Exhibit 10.20(b)

NTH CYCLE, INC.

AMENDMENT NO. 2 TO NOTE AND WARRANT PURCHASE AGREEMENT

This Amendment No. 2 to the Note and Warrant Purchase Agreement dated as of August 31, 2025 (this “Amendment”), is made by and among Nth Cycle, Inc., a Delaware corporation (the “Company”), and the undersigned holders of subordinated convertible promissory notes (the “Notes”) sold pursuant to that certain Note and Warrant Purchase Agreement dated as of June 27, 2025, by and among the Company and the Purchasers named therein, as amended by that certain Amendment to Note and Warrant Purchase Agreement, dated July 9, 2025 (as amended, the “Purchase Agreement”). Capitalized terms used but not otherwise defined in this Amendment shall have the meanings given to them in the Purchase Agreement.

WHEREAS, pursuant to Section 8.7 of the Purchase Agreement, any term of the Purchase Agreement may be amended, modified, or terminated with the written consent of the holders of a majority of the then-outstanding aggregate principal amount of the Notes (such majority the “Note Approval Amount”);

WHEREAS, the parties desire to amend the Purchase Agreement to extend the time period during which the Company may sell Notes following the initial Closing Date; and

WHEREAS, the undersigned holders of Notes, constituting at least the Note Approval Amount, desire to enter into this Amendment.

NOW, THEREFORE, in consideration of the premises and the mutual covenants and agreements contained herein and in the Purchase Agreement, the parties hereto agree as follows:

1. Amendment. Section 2.1 of the Purchase Agreement is hereby amended and restated in its entirety as follows:

“Notes. Subject to the terms and conditions of this Agreement, each closing (collectively, the “Closings”) of the sale and purchase of Notes under this Agreement shall take place at Foley Hoag LLP, Seaport West, 155 Seaport Boulevard, Boston, MA 02210-2600 (or remotely via the exchange of documents and signatures) on or after the date hereof (the date of each such Closing, a “Closing Date”). The Company may conduct one or more additional closings to sell the remaining Notes at any time until the earlier of (i) October 31, 2025, and (ii) the time at which the Company has executed project term sheets with tolling partners (such date, the “Final Closing Date”). At each Closing, the Company shall deliver a Note to each Purchaser participating in such Closing in the original principal amount set forth next to such Purchaser’s name on its signature page hereto, and each Purchaser shall pay to the Company the purchase price therefor, which shall be equal to such original principal amount. The Company is under no obligation to sell, and makes no representation or warranty regarding its ability to secure subscriptions for the purchase of, the full principal amount of the Notes available for issuance hereunder.”

2. No Other Amendment. Except as modified by this Amendment, the Purchase Agreement, the Notes, the Warrants, and the Subordination Agreements shall remain in full force and effect in all respects without any modification. This Amendment shall be effective upon the execution by the Company and the Purchasers representing the Note Approval Amount and shall be binding on all Purchasers.

3. Governing Law. This Amendment shall be governed by and construed in accordance with the internal laws of the State of Delaware without reference to the conflicts of law provisions thereof.

4. Counterparts; Signatures. This Amendment may be executed in any number of counterparts, each of which shall be deemed to be an original, and all of which shall constitute one and the same document. This Amendment may be executed by electronic or facsimile signatures.

[Signature page follows.]