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EXHIBIT 10.31

AEON Biopharma, Inc.

Lake Street Capital Markets, LLC

121 South 8th Street, Suite 1000

Minneapolis, Minnesota 55402

Laidlaw & Company (UK) Ltd.

521 Fifth Avenue, 12th Floor

New York, NY 10175

July [●], 2026

Private and Confidential

AEON Biopharma, Inc.

5 Park Plaza

Suite 1750

Irvine, CA 92614

Attention:                Robert Bancroft

President and Chief Executive Officer

Dear Robert:

We understand that AEON Biopharma, Inc., a Delaware corporation (the “Company”), has requested that Lake Street Capital Markets, LLC and Laidlaw & Company (UK) Ltd. (collectively, the “Agents”) act as the Company’s solicitation agents in connection with the exercise of the Common Warrants (as defined in the Underwriting Agreement) and the Option Common Warrants (as defined in the Underwriting Agreement) (the Common Warrants and the Option Common Warrants together, the “Milestone Warrants”) to be issued pursuant to that certain Underwriting Agreement, dated as of the date hereof (the “Underwriting Agreement”), between the Company and Lake Street Capital Markets, LLC, as representative of the several unde

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EX-10.31·S-1·CIK 1837607·ACC 0001104659-26-081860·Filed Jul 08, 2026, 17:26 ET

** **

**INVESTMENT MANAGEMENT TRUST AGREEMENT **

This Investment Management Trust Agreement (this “Agreement”) is made effective as of [●], 2026 by and between Catalyst Acquisition Corp., a Cayman Islands exempted company (the “Company”), and Continental Stock Transfer & Trust Company, a New York corporation (the “Trustee”).

WHEREAS, the Company’s registration statement on Form S-1 (File No. 333-[ ]) (the “Registration Statement”) and prospectus (the “Prospectus”) for the initial public offering of the Company’s units (the “Units”), each of which consists of one of the Company’s Class A ordinary shares, par value $0.0001 per share (the “Ordinary Shares”), and one right to receive one-seventh (1/7) of one Ordinary Share upon the consummation of the Company’s initial business combination (such initial public offering hereinafter referred to as the “Offering”), has been declared effective as of the date hereof by the U.S. Securities and Exchange Commission;

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EX-10.2·S-1·CIK 2104391·ACC 0001213900-26-076132·Filed Jul 07, 2026, 20:51 ET

REGISTRATION RIGHTS AGREEMENT

THIS REGISTRATION RIGHTS AGREEMENT (this “Agreement”), dated as of [ ], 2026, is made and entered into by and among Catalyst Acquisition Corp., a Cayman Islands exempted company (the “Company”), and Catalyst Sponsor LLC, a Delaware limited liability company (the “Sponsor’) (the Sponsor with any person or entity who hereafter becomes a party to this Agreement pursuant to Section 5.2 of this Agreement, a “Holder” and collectively the “Holders”).

RECITALS

WHEREAS, the Company intends to consummate an initial public offering of the Company’s units (the “IPO”), each unit consisting of one Class A Ordinary Share, par value $0.0001 per share (the “Ordinary Shares”), of the Company, and one right to receive one-seventh (1/7) of one Ordinary Share upon the consummation of the Company’s initial business combination (a “Public Share Right”);

** **

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EX-10.3·S-1·CIK 2104391·ACC 0001213900-26-076132·Filed Jul 07, 2026, 20:51 ET

** **

CATALYST ACQUISITION CORP.

1007 Ocean Avenue, Suite 501

Santa Monica, CA 90403

[_], 2026

Catalyst Sponsor LLC

1007 Ocean Avenue, Suite 401

Santa Monica, CA 90403

Re: Administrative Services Agreement

Ladies and Gentlemen:

This letter agreement by and between Catalyst Acquisition Corp. (the “Company”) and Catalyst Sponsor LLC (the “Services Provider” and “Sponsor”), dated as of the date hereof, will confirm our agreement that, commencing on the date the securities of the Company are first listed on The Nasdaq Market LLC (the “Listing Date”), pursuant to a Registration Statement on Form S-1 and prospectus filed with the U.S. Securities and Exchange Commission (the “Registration Statement”) and continuing until the earlier of the consummation by the Company of an initial business combination and the Company’s liquidation (in each case as described in the Registration Statement) (such earlier date hereinafter referred to as the “***

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EX-10.8·S-1·CIK 2104391·ACC 0001213900-26-076132·Filed Jul 07, 2026, 20:51 ET

[●], 2026

Catalyst Acquisition Corp.

