Exhibit 10.32

Term Sheet for an Equity Line of Credit

The purpose of this letter is to set forth the indicative terms pursuant to which, subject to certain conditions set forth herein, the Investor (defined on signature page) would invest in certain securities of the Company (defined below). The terms and conditions set forth herein are subject to change and this letter does not constitute an offer. The issuance and sale of such securities is subject to completion of due diligence to the Investor’s satisfaction, the preparation of definitive documentation to effect the transaction that is mutually satisfactory to the parties and, in the case of the Investor, that the Investor shall have determined that subsequent to the date hereof and prior to the closing of the transaction, there shall have been no material adverse developments relating to the business, assets, operations, properties, condition (financial or otherwise) or prospects of the Company and its subsidiaries, taken as a whole.

On the terms and subject to the conditions set forth below, Investor will commit to invest up to $25,000,000 in an Equity Line of Credit with the Company as indicated below.

Company	The surviving post-merger entity of Alpha Healthcare Acquisition Corp. III (the “Parent”) and Carmell Therapeutics (the “Target”).
Securities	Registered Common Stock of the Company.
Term & Termination	12 months. The Agreement may be terminated by the Company upon five (5) trading days prior written notice to the Investor. The Agreement may be terminated by the Investor upon five (5) trading days prior written notice, if (i) any condition, occurrence, state of facts or event constituting a material adverse effect has occurred and is continuing; (ii) the Company has undergone a change of control transaction, (iii) the registration statement has not been deemed by the agreed upon effectiveness deadline, or the Company is otherwise in breach or default in any material respect under any of the other provisions of the Agreement, and, such breach or default has not been cured within ten (10) trading days prior written notice, (iv) any required registration statement does not remain effective for certain time periods set forth in the Agreement; (iv) trading in the Securities on the trading market shall have been suspended and such suspension continues for a period of three (3) consecutive trading days; (F) the Company is in material breach or default of the Agreement, and such breach or default is not cured within ten (10) trading days prior written notice; or (G) the Business Combination Closing Date shall not have occurred prior to September 30, 2023. In the event of any early termination of the Agreement, the Company shall have paid to the Investor the Commitment Fee and the Reimbursable Fees in full prior to the effectiveness of such early termination.
Equity Line of Credit (“ELOC”)	Up to $25,000,000 (the “Investment Amount”) in Securities.

ELOC Purchase Notice	Company may send an ELOC Purchase Notice between 4:00pm and 6:30pm EST, stating number of Securities Investor is required to purchase, subject to Purchase Limit. Company may raise additional ELOC capital from the Investor after 3 trade days. ELOC Purchase Price: 97% of the lowest daily VWAP during the 3 trade days following the Purchase Notice Date. ELOC Purchase Limit: Lesser of (i) 100% of the average daily trading volume over the 5 days before the Purchase Notice Date, (ii) 40% of the daily trading volume on the Purchase Notice Date, or (iii) $5,000,000.
Registration	Company shall file a registration statement within 30 days of the completion of the Business Combination and make commercially reasonable efforts to have it declared effective within 60 days of filing.
Concentration Restriction	At no time may Investor hold or be required to take, either directly or beneficially, more than 4.99% of outstanding Securities.
No Shorting	Investor agrees that it will not, directly or indirectly, engage in any “short sale” (as such term is defined in Rule 200 of Reg SHO), which establishes a short position with respect to Common Stock while this Agreement is outstanding.
Variable Rate Prohibition	Company shall not enter into any variable, reset, or otherwise adjustable equity or equity-linked transactions while this Agreement is outstanding.
Commitment Fee	0.875% of the Investment Amount, paid in cash or Securities at a price equal to the 5-day average VWAP prior to the filing of the registration statement. If Company enters into a Forward Purchase Agreement (“FPA”) financing structure, half of the Commitment Amount will be paid in cash, with the remainder paid in Securities. If Company desires to enter into an FPA, Investor must approve.
Legal & Diligence Fees	$50,000 deposit (the “Initial Deposit”) upon signing term sheet to Investor Counsel for legal fees. Actual remaining balance to be paid upon closing.
Expiration	This Term Sheet has an expiration date of 5 business days.