Exhibit 10.1

CONFIDENTIAL

Jul 31, 2025

Shawn Matthews

Chief Executive Officer

HCM III Acquisition Corp.

100 First Stamford Place, Suite 330

Stamford, CT 06902

Re:

Engagement of Services

Dear Mr. Matthews:

This will confirm the basis upon which HCM III Acquisition Corp. (“Client”) has engaged Zenith Securities, LLC (“Zenith”), to provide consulting and advisory services (the ”Engagement”) in connection with Client’s special purpose acquisition company (“SPAC”) initial public offering (“IPO”) of its securities (the “Transaction”). Such services include:

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Evaluating the feasibility of Client pursuing a potential SPAC IPO transaction, including evaluation of current SPAC market conditions, advising on Client’s sponsor promote structure and terms, and counseling Client as to strategy and tactics for a potential Transaction;

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Strategic advice and guidance with respect to fee and economics recommendations;

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Advice with respect to broad categories of prospective investors that may be interested in the Transaction (although Zenith will not identify specific prospective investors and will not have direct or indirect contact with, or otherwise be involved in soliciting, prospective investors as part of the Transaction);

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Marketing message development, including advice and support on positioning as well as “testing the waters” activities;

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Review of Transaction-related material prepared by Client and/or the underwriters;

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Book-building analysis;

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Deal size analysis; and

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Review of share allocations.

In addition, following the successful completion of the SPAC’s IPO and as part of this Engagement, Zenith will provide consulting and advisory services in support of the SPAC’s initial business combination. Such services include evaluation of potential targets and related due diligence support, strategic advice and guidance on transaction structuring, review of informational and investor materials and consultations on marketing materials and investor relations activities.

The parties acknowledge that Zenith is being retained solely to provide the services set forth herein, and that Zenith is not being retained to act as an underwriter or member of any selling syndicate in connection with the Transaction. Client agrees that Zenith shall (a) serve as an ”independent financial adviser” as defined in FINRA Rule 5110G)(9); (b) provide the services set forth herein independently of the underwriter(s); (c) have no liability to Client, its affiliates or its securities holders for any actions or omissions of the underwriter(s); and (d) have no responsibility or liability to the underwriter(s) in connection with the services set forth herein.

Further, Zenith is providing the services set forth herein solely in an advisory capacity, and Client retains full discretion as to whether or not to follow such advice. For the avoidance of doubt, Zenith will not participate in the Transaction (as defined in FINRA Rule 5110(i)(16)); the execution of the Transaction (including, but not limited to, structuring of the IPO, solicitation of prospective investors, and negotiation of the terms of the IPO) will be the responsibility of the underwriter(s). Zenith will not advise on the proposed price range for the offered securities or the key SPAC terms or structure for which securities are offered in the Transaction.

Fee. Client shall pay Zenith an advisory fee in an amount equal to 0.65% of the aggregate proceeds of the IPO (including proceeds from the overallotment option if exercised), after deducting the reasonable out-of-pocket expenses incurred by the underwriters (the “Advisor IPO Fee”), in connection with Transaction. Zenith agrees to defer the portion of the Advisor IPO Fee resulting from the exercise of the overallotment option until the consummation of the SPAC’s initial business combination. The portion of the Advisor IPO Fee resulting from the base deal (i.e., 0.20% of the of the aggregate proceeds of the IPO (excluding the proceeds from the overallotment option if exercised) shall be payable at the closing of the IPO. In addition, Client shall pay Zenith an advisory fee in an amount equal to 0.45% of the aggregate proceeds of the IPO (including proceeds from the overallotment option if exercised), after deducting the reasonable out-of-pocket expenses incurred by the underwriters (the “Advisor IBC Fee” and together with the Advisor IPO Fee, the “Advisor Fees”), in connection with Zenith’s consulting and advisory services in support of the SPAC’s initial business combination. The Advisor IBC Fee and any portion of the aggregate 0.65% Advisor Fee attributable to the exercise of the overallotment option will be payable at the closing of the SPAC’s initial business combination. If the IPO does not occur during the Term, then no Advisor Fees shall be payable to Zenith.

The fees described in this paragraph 1 are compensation for the Engagement, which consists of work directly related to the Engagement. Any work outside of the scope of the Engagement shall be subject to additional compensation as separately agreed by the parties hereto.

