Exhibit 10.4

EXHIBIT A

AMENDMENT TO FACILITY AGREEMENT

This AMENDMENT TO FACILITY AGREEMENT (this “Amendment”) is dated and effective as of the September 11, 2026 (the “Amendment Effective Date”), by and between BLUE GOLD LIMITED, a Cayman Islands exempt company (the “Company”) and Kaela Ritchie (the “Lender,” and together with the Company, the “Parties”).

RECITALS

WHEREAS, the Company and the Lender entered into and executed that certain Facility Agreement, dated as of May 5, 2026 (such Facility Agreement, together with all renewals, extensions, future advances, further amendments, modifications, substitutions, or replacements thereof, collectively referred to as the “Facility Agreement”); and

WHEREAS, pursuant to the Facility Agreement, the Lender is providing a drawdown loan facility to the Company of up to US $4,000,000 (Four Million United States Dollars), subject to increase upon the mutual agreement of Lender and Company; and

WHEREAS, the Lender and the Company desire to amend the Facility Agreement in certain respects as set forth in Section 4 of this Amendment; and

NOW, THEREFORE, in consideration of the premises and the mutual covenants of the parties hereinafter expressed and other good and valuable consideration, the receipt and sufficiency of which is hereby acknowledged, the parties hereto, each intending to be legally bound, agree as follows:

1. Recitals. The recitations set forth in the preamble of this Amendment are true and correct and incorporated herein by this reference.

2. Capitalized Terms. All capitalized terms used in this Amendment shall have the same meaning ascribed to them in the Facility Agreement, as applicable, except as otherwise specifically set forth herein.

3. Conflicts. In the event of any conflict or ambiguity by and between the terms and provisions of this Amendment and the terms and provisions of the Facility Agreement, as the case may be, the terms and provisions of this Amendment shall control, but only to the extent of any such conflict or ambiguity.

4. Amendment to Facility Agreement.

(a) Section 2.2 of the Facility Agreement is hereby deleted in its entirety and replaced with the following:

“Notwithstanding anything to the contrary contained herein, at any time and from time to time prior to the date of Maturity, the Lender shall have the right, but not the obligation, to deliver a mandatory conversion notice to the Borrower requiring the Borrower to convert all or any portion of the outstanding Advance Balance into shares of the Borrower’s Class A ordinary shares, par value $0.0001 per share (collectively, the “Conversion Shares”), at a conversion price per share of $0.50 (subject to adjustment for any stock splits, stock dividends, stock combinations, recapitalizations or other similar transactions that occur with respect to the Class A ordinary shares following the Effective Date).”

5. Representations and Warranties of the Company. The Company hereby represents and warrants to the Lender that Lender: the execution and delivery by the Company of this Amendment, and all other documents executed and delivered in connection herewith and therewith, and the performance by Company of all of its obligations hereunder and thereunder, have been duly and validly authorized and approved by the Company and its board of directors pursuant to all applicable laws, and no other corporate or company action or consent on the part of the Company or its board of directors, is necessary or required by the Company to execute this Amendment, and the documents executed and delivered in connection herewith and therewith, to consummate the transactions contemplated herein and therein, or perform all of the Company’s obligations hereunder and thereunder. This Amendment, and each of the documents executed and delivered in connection herewith and therewith have been duly and validly executed by the Company (and the Person executing this Amendment, and all such other documents for the Company is duly authorized to act and execute same on behalf of Company) and constitute the valid and legally binding agreements of the Company, enforceable against the Company in accordance with their respective terms, except as such enforceability may be limited by general principles of equity or applicable bankruptcy, insolvency, reorganization, moratorium, liquidation and other similar laws relating to, or affecting generally, the enforcement of applicable creditors’ rights and remedies.

6. Governing Law. All questions concerning the construction, validity, enforcement and interpretation of this Amendment shall be governed by the internal law of the State of New York.

7. Effect on Agreement and Transaction Documents. Except as expressly amended by this Amendment, all of the terms and provisions of the Facility Agreement shall remain and continue in full force and effect after the execution of this Amendment, are hereby ratified and confirmed, and incorporated herein by this reference.

8. Execution. This Amendment may be executed in one or more counterparts, all of which taken together shall be deemed and considered one and the same Amendment. In the event that any signature is delivered by facsimile transmission or by e-mail delivery of a “.pdf’ format file or other similar format file, such signature shall be deemed an original for all purposes and shall create a valid and binding obligation of the party executing same with the same force and effect as if such facsimile or “.pdf’ signature page was an original thereof.

[Signatures on the following page]

IN WITNESS WHEREOF, the parties hereto have duly executed this Amendment as of the day and year first above written.