UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 8-K

CURRENT REPORT

PURSUANT TO SECTION 13 OR 15(d) OF THE

SECURITIES EXCHANGE ACT OF 1934

Date of Report (Date of earliest event reported): July 13, 2026

Archimedes Tech SPAC Partners III Co.

(Exact name of registrant as specified in its charter)

Registrant’s telephone number, including area code: (725) 312-2430

Not Applicable

(Former name or former address, if changed since last report)

Check the appropriate box below if the Form 8-K filing is intended to simultaneously satisfy the filing obligation of the registrant under any of the following provisions:

Securities registered pursuant to Section 12(b) of the Act:

Indicate by check mark whether the registrant is an emerging growth company as defined in Rule 405 of the Securities Act of 1933 (§230.405 of this chapter) or Rule 12b-2 of the Securities Exchange Act of 1934 (§240.12b-2 of this chapter).

Emerging growth company ☒

If an emerging growth company, indicate by check mark if the registrant has elected not to use the extended transition period for complying with any new or revised financial accounting standards provided pursuant to Section 13(a) of the Exchange Act. ☐

Item 5.02. Departure of Directors or Certain Officers; Election of Directors; Appointment of Certain Officers; Compensatory Arrangements of Certain Officers.

On July 13, 2026, the board of directors (the “Board”) of Archimedes Tech SPAC Partners III Co. (the “Company”) appointed Stephen N. Cannon as a Class II director of the Board, effective immediately. The Board has determined that Mr. Cannon qualifies as an independent director and appointed him to serve as a member of the audit committee, the compensation committee and the nominating and corporate governance committee of the Board.

Stephen N. Cannon, 58, serves as a director of Archimedes Tech SPAC Partners II Co. (“Archimedes II”), which completed its initial public offering in February 2025 and has announced a definitive merger agreement with Forge Nano Inc. Since 2014, Mr. Cannon has been President of Everest Partners Limited, a privately-owned investment firm focused on Asian private investments. From 2020 to 2022, Mr. Cannon served as Chief Executive Officer and President of Archimedes Tech SPAC Partners Co. (“Archimedes I”), a blank check company with $133 million held in trust which consummated its business combination with SoundHound AI, Inc. in April 2022. From 2020 to 2022, Mr. Cannon served as Chief Operating Officer and President of Global SPAC Partners Co., a blank check company with $169 million held in trust which consummated its business combination with Gorilla Technology Group Inc. in 2022. From 2019 to 2022, Mr. Cannon served as Chief Operating Officer and President of Ackrell SPAC Partners I Co., a blank check company with $140 million held in trust which liquidated its trust and delisted from Nasdaq in August 2022. From 2017 to 2019, Mr. Cannon served as Chief Financial Officer of Twelve Seas Investment Company, a blank check company with $207 million held in trust which consummated its initial business combination with Brooge Energy Limited in December 2019. From 2017 to 2019, Mr. Cannon served as President, Chief Financial Officer and a director of CM Seven Star Acquisition Corp., a Nasdaq-listed SPAC, sponsored by a leading Chinese private equity firm, which consummated its business combination with Kaixin Auto Holdings in April 2019. From 2014 to 2016, Mr. Cannon served as Chief Executive Officer and a director of DT Asia Acquisition Corp., a Nasdaq-listed SPAC, which consummated its business combination with China Direct Lending Corp. in July 2016. From 2010 to 2014, Mr. Cannon was a Partner and Head of China for RedBridge Group Ltd., a boutique merchant banking firm focused on Chinese and Arabian Gulf cross-border investments. From 2009 to 2014, Mr. Cannon was a registered representative of, and senior advisor to, Ackrell Capital. From 2007 to 2010, Mr. Cannon served as Chief Financial Officer and a director of Hambrecht Asia Acquisition Corp., a Nasdaq-listed SPAC, which consummated its business combination with SGOCO Technology Ltd in April 2010. From 2005 to 2008, Mr. Cannon served as a Managing Director of Asian investment banking for WR Hambrecht+Co. Prior to WR Hambrecht+Co., Mr. Cannon worked at ABN AMRO, Donaldson, Lufkin & Jenrette, Smith Barney Shearson and Salomon Brothers. Mr. Cannon graduated from the University of Notre Dame with a Bachelor of Arts degree in Economics and a Bachelor of Science degree, majoring in Mechanical Engineering.

No family relationships exist between Mr. Cannon and any of the Company’s directors or other executive officers. There is no arrangement or understanding between Mr. Cannon and any other persons pursuant to which he was selected as an officer. Other than as previously disclosed in the Company’s filings with the Securities and Exchange Commission, there are no related party transactions involving Mr. Cannon that are reportable under Item 404(a) of Regulation S-K.

In connection with the appointment, the Company and Mr. Cannon entered into a joinder to the letter agreement and registration rights agreement, each dated January 22, 2026, by and among the Company and the parties named therein as well as an indemnification agreement, which are substantially similar to the letter agreement, registration rights agreement and indemnification agreements, respectively, entered into by the current officers and directors of the Company.

SIGNATURE

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned hereunto duly authorized.

Dated: July 17, 2026

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