1007 Ocean Avenue, Suite 501

Santa Monica, CA 90403

Re: Initial Public Offering

Ladies and Gentlemen:

This letter (this “Letter Agreement”) is being delivered to you in accordance with the Underwriting Agreement (the “Underwriting Agreement”) entered into by and among Catalyst Acquisition Corp., a Cayman Islands exempted company (the “Company”) and Santander US Capital Markets LLC as representative (the “Representative”) of the underwriters (the “Underwriters”), relating to an underwritten initial public offering (the “Public Offering”), of up to 23,000,000 of the Company’s units (including up to 3,000,000 units which may be purchased to cover over-allotments, if any) (the “Units”), each comprised of one Class A ordinary share, par value $0.0001 per share, of the Company (the “Class A Ordinary Shares”) and one right to receive one-seventh (1/7) of a Class A ordinary share upon the consummation of an ini

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EX-10.1·S-1·CIK 2104391·ACC 0001213900-26-076132·Filed Jul 07, 2026, 20:51 ET

PRIVATE PLACEMENT UNITS PURCHASE AGREEMENT

THIS PRIVATE PLACEMENT UNITS PURCHASE AGREEMENT, dated as of [ ], 2026 (as it may from time to time be amended, this “Agreement”), is entered into by and between Catalyst Acquisition Corp., a Cayman Islands exempted company (the “Company”), and Catalyst Sponsor LLC, a Delaware limited liability company (the “Purchaser”).

WHEREAS, the Company intends to consummate an initial public offering of the Company’s units (the “Public Offering”), each unit consisting of one Class A Ordinary Share, par value $0.0001 per share, of the Company (an “Ordinary Share”), and one right to receive one-seventh (1/7) of one Ordinary Share upon the consummation of the Company’s initial business combination. The Purchaser has agreed to purchase an aggregate of 270,000 private placement units (whether or not the over-allotment option in connection with the Public Offering is exercised in full) (the “Private Placement Units”), each Private Placement Unit comprised of one Ordinary Share (each, a “Private Placement Share”) and one rig

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EX-10.4·S-1·CIK 2104391·ACC 0001213900-26-076132·Filed Jul 07, 2026, 20:51 ET

FORM OF INDEMNITY AGREEMENT

Catalyst Acquisition Corp.

FORM OF INDEMNITY AGREEMENT

THIS INDEMNITY AGREEMENT (this “Agreement”) is made as of [ ], 2026, by and between Catalyst Acquisition Corp., a Cayman Islands exempted company (the “Company”), and the undersigned (“Indemnitee”).

RECITALS

WHEREAS, highly competent persons have become more reluctant to serve publicly-held companies as directors, officers or in other capacities unless they are provided with adequate protection through insurance or adequate indemnification against inordinate risks of claims and actions against them arising out of their service to and activities on behalf of such companies;

WHEREAS, the Board of Directors of the Company (the “Board”) has determined that, in order to attract and retain qualified individuals, the Company will attempt to maintain on an ongoing basis, at its sole expense, liability insurance to protect persons serving the Company and its Subsidiaries (as defined below) from certain liabilities;

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EX-10.5·S-1·CIK 2104391·ACC 0001213900-26-076132·Filed Jul 07, 2026, 20:51 ET

THIS PROMISSORY NOTE (THIS “NOTE”) HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “SECURITIES ACT”). THIS NOTE HAS BEEN ACQUIRED FOR INVESTMENT ONLY AND MAY NOT BE SOLD, TRANSFERRED OR ASSIGNED IN THE ABSENCE OF REGISTRATION OF THE RESALE THEREOF UNDER THE SECURITIES ACT OR AN OPINION OF COUNSEL REASONABLY SATISFACTORY IN FORM, SCOPE AND SUBSTANCE TO THE COMPANY THAT SUCH REGISTRATION IS NOT REQUIRED.

PROMISSORY NOTE

Principal Amount: Up to $300,000 Dated as of January 7, 2026

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EX-10.6·S-1·CIK 2104391·ACC 0001213900-26-076132·Filed Jul 07, 2026, 20:51 ET

CATALYST ACQUISITION CORP.