Term of Engagement. This letter agreement shall remain in force until terminated in writing by either party hereto in accordance with the terms hereof (the “Term”). The Term may be terminated by either Zenith or Client at any time with thirty (30) days’ advance written notice to the other. Termination of this letter agreement shall not affect Zenith’s right to indemnification or contribution or payment of the Advisor Fee in accordance with the terms of this letter agreement if the closing of the IPO occurs within twelve (12) months following the termination of this letter agreement. Without limiting the foregoing, notwithstanding the termination of this letter agreement, the provisions of this letter agreement shall survive and remain operative in accordance with their respective terms.

Scope of Liability. Neither Zenith nor any of its control persons, members, managers, officers, employees, or agents shall be liable to Client or to any other person claiming through Client for any error of judgment or for any claim, loss or expense suffered by Client or any such other person in connection with the matters to which the Engagement relates except to the extent a claim, loss or expense arises out of or is based upon any action or failure to act by Zenith or any of its control persons, members, managers, officers, employees, or agents that is found in a final judicial determination (or a settlement tantamount thereto) to constitute bad faith, willful misconduct or gross negligence on the part of Zenith or any such other person.

Indemnity and Contribution. Subject to Section 8 below and recognizing that transactions of the type contemplated by the Engagement sometimes result in litigation and that Zenith’s role is limited to acting in the capacities described herein, Client agrees to indemnify Zenith and its control persons, members, managers, officers, employees, and agents (each, including Zenith, an “Indemnified Person” to the full extent lawful against any and all claims, losses and expenses as incurred (including all reasonable fees and disbursements of each such Indemnified Person’s counsel and all reasonable travel and other out-of-pocket expenses incurred by each such Indemnified Person in connection with investigation of and preparation for any such pending or threatened claims and any litigation or other proceedings arising therefrom) arising out of any actual or proposed Transaction or the Engagement; provided; however, that there shall be excluded from such indemnification any such claim, loss or expense to the extent that such claim, loss or expense arises out of, or is related to, any action or failure to act by any Indemnified Person that is found in a final judicial determination (or a settlement tantamount thereto) to constitute bad faith, willful misconduct or gross negligence on the part of any Indemnified Person.

Zenith shall notify Client in writing if any action, suit or investigation (an ”Action” is commenced against Zenith within five (5) days after Zenith or any other Indemnified Person shall have been served with a summons or other first legal process, but failure so to notify Client shall not relieve Client from any liability that it may have hereunder, except to the extent that such failure so to notify Client materially prejudices Client’s rights. Client may assume, at its own expense, the defense of any Action exercisable upon written notice to Zenith and any such Indemnified Person(s), if applicable, within fifteen (15) days of notice by Zenith or such Indemnified Person provided pursuant to the preceding sentence, and such defense shall be conducted by counsel chosen by Client and reasonably satisfactory to Zenith and such Indemnified Person(s), if applicable. The Indemnified Person shall have the right to participate in the defense of any Action with counsel selected by it subject to the Client’s right to control the defense thereof. The fees and disbursements of such counsel shall be at the expense of the Indemnified Person, provided, that if in the reasonable opinion of counsel to the Indemnified Person, there exists a conflict of interest between the Client and the Indemnified Person that cannot be waived, the Client shall be liable for the reasonable fees and expenses of counsel to the Indemnified Person in each jurisdiction for which the Indemnified Person determines counsel is required. If the Client elects not to compromise or defend such Action, fails to promptly notify the Indemnified Person in writing of its election to defend as provided in this letter agreement, or fails to diligently prosecute the defense of such Action (and such failure to diligently prosecute is judicially determined), the Indemnified Person may, subject to the next paragraph, pay, compromise, defend such Action and seek indemnification for any and all damages, expenses, liabilities and losses based upon, arising from or relating to such Action. The parties hereto shall cooperate with each other in all reasonable respects in connection with the defense of any Action.

Notwithstanding any other provision of this letter agreement, Client shall not enter into any settlement of any Action without the prior written consent of the Indemnified Person, which consent will not be unreasonably withheld or delayed, except as provided in this paragraph. If a firm offer is made to settle an Action without permitting or leading to further claims, losses, liability or expense or the creation of a financial or other obligation on the part of the Indemnified Person and provides, in customary form, for the unconditional release of each Indemnified Person from all liabilities and obligations in connection with such Action, and Client desires to accept and agree to such offer, Client shall give written notice to that effect to the Indemnified Person. If the Indemnified Person fails to consent to such firm offer within ten (10) days after its receipt of such notice, the Indemnified Person may continue to contest or defend such Action and in such event, the maximum liability of the Client as to such Action shall not exceed the amount of such settlement offer plus the Indemnified Person’s costs and expenses (including reasonable fees and disbursements of counsel and other out-of-pocket expenses) through the end of such ten (10) day period. If the Indemnified Person fails to consent to such firm offer and also fails to assume defense of such Action, Client may settle the Action upon the terms set forth in such firm offer to settle such Action. If the Indemnified Person has assumed the defense pursuant to the previous paragraph, it shall not agree to any settlement without the written consent of Client (which consent shall not be unreasonably withheld or delayed).

