liability company, Pangiam Intermediate II Holdings, LLC, a Delaware limited liability company, Pangiam Holdings, LLC, a Delaware limited liability company, Pangiam Labs, LLC, a Virginia limited liability company, Linkware, LLC, a Virginia limited liability company, Pre, LLC, a Delaware limited liability company, veriScan, LLC, a Delaware limited liability company, and 214 Technologies, Inc. d/b/a Trueface, a Delaware corporation (each an “Undersigned”) and WILMINGTON TRUST, NATIONAL ASSOCIATION, as trustee (the “Trustee”).

RECITALS

WHEREAS, the Company, the Guarantors party thereto and the Trustee entered into an Indenture, dated as of December 7, 2021 (as amended, supplemented, or otherwise modified prior to the date hereof, the “Indenture”), relating to the Company’s 6.00% Convertible Senior Notes due 2026 (the “Notes”);

WHEREAS, Section 10.02 of the Indenture provides, subject to certain exceptions, that the Indenture may be amended and supplemented with the written consent of the Holders of at least a majority of the aggregate principal amount of the Notes then outstanding (including, without limitation, consents obtained in connection with a repurchase of, or tender or exchange offer for, Notes) (the “Requisite Consents”);

WHEREAS, the Company and the Guarantors entered into those certain exchange agreements, each dated as of December 19, 2024 (the “Exchange Agreements”), each by and among the Company, the Guarantors and certain of the beneficial owners of the Notes named therein (collectively, the “Exchanging Holders”), pursuant to which the Company agrees to exchange the Exchanging Holders’ Notes specified therein for new convertible senior secured notes to be issued pursuant to that certain indenture, to be dated as of the date hereof, by and among the Company, the Guarantors and Wilmington Trust, National Association, as trustee and collateral agent;

WHEREAS, the Company has distributed this Supplemental Indenture, including the Proposed Amendments (as defined below) to the Indenture, to the Exchanging Holders in connection with the solicitation of the Requisite Consents from such Exchanging Holders as to the Proposed Amendments;

WHEREAS, certain of the Exchanging Holders representing more than a majority in aggregate principal amount of Notes outstanding, have consented to the amendments, deletions and revisions provided in Section 2 of this Supplemental Indenture (collectively, the “Proposed Amendments”);

WHEREAS, the Board of Directors (or similar governing body) of the Company and the Guarantors have approved the Proposed Amendments and the execution of this Supplemental Indenture;

WHEREAS, the Company has heretofore delivered, or is delivering contemporaneously herewith, to the Trustee, (i) evidence that the Requisite Consents have been received and (ii) the Officer’s Certificate and the Opinion of Counsel described in Sections 7.02, 7.07, 10.05, and 17.05 of the Indenture with respect to this Supplemental Indenture;

WHEREAS, all other acts and proceedings required by law and the Indenture necessary to authorize the execution and delivery of this Supplemental Indenture and to make this Supplemental Indenture a valid and binding agreement for the purposes expressed herein, in accordance with its terms, have been complied with or have been duly done or performed;

WHEREAS, having received the Requisite Consents pursuant to Section 10.02 of the Indenture, the Company and the Guarantors desire to amend the Indenture to effectuate the Proposed Amendments immediately prior to, and subject to the occurrence of, the consummation of transactions contemplated in the Exchange Agreements to be consummated (or substantially consummated) on the date hereof, in accordance with the terms set forth in the Indenture; and

WHEREAS, pursuant to Section 10.02 of the Indenture, the Trustee is authorized to execute and deliver this Supplemental Indenture.

AGREEMENT

NOW, THEREFORE, in consideration of the premises and mutual covenants herein contained and intending to be legally bound, the parties to this Supplemental Indenture hereby agree as follows:

Section 1. Capitalized terms used herein and not otherwise defined herein are used as defined in the Indenture.

Section 2. The Indenture is hereby amended to delete the following sections or clauses, as applicable, in their entirety, and, in the case of each such section or clause, as applicable, insert in lieu thereof the phrase “[Intentionally Omitted]”, and any and all references thereto (including any definitions the references to which would be eliminated as a result of such deletions), and any and all obligations thereunder, and any events of default related thereto, are hereby deleted throughout the Indenture, and such sections, clauses and references shall be of no further force or effect.

(a) Section 4.08 entitled “Limitation on Certain Restricted Payments.”

(b) Section 4.09 entitled “Limitation on Incurrence of Indebtedness and Issuance of Preferred Stock or Disqualified Stock.”

(c) Section 4.10 entitled “Limitation on Liens.”

(d) Section 4.11 entitled “Transactions with Affiliates.”

(e) Section 4.12 entitled “Material Intellectual Property.”

Section 3. This Supplemental Indenture shall be governed by and construed in accordance with the laws of the State of New York.

Section 4. This Supplemental Indenture may be signed in various counterparts which together shall constitute one and the same instrument.

Section 5. This Supplemental Indenture is an amendment supplemental to the Indenture, and the Indenture and this Supplemental Indenture shall henceforth be read together. Except as expressly amended hereby, the Indenture shall remain in full force and effect.

Section 6. The recitals and statements herein are deemed to be those of the Company and the Undersigned and not the Trustee. The Trustee shall not be responsible in any manner whatsoever for or in respect of the validity or sufficiency of this Supplemental Indenture or for the recitals.

[Signature Page Follows]

IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed as of the date first above written.