Material Agreement (Form 8-K)

Amendment to Business Combination Agreement

As previously reported on a Current Report on Form 8-K of Cartesian Growth Corporation III, a Cayman Islands exempted company ("Cartesian III"), filed with the U.S. Securities and Exchange Commission (the "SEC") on December 18, 2025 (the "Prior 8-K"), Cartesian III announced that it had entered into a business combination agreement, dated December 17, 2025 (as amended, the "Business Combination Agreement" and, the transactions described within, the "Business Combination"), with Fenway MS, Inc., a Delaware corporation ("Merger Sub"), and Factorial Inc., a Delaware corporation ("Factorial"). Capitalized terms used but not expressly defined in this Current Report on Form 8-K shall have the meanings ascribed to them in the Business Combination Agreement.

On May 18, 2026, Cartesian III, Merger Sub and Factorial entered into Amendment No. 2 to the Business Combination Agreement (the "BCA Amendment"). The BCA Amendment amends the Business Combination Agreement (and the form of post-closing certificate of incorporation and bylaws attached as annexes thereto) to reflect that, in connection with the closing of the Business Combination and upon its domestication as a Delaware corporation, Cartesian III will change its name to "Factorial Energy, Inc.".

The foregoing description of the BCA Amendment does not purport to be complete and is qualified in its entirety by reference to the full text of the BCA Amendment, a copy of which is attached hereto as Exhibit 2.1 and is incorporated herein by reference.

Letter Agreement

As previously reported on the Prior 8-K, on December 17, 2025, Cartesian III entered into a Stock Purchase Agreement (the "Institutional Investor Stock Purchase Agreement") with a certain institutional investor (the "Institutional Investor"). Pursuant to the Institutional Investor Stock Purchase Agreement, the Institutional Investor agreed to subscribe for and purchase, and Cartesian III agreed to issue and sell to the Institutional Investor at the closing (the "Closing") of the Business Combination, 7,500,000 shares of Series A common stock of the combined company at a subscription price of $10.00 per share. Pursuant to the terms of the Institutional Investor Stock Purchase Agreement, to the extent the Institutional Investor purchases Class A ordinary shares of Cartesian III on the open market, and agrees (i) not to transfer directly or indirectly such shares until the Closing and (ii) to vote such shares in favor of the Business Combination and related proposals, it will reduce, on a share for share basis, the Institutional Investors' purchase obligation under the Institutional Investor Stock Purchase Agreement.

On May 18, 2026, the Institutional Investor entered into an agreement (the "Letter Agreement") with Factorial and CGC III Sponsor LLC, a Cayman Islands limited liability company and sponsor of Cartesian III ("Sponsor"), pursuant to which (a) the Institutional Investor agreed to satisfy in part its purchase obligation under the Institutional Investor Stock Purchase Agreement through the purchase of up to 2 million Class A ordinary shares of Cartesian III under the terms of the Letter Agreement, in open market transactions or privately negotiated transactions at market prices, (b) Sponsor agreed to transfer, in connection with the Closing, a number of Class B ordinary shares of Cartesian III equal to the quotient of the Differential Amount divided by $10.00, and (c) Factorial agreed to reimburse Sponsor in cash the Differential Amount. The "Differential Amount" is calculated as the difference between (x) the aggregate purchase price of the open market shares purchased by the Institutional Investor pursuant to the Letter Agreement minus (y) the product of (A) the number of shares so purchased and (B) $10.00.