In the event that the foregoing indemnity is unavailable or insufficient to hold such Indemnified Person(s) harmless, then subject to Section 8 below, Client shall contribute to amounts paid or payable by such Indemnified Person(s) in respect of such claims, losses and expenses in such proportion as appropriately reflects the relative benefits received by, and fault of, Client and such Indemnified Person(s) in connection with the matters as to which such claims, losses and expenses relate and other equitable considerations.

Information Provided to Zenith. In performing the services described above, Client agrees to furnish or cause to be furnished to Zenith such information as Zenith reasonably believes appropriate to permit Zenith to provide the services contemplated by this letter agreement to or for Client (all such information so furnished being the “Information”). Client represents and covenants that all Information furnished by Client or its agents will be complete and correct in all material respects, to the best of Client’s knowledge, and that Client will advise Zenith immediately of the occurrence of any event or any other change known by Client or its agents which results in the Information ceasing to be complete and correct in all material Zenith. Client also represents and warrants that any projections or forecasts that it provides to ZENITH will be prepared in good faith and will be based upon assumptions which the management of Client believes in light of the circumstances in which they are made, are reasonable. Client recognizes and confirms that Zenith (a) will use and rely primarily on the Information and on information available from generally recognized public sources in performing the services contemplated hereby without having independently verified any of the same, (b) does not assume responsibility for the accuracy or completeness of the Information and such other information, and (c) will not make any appraisal of any of the assets or liabilities of Client.

Confidentiality. In the event of the consummation and public disclosure of any Transaction, Zenith shall have the right to disclose its advisory role in the Transaction by listing the client name and logo on its website and in its marketing materials.

No analysis, information or advice, whether communicated in written, electronic, oral or other form, provided by Zenith or its affiliates to Client or to its Client Representatives (as such term is defined below) in connection with the Engagement (the ”Zenith Information”) shall be disclosed by Client or such Client Representatives, in whole or in part, to any third party, or circulated or referred to publicly, or used for any purpose other than in connection with the Engagement and the Transaction without the prior written consent of Zenith. Neither party may disclose to any third party the existence or terms of this letter agreement without the prior written consent of the other party. Notwithstanding anything herein to the contrary, the fact of Zenith’s Engagement may be disclosed by Client to its affiliates and its directors, officers, accountants, legal advisors and employees (the “Client Representatives”) and to its underwriters to the extent required for the exclusive purpose of the Engagement or as required by law, rule or regulation. Client may disclose Zenith Information to its Client Representatives solely for purposes directly related to the Engagement and the Transaction and shall cause each of its Client Representatives to whom the Zenith Information is disclosed to commit to keeping such Zenith Information confidential as provided by this Section 6. Client shall be responsible for any direct damages to Zenith to the extent caused by breaches of this Section 6 by any of its Client Representatives.

Zenith agrees to keep confidential all nonpublic information provided to it by Client, including without limitation trade information, business practices, trade secrets, and other proprietary information (the “Client Information”). Notwithstanding any provision herein to the contrary, Zenith may disclose Client Information to its affiliates, members, officers, accountants, agents, legal advisors and employees (the “Zenith Representatives”) to the extent required for the exclusive purpose of the Engagement. Zenith shall cause each of its Zenith Representatives to whom the Client Information is disclosed to commit to keeping such Client Information confidential as provided by this Section 6. Zenith shall be responsible for any direct damages to Client to the extent caused by breaches of this Section 6 by any of its Zenith Representatives.

Client Information and Zenith Information shall be considered public and not protected by this letter agreement if (a) it is or becomes generally available to the public other than as a result of a disclosure by the receiving party or a representative of the receiving party in breach of the terms of this Section 6, (b) it becomes available to the receiving party on a non-confidential basis from a source not known by the receiving party to be under a duty of confidentiality to the disclosing party, or (c) if it is already known to the receiving party at the time of disclosure.

