Exhibit 10.20(b)

NTHCYCLE, INC.

AMENDMENTNO.2TONOTEANDWARRANT PURCHASEAGREEMENT

ThisAmendmentNo.2totheNoteandWarrantPurchaseAgreementdatedasof August 31, 2025 (this “Amendment”), is made by and among Nth Cycle, Inc., a Delaware corporation(the“Company”),andtheundersignedholdersofsubordinatedconvertiblepromissory 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,pursuanttoSection8.7ofthePurchaseAgreement,anytermofthePurchase Agreement maybe amended, modified, orterminated with thewrittenconsent oftheholders of a majorityofthethen-outstandingaggregateprincipalamountoftheNotes(suchmajoritythe“Note Approval Amount”);

WHEREAS,thepartiesdesiretoamendthePurchaseAgreementtoextendthetimeperiod 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.Section2.1ofthePurchaseAgreementisherebyamendedandrestated in its entirety as follows:

“Notes. Subject to the terms and conditions of this Agreement, each closing (collectively,the“Closings”)ofthesaleandpurchaseofNotesunderthisAgreementshall takeplaceatFoleyHoagLLP,SeaportWest,155SeaportBoulevard,Boston,MA02210-2600(orremotelyviatheexchangeofdocumentsandsignatures)onorafterthedatehereof (thedateofeachsuchClosing,a“ClosingDate”).TheCompanymayconductoneormore 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 tollingpartners(suchdate,the“FinalClosingDate”).AteachClosing,theCompanyshall 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 suchoriginalprincipalamount.TheCompanyisundernoobligationtosell,andmakesno representationorwarrantyregardingitsabilitytosecuresubscriptionsforthepurchaseof, the full principal amount of the Notes available for issuance hereunder.”

2. NoOtherAmendment. ExceptasmodifiedbythisAmendment,thePurchase Agreement,theNotes,theWarrants,andtheSubordinationAgreements shallremaininfullforce 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,eachofwhichshallbedeemedtobeanoriginal,andallofwhichshallconstituteone andthesamedocument.ThisAmendmentmaybeexecutedbyelectronicorfacsimilesignatures.

[Signaturepagefollows.]

INWITNESSWHEREOF,thepartieshaveexecutedthis AmendmentNo.2toNoteand Warrant Purchase Agreement as of the day and year first written above.

SignaturePagetoAmendmentNo.2toNoteandWarrantPurchaseAgreement

IN WITNESS WHEREOF, the parties have executed this Amendment No. 2 to Note and Warrant Purchase Agreement as of the day and year first written above.

SignaturePagetoAmendmentNo.2toNoteandWarrantPurchaseAgreement

IN WITNESS WHEREOF, the parties have executed this Amendment No. 2 to Note and Warrant Purchase Agreement as of the day and year first written above.

SignaturePagetoAmendmentNo.2toNoteandWarrantPurchaseAgreement

IN WITNESS WHEREOF, the parties have executed this Amendment No. 2 to Note and Warrant Purchase Agreement as of the day and year first written above.

SignaturePagetoAmendmentNo.2toNoteandWarrantPurchaseAgreement

IN WITNESS WHEREOF, the parties have executed this Amendment No. 2 to Note and Warrant Purchase Agreement as of the day and year first written above.

Signature Page to Amendment No. 2 to Convertible Note Purchase Agreement

IN WITNESS WHEREOF, the parties have executed this Amendment No. 2 to Note and Warrant Purchase Agreement as of the day and year first written above.

SignaturePagetoAmendmentNo.2toNoteandWarrantPurchaseAgreement