1007 Ocean Avenue, suite 401

Santa Monica, CA 90403

** **

January 7, 2026

Catalyst Sponsor LLC

1007 Ocean Avenue, Suite 401

Santa Monica, CA 90403

Ladies and Gentlemen:

Catalyst Acquisition Corp., a Cayman Islands exempted company (the “Company”), is pleased to accept the offer Catalyst Sponsor LLC, a Delaware limited liability company (the “Subscriber”) has made to purchase 8,625,000 shares of the Company’s Class B ordinary shares (the “Founder Shares”), $0.0001 par value per share (the “Class B Ordinary Shares”), up to 1,125,000 of which are subject to complete or partial forfeiture by the Subscriber if the underwriters of the proposed initial public offering (“IPO”) of the Company pursuant to the registration statement on Form S-1 expected to be filed by the Company in connection with the IPO (the “Registration Statement”) do not fully exercise their over-allotment option (the “Over-allotment Option”). For the purposes of this Agreement, references to “Ordinary Shares” are to, collectively, the Class B

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EX-10.7·S-1·CIK 2104391·ACC 0001213900-26-076132·Filed Jul 07, 2026, 20:51 ET

EX-10.3

Syntiant Corp.

Portions of this exhibit have been omitted in accordance with Item 601(a)(5) of Regulation S-K.

The Registrant undertakes to furnish a copy of all omitted information, schedules, and exhibits to the U.S. Securities and Exchange Commission upon its request.

LIMITED WAIVER AND CONSENT

This Limited Waiver and Consent (this “Limited Waiver and Consent”) is entered into as of May 11, 2026, by and among Structural Capital Investments III, LP (“SCI”), Structural DCO II Series of Structural Capital DCO LLC (“DCO”), Series PCI Syntiant, a series of Structural Capital Primary Co-Investment Fund, LLC (“PCI”), Structural Capital Investments IV, LP (“SCI IV” and together with SCI, DCO and PCI, “Lenders” and each, a “Lender”), Ocean II PLO LLC, a California limited liability company,as administrative and collateral agent for Lenders (“Agent”), Syntiant Corp., a Delaware corporation (“Parent”), Pilot AI Labs, Inc., a Delaware corporation (“Pilot”), Syntiant Taiwan LLC, a Delaware limited liability company (“Syntiant Taiwan”), Syntiant Holdings LLC, a Delaware limited liability company (“Syntiant

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EX-10.3·S-1·CIK 1718728·ACC 0001193125-26-296426·Filed Jul 06, 2026, 17:22 ET

EX-10.8

Syntiant Corp.

Portions of this exhibit, indicated by [***], have been omitted in accordance with Item 601(b)(10)(iv) of Regulation S-K. The omitted information is (i) not material and (ii) treated by the Registrant as private or confidential.

The Registrant undertakes to furnish a copy of all omitted information, schedules, and exhibits to the U.S. Securities and Exchange Commission upon its request.

PRODUCT SUPPLY AGREEMENT

Between

Knowles Electronics (Malaysia) Sdn. Bhd. and

Syntiant Malaysia Manufacturing Sdn. Bhd.

December 27, 2024


This Product Supply Agreement (“Agreement”) is entered into this December 27, 2024 (“Effective Date”) between Syntiant Malaysia Manufacturing Sdn. Bhd. (“Syntiant”) having its place of business at Plot 104, Lebuhraya Kampung Jawa, Bayan Lepas Industrial Estate, 11900 Penang, Malaysia, and Knowles Electronics (Malaysia) Sdn. Bhd. (“Knowles”), having its place of business at lot 104, Lebuhraya Kg. Jawa, Bayan Lepas Industrial Estate, Penang, Malaysia, 11960.

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EX-10.8·S-1·CIK 1718728·ACC 0001193125-26-296426·Filed Jul 06, 2026, 17:22 ET

EX-10.5

Syntiant Corp.

FIRST AMENDMENT TO SELLER LOAN AND SECURITY AGREEMENT

This First Amendment to Seller Loan and Security Agreement (as amended, restated, amended and restated, supplemented or otherwise modified from time to time, this “Amendment”) is entered into as of February 3, 2026, by and among Knowles Corporation, a Delaware corporation (together with its successors and permitted assigns, collectively, “Lenders”), and as administrative agent and collateral agent for Lenders (in such capacity, “Agent”), Syntiant Corp., a Delaware corporation (“Parent”), Pilot AI Labs, Inc., a Delaware corporation (“Pilot”), Syntiant Taiwan LLC, a Delaware limited liability company (“Syntiant Taiwan”), Syntiant Holdings LLC, a Delaware limited liability company (“Syntiant Holdings”; and, together with Parent, Pilot, and Syntiant Taiwan, each, a “Borrower” and collectively, the “Borrowers”), Syntiant Malaysia Logistics Sdn. Bhd. (Registration No. 202401025332 (1571181-W)), a company incorporated under the laws of Malaysia (“Syntiant Malaysia Logistics”), and Syntiant Malaysia Manufacturing Sdn. Bhd. (Registration

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EX-10.5·S-1·CIK 1718728·ACC 0001193125-26-296426·Filed Jul 06, 2026, 17:22 ET