Nothing in this letter agreement shall obligate either party to refrain from disclosure of Zenith Information or Client Information (as the case may be, “Confidential Information”) hereunder to the extent such disclosure is required by law, regulation or judicial process or at the request of a regulatory authority. In the event that any Confidential Information is required to be disclosed by law, including without limitation, pursuant to the terms of a subpoena or similar document or in connection with litigation or other legal proceedings, the receiving party of such information hereby agrees, to the extent permitted by applicable law or regulation, to notify the disclosing party promptly of the existence, terms and circumstances surrounding such request. To the extent permitted by applicable law or regulation, the receiving party shall allow the disclosing party, in its sole discretion and at its sole expense, to contest the disclosure of Confidential Information on the disclosing party’s behalf, and the receiving party will reasonably cooperate with the disclosing party in such efforts to contest such disclosure at disclosing party’s expense.

Each party hereto acknowledges and agrees that irreparable damage would occur to the other in the event any of the provisions of this Section 6 were not performed in accordance with their specific terms or were otherwise breached and monetary damages would not be a sufficient remedy for any such non-performance or breach. Accordingly, each party shall be entitled to specific performance of the terms of this Section 6, including, without limitation, an injunction or injunctions to prevent breaches of the provisions of this Section 6 and to enforce specifically the terms and provisions hereof in any court of competent jurisdiction in the State of New York and of the United States of America located in the Borough of Manhattan, New York City (and appellate courts therefrom) in addition to any other remedy to which such party may be entitled at law or in equity.

The parties hereto agree that the provisions of this Section 6 will survive the termination of this letter agreement for two (2) years after such termination.

Governing Law. This letter agreement shall be governed and construed in accordance with the laws of the State of New York, without regard to conflicts-of-law principles that would result in the application of the laws of another jurisdiction. Each party hereby irrevocably and unconditionally (a) consents to submit to the exclusive jurisdiction of the courts of the State of New York and of the United States of America located in the Borough of Manhattan, New York City (and appellate courts therefrom) for any action, suit or proceeding arising out of or relating to this this agreement (and each party hereby irrevocably and unconditionally agrees not to commence any such action, suit, or proceeding except in such courts), (b) waives any objection to the laying of venue of any such action, suit or proceeding in any such courts, and (c) waives and agrees not to plead or claim that any such action, suit or proceeding brought in any such court has been brought in an inconvenient forum. EACH PARTY HERETO IRREVOCABLY WAIVES ANY AND ALL RIGHT TO TRIAL BY JURY IN ANY LEGAL PROCEEDING ARISING OUT OF OR RELATING TO THIS AGREEMENT. To the extent permitted by applicable law, Client hereby waives rights of setoff, and the right to interpose counterclaims in any lawsuit with respect to, in connection with or arising out of this Engagement, or any other claim or dispute relating to the engagement of Zenith arising between the parties hereto. The provisions of this letter agreement shall be binding solely upon and inure to the benefit of the Parties hereto and their respective successors and assigns.

Trust Account Waiver. Zenith acknowledges it has read the registration statement/preliminary prospectus of the Client and understands that the Client will establish the trust account referred to in the prospectus for the benefit of the public stockholders of the Client (“Trust Account”) and that, except for a portion of the interest earned on the amounts held in the Trust Account, the Client may disburse monies from the trust account only (a) to the public stockholders in the event they elect to redeem shares of the Client’s common stock in connection with the consummation of a business combination, (b) to the public stockholders if the Client fails to consummate a business combination within the time period set forth in the Client’s organizational documents, as disclosed in the prospectus, or (c) to the Client after or concurrently with the consummation of a business combination. Zenith hereby agrees that, notwithstanding anything to the contrary in this agreement, Zenith does not now, nor shall at any time hereafter, have any right, title, interest or claim of any kind in or to any monies in the Trust Account, or make any claim against the Trust Account, in connection with or relating to this agreement, the Engagement or the Transaction, regardless of whether such claim arises based on contract, tort, equity or any other theory of legal liability (collectively, the “Released Claims”); provided, however, that the foregoing waiver will not limit or prohibit Zenith from pursuing (i) a claim against Client or any other person for legal relief against monies or other assets of Client held outside of the Trust Account (including any funds that have been released from the Trust Account and any asset that have been purchased or acquired with any such funds) or for specific performance or other equitable relief in connection with a claim for Client to specifically perform its obligations under this agreement or for fraud or (ii) a claim Zenith may have with respect to its ownership of the SPAC’s public securities (the “Retained Claims”). Zenith hereby irrevocably waives any Released Claims that ZENITH may have against the Trust Account now or in the future as a result of, or arising out of this agreement, the Engagement or the Transaction and will not seek recourse against the Trust Account for any Released Claims; provided, however, that Zenith does not waive any Retained Claims.

