SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

SCHEDULE 13G

UNDER THE SECURITIES EXCHANGE ACT OF 1934

HCM III Acquisition Corp.

(Name of Issuer)

Units, no par value

(Title of Class of Securities)

000000000

(CUSIP Number)

08/01/2025

(Date of Event Which Requires Filing of this Statement)

Check the appropriate box to designate the rule pursuant to which this Schedule is filed:

Rule 13d-1(b)

Rule 13d-1(c)

Rule 13d-1(d)

SCHEDULE 13G

CUSIP No.

000000000

Names of Reporting Persons

Saba Capital Management, L.P.

Check the appropriate box if a member of a Group (see instructions)

(a)

(b)

Sec Use Only

Citizenship or Place of Organization

DELAWARE

Number of Shares Beneficially Owned by Each Reporting Person With:

5	Sole Voting Power 0.00
6	Shared Voting Power 3,241,667.00
7	Sole Dispositive Power 0.00
8	Shared Dispositive Power 3,241,667.00

Aggregate Amount Beneficially Owned by Each Reporting Person

3,241,667.00

Check box if the aggregate amount in row (9) excludes certain shares (See Instructions)

Checkbox not checked

Percent of class represented by amount in row (9)

12.81 %

Type of Reporting Person (See Instructions)

PN, IA

Comment for Type of Reporting Person: The percentages used herein are calculated based upon 25,300,000 Units outstanding, as disclosed in the company's 8-K filed 8/5/25. Rows 8, 10 and 11 include (i) 1,200,000 Units, (ii) 875,000 Class A Private Units, and (iii) 1,666,667 Class B Private Units.

SCHEDULE 13G

CUSIP No.

000000000

Names of Reporting Persons

Boaz R. Weinstein

Check the appropriate box if a member of a Group (see instructions)

(a)

(b)

Sec Use Only

Citizenship or Place of Organization

NEW YORK

Number of Shares Beneficially Owned by Each Reporting Person With:

5	Sole Voting Power 0.00
6	Shared Voting Power 3,241,667.00
7	Sole Dispositive Power 0.00
8	Shared Dispositive Power 3,241,667.00

Aggregate Amount Beneficially Owned by Each Reporting Person

3,241,667.00

Check box if the aggregate amount in row (9) excludes certain shares (See Instructions)

Checkbox not checked

Percent of class represented by amount in row (9)

12.81 %

Type of Reporting Person (See Instructions)

SCHEDULE 13G

CUSIP No.

000000000

Names of Reporting Persons

Saba Capital Management GP, LLC

Check the appropriate box if a member of a Group (see instructions)

(a)

(b)

Sec Use Only

Citizenship or Place of Organization

DELAWARE

Number of Shares Beneficially Owned by Each Reporting Person With:

5	Sole Voting Power 0.00
6	Shared Voting Power 3,241,667.00
7	Sole Dispositive Power 0.00
8	Shared Dispositive Power 3,241,667.00

Aggregate Amount Beneficially Owned by Each Reporting Person

3,241,667.00

Check box if the aggregate amount in row (9) excludes certain shares (See Instructions)

Checkbox not checked

Percent of class represented by amount in row (9)

12.81 %

Type of Reporting Person (See Instructions)

SCHEDULE 13G

Item 1.

(a)

Name of issuer:

HCM III Acquisition Corp.

(b)

Address of issuer's principal executive offices:

100 First Stamford Place, #330, STAMFORD, CONNECTICUT 03902

Item 2.

(a)

Name of person filing:

Saba Capital Management, L.P., a Delaware limited partnership ("Saba Capital"), Saba Capital Management GP, LLC, a Delaware limited liability company ("Saba GP"), and Mr. Boaz R. Weinstein (together, the "Reporting Persons". The Reporting Persons have entered into a Joint Filing Agreement, dated August 5, 2025, pursuant to which the Reporting Persons have agreed to file this statement and any subsequent amendments hereto jointly in accordance with the provisions of Rule 13d-1(k)(1) under the Act. Any disclosures herein with respect to persons other than the Reporting Persons are made on information and belief after making inquiry to the appropriate party. The filing of this statement should not be construed as an admission that any of the forgoing persons or the Reporting Persons is, for the purposes of Section 13 of the Act, the beneficial owner of the Common Stock reported herein.

(b)

Address or principal business office or, if none, residence:

The address of the business office of each of the Reporting Persons is 405 Lexington Avenue, 58th Floor, New York, New York 10174.

(c)

Citizenship:

Saba Capital is organized as a limited partnership under the laws of the State of Delaware. Saba GP is organized as a limited liability company under the laws of the State of Delaware. Mr. Weinstein is a citizen of the United States.

(d)

Title of class of securities:

Units, no par value

(e)

CUSIP No.:

000000000

Item 3.

If this statement is filed pursuant to §§ 240.13d-1(b) or 240.13d-2(b) or (c), check whether the person filing is a:

(a)

Broker or dealer registered under section 15 of the Act (15 U.S.C. 78o);

(b)

Bank as defined in section 3(a)(6) of the Act (15 U.S.C. 78c);

(c)

Insurance company as defined in section 3(a)(19) of the Act (15 U.S.C. 78c);

(d)

Investment company registered under section 8 of the Investment Company Act of 1940 (15 U.S.C. 80a-8);

(e)

An investment adviser in accordance with § 240.13d-1(b)(1)(ii)(E);

(f)

An employee benefit plan or endowment fund in accordance with § 240.13d-1(b)(1)(ii)(F);

(g)

A parent holding company or control person in accordance with § 240.13d-1(b)(1)(ii)(G);

(h)

A savings associations as defined in Section 3(b) of the Federal Deposit Insurance Act (12 U.S.C. 1813);

(i)

A church plan that is excluded from the definition of an investment company under section 3(c)(14) of the Investment Company Act of 1940 (15 U.S.C. 80a-3);

(j)

A non-U.S. institution in accordance with § 240.13d-1(b)(1)(ii)(J). If filing as a non-U.S. institution in accordance with § 240.13d-1(b)(1)(ii)(J),
please specify the type of institution:

(k)

Group, in accordance with Rule 240.13d-1(b)(1)(ii)(K).

Item 4.

Ownership

(a)

Amount beneficially owned:

SEC Form SCHEDULE 13G filed by HCM Acquisition Corp