Exhibit 10.20(a)

NTH CYCLE, INC.

AMENDMENT TO NOTE AND WARRANT PURCHASE AGREEMENT

This Amendment to the Note and Warrant Purchase Agreement dated as of July 09, 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”)soldpursuanttothatcertainNoteandWarrantPurchaseAgreementdatedasofJune27, 2025, by and among the Company and the Purchasers named therein (the “Purchase Agreement”).CapitalizedtermsusedbutnototherwisedefinedinthisAmendmentshallhavethe meanings given to them in the Purchase Agreement.

WHEREAS,pursuanttoSection8.7ofthePurchaseAgreement,anytermofthePurchase Agreementmaybeamended,modified,orterminatedwiththewrittenconsentoftheholdersofa majorityofthethen-outstandingaggregateprincipalamountoftheNotes(suchmajoritythe“Note Approval Amount”);

WHEREAS,thepartiesdesiretoamendthePurchaseAgreementtoextendthetimeperiod during which the Company may issue a Warrant to a Purchaser who purchases a Note under the Purchase Agreement; 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.Section2.2ofthePurchaseAgreementisherebyamendedandrestated in its entirety as follows:

“Warrants.TheCompanyshallalsoissuetoeachPurchaserthatpurchasesaNote on or before July 18, 2025 a Warrant exercisable for shares of Qualified Financing Securities (or Shadow Financing Securities, if applicable), into which such Purchaser’s NoteconvertsinaQualifiedFinancing(collectively,the“WarrantShares”),inanamount equal to the quotient of (i) fifteen percent (15%) of the principal amount of the Note purchased by the Holder on or before July 18, 2025 divided by (ii) the Capped Price (as definedbelow).SuchWarrantshallbeexercisableatanexercisepriceequaltotheCapped Price, for a period and on such terms as set forth in the Warrant.”

2.

No Other Amendment.Except as modified by this Amendment, the Purchase Agreement,theNotes,theWarrants,andtheSubordinationAgreementsshallremaininfullforce and effect in all respects without any modification. This Amendment shall be effective upon the execution by theCompany and the Purchasersrepresenting theNote 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.

[Signature page follows.]

INWITNESSWHEREOF,thepartieshaveexecutedthisAmendmenttoNoteand Warrant Purchase Agreement as of the day and year first written above.

Signature Page to Amendment to Note and Warrant Purchase Agreement

INWITNESSWHEREOF,thepartieshaveexecutedthisAmendmenttoNoteandWarrant Purchase Agreement as of the day and year first written above.

Signature Page to Amendment to Note and Warrant Purchase Agreement

INWITNESSWHEREOF,thepartieshaveexecutedthisAmendmenttoNoteandWarrant Purchase Agreement as of the day and year first written above.

Signature Page to Amendment to Note and Warrant Purchase Agreement

INWITNESSWHEREOF,thepartieshaveexecutedthisAmendmenttoNoteandWarrant Purchase Agreement as of the day and year first written above.

Signature Page to Amendment to Note and Warrant Purchase Agreement

INWITNESSWHEREOF,thepartieshaveexecutedthisAmendmenttoNoteandWarrant Purchase Agreement as of the day and year first written above.

Signature Page to Amendment to Note and Warrant Purchase Agreement