FORM 10-Q (Mark One) ☒QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934 For the quarterly period ended June 30, 2026 ☐TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934 Commission File Number: 001-43071 ARCHIMEDES TECH SPAC PARTNERS III CO.(Exact name of registrant as specified in its charter) Indicate by check mark whether the registrant (1) has filed all reports required to be filed by Section 13 or 15(d) of the SecuritiesExchange Act of 1934 during the preceding 12 months (or for such shorter period that the registrant was required to file such reports),and (2) has been subject to such filing requirements for the past 90 days. Yes☒No☐ Indicate by check mark whether the registrant has submitted electronically every Interactive Data File required to be submittedpursuant to Rule 405 of Regulation S-T (§232.405 of this chapter) during the preceding 12 months (or for such shorter period that theregistrant was required to submit such files). Yes☒No☐ Indicate by check mark whether the registrant is a large accelerated filer, an accelerated filer, a non-accelerated filer, a smallerreporting company, or an emerging growth company. See the definitions of “large accelerated filer,” “accelerated filer,” “smallerreporting company,” and “emerging growth company” in Rule 12b-2 of the Exchange Act. Large accelerated filer☐Non-accelerated filer☒ If an emerging growth company, indicate by check mark if the registrant has elected not to use the extended transition period forcomplying with any new or revised financial accounting standards provided pursuant to Section 13(a) of the Exchange Act.☐ Indicate by check mark whether the registrant is a shell company (as defined in Rule 12b-2 of the Exchange Act). Yes☒No☐ As of August 12, 2026, there were 35,262,000 ordinary shares (inclusive of ordinary shares included in outstanding units), $0.0001 parvalue each, issued and outstanding. ARCHIMEDES TECH SPAC PARTNERS III CO. FORM 10-Q FOR THE QUARTERLY PERIOD ENDED JUNE 30, 2026 TABLE OF CONTENTS PagePart I. Financial Information1Item 1. Financial Statements1Condensed Balance Sheets as of June 30, 2026 (Unaudited) and December 31, 20251Unaudited Condensed Statements of Operations for the Three and Six Months Ended June 30, 20262Unaudited Condensed Statements of Changes in Shareholders’ Deficit for the Three and Six Months Ended June 30,20263Unaudited Condensed Statement of Cash Flows for the Six Months Ended June 30, 20264Notes to Condensed Financial Statements (Unaudited)5Item 2. Management’s Discussion and Analysis of Financial Condition and Results of Operations16Item 3. Quantitative and Qualitative Disclosures About Market Risk18Item 4. Controls and Procedures18Part II. Other Information19Item 1. Legal Proceedings19Item 1A. Risk Factors19Item 2. Unregistered Sales of Equity Securities and Use of Proceeds19Item 3. Defaults Upon Senior Securities19Item 4. Mine Safety Disclosures19Item 5. Other Information19Item 6. Exhibits20Part III. Signatures21 PART I - FINANCIAL INFORMATION ARCHIMEDES TECH SPAC PARTNERS III CO.CONDENSED BALANCE SHEETS (1)On January 22, 2026, through a share capitalization, the Company issued an additional 1,150,000 Founder Shares to the Sponsor,resulting in the Sponsor holding an aggregate of 6,900,000 Founder Shares. All share and per share amounts have beenretroactively presented. The Founder Shares included an aggregate of 900,000 shares subject to forfeiture if the over-allotmentoption is not exercised in full by the underwriters. On January 26, 2026, the underwriters exercised their over-allotment option infull as part of the closing of the Initial Public Offering. As such, the 900,000 Founder Shares are no longer subject to forfeiture(Note 5). The accompanying notes are an integral part of these unaudited condensed financial statements. ARCHIMEDES TECH SPAC PARTNERS III CO.CONDENSED STATEMENTS OF OPERATIONS(UNAUDITED) ARCHIMEDES TECH SPAC PARTNERS III CO.CONDENSED STATEMENTS OF CHANGES IN SHAREHOLDERS’ DEFICITFOR THE THREE AND SIX MONTHS ENDED JUNE 30, 2026(UNAUDITED) (1)On January 22, 2026, through a share capitalization, the Company issued an additional 1,150,000 Founder Shares to the Sponsor,resulting in the Sponsor holding an aggregate of 6,900,000 Founder Shares. All share and per share amounts have beenretroactively presented. The Founder Shares included an aggregate of 900,000 shares subject to forfeiture if the over-allotmentoption is not exercised in full by the underwriters. On January 26, 2026, the underwriters exercised their over-allotment option infull as part of the closing of the Initial Public Offering. As such, the 900,000 Founder Shares are no longer subject to forfeiture(Note 5). The accompanying notes are an integral part of these unaudited condensed financial statements. ARCHIMEDES TECH SPAC PARTNERS III CO.CONDENSED STATEMENT OF CASH FLOWSFOR THE SIX MONTHS ENDED JUNE 30, 2026(UNAU