Miscellaneous.

Client acknowledges and agrees that the services to be provided pursuant to the Engagement will not include any accounting, tax or legal advice.

All notices or other communications to be given hereunder shall be in writing and shall be sent by delivery in person, by courier service, by electronic mail transmission (including, for the avoidance of doubt, by electronic mail transmission containing an electronic link to a communication or notification that is electronically accessible) or telecopy or by registered or certified mail (postage prepaid, return receipt requested) addressed as follows or such other address as may be substituted by notice as herein provided:

If to Client:

HCM III Acquisition Corp.

100 First Stamford Place, Suite 330

Stamford, CT 06902

If to Zenith:

Zenith Securities LLC

100 First Stamford Place, Suite 330

Stamford, CT 06902

Any notice given hereunder shall be deemed to have been given upon the earliest of: (i) receipt, (ii) three (3) days after being deposited in the U.S. mail, postage prepaid, registered or certified mail, return receipt requested and (iii) one (1) day after being sent by Federal Express or other recognized overnight delivery service, return receipt requested. In the case of notices to and from the U.S. to any other country, such notices shall be deemed to have been given upon the earlier of (A) receipt and (B) two (2) days after being sent by Federal Express or other recognized courier service, return receipt requested. In the case of notices sent by electronic mail transmission or telecopy, such notices shall be deemed to have been given when sent.

(c)

The parties understand that Zenith is being engaged hereunder as an independent contractor to provide the services described above solely to Client, and that Zenith is not acting as a fiduciary of Client, the security holders or creditors of Client or any other persons in connection with the Engagement.

(d)

Client understands and acknowledges that Zenith engages in providing a wide variety of financial consulting services and other investment banking products and services to a wide range of institutions and individuals. In the ordinary course of business, Zenith and certain of its employees, as well as investment funds in which they may have financial interests, may acquire, hold or sell, long or short positions, or trade or otherwise effect transactions, in debt, equity, and other securities and financial instruments (including bank loans and other obligations) of, or investments in, a party that may be involved in the matters contemplated by this letter agreement. With respect to any such securities, financial instruments and/or investments, all rights in respect of such securities, financial instruments and investments, including any voting rights, will be exercised by the holder of the rights, in its sole discretion. In addition, Zenith may currently, and may in the future, have relationships with parties other than Client, including parties that may have interests with respect to Client, the Transaction or other parties involved in the Transaction, from which conflicting interests or duties may arise. Although Zenith in the course of such other activities and relationships may acquire information about Client, the Transaction or such other parties, Zenith shall have no obligation to, and may not be contractually permitted to, disclose such information, or the fact that Zenith is in possession of such information, to Client or to use such information on the Client’s behalf.

(e)

If any term or provision of this letter agreement or the application thereof to any person or circumstances shall be held invalid or unenforceable, the remaining terms and provisions hereof and the application of such term or provision to any person or circumstances other than those to which it is held invalid or unenforceable shall not be affected thereby.

(f)

It is understood and agreed among the parties that this letter agreement and the covenants made herein are made expressly and solely for the benefit of the parties hereto, and that no other person, other than an Indemnified Person, shall be entitled or be deemed to be entitled to any benefits or rights hereunder, nor be authorized or entitled to enforce any rights, claims or remedies hereunder or by reason hereof.

(g)

This letter agreement incorporates the entire agreement, and supersedes all prior agreements, arrangements or understandings (whether oral or written), between the parties with respect to the subject matter hereof and may not be amended or modified except in writing signed by each party hereto.

(h)

This letter agreement may be executed in one or more counterparts, each of which will be deemed to be an original and all of which together will be deemed to be one and the same document.

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If you are in agreement with the foregoing, please sign and return the attached copy of this letter agreement, whereupon this letter agreement shall become effective as of the date

Acknowledged and Agreed:

HCM III ACQUISITION CORP.

By:	/s/ Shawn Matthews
Name:	Shawn Matthews
Title:	Chief Executive Officer

ZENITH SECURITIES, LLC

By:	/s/ Steven Bischoff
Name:	Steven Bischoff
Title:	CEO

HCM III ACQUISITION CORP. 8-K