木星神经科学公司美国存托凭证招股说明书（2026年6月30日版）

JUPITER NEUROSCIENCES, INC. This prospectus supplement updates, amends and supplements the prospectus dated December 11, 2025 (the “Prospectus”), whichforms a part of our Registration Statement on Form S-1 (Registration No. 333-291832) and is being filed to update, amend andsupplement the information included in the Prospectus with information contained in our Current Report on Form 8-K, which wasfiled with the Securities and Exchange Commission (the “SEC”) on June 30, 2026 (the “Current Report”). Accordingly, we haveattached the Current Report to this prospectus supplement. Capitalized terms used in this prospectus supplement and not otherwise This prospectus supplement is not complete without the Prospectus. This prospectus supplement should be read in conjunction withthe Prospectus, which is to be delivered with this prospectus supplement, and is qualified by reference thereto, except to the extent thatthe information in this prospectus supplement updates or supersedes the information contained in the Prospectus. Please keep this Shares of our common stock, par value $0.0001 per share (our “Common Stock”), are listed on The Nasdaq Stock Market, LLC underthe symbol “JUNS.” On June 29, 2026, the closing price of our Common Stock was $0.21 per share. Investing in our securities involves risks that are described in the “Risk Factors” section of the Prospectus. Neither the SEC nor any state securities commission has approved or disapproved of the securities to be issued under theProspectus or this prospectus supplement or determined if the Prospectus or this prospectus supplement is truthful orcomplete. Any representation to the contrary is a criminal offense. The date of this prospectus supplement is June 30, 2026. UNITED STATESSECURITIES AND EXCHANGE COMMISSIONWashington, D.C. 20549 FORM 8-K CURRENT REPORTPursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934 June 26, 2026Date of Report (Date of earliest event reported) JUPITER NEUROSCIENCES, INC.(Exact name of registrant as specified in its charter) 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 forcomplying 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; CompensatoryArrangements of Certain Officers. Appointment of Director On June 26, 2026, the Board of Directors (the “Board”) of Jupiter Neurosciences, Inc. (the “Company”) appointed Tomas J. Philipson,Ph.D. to serve as a member of the Board, effective immediately. Dr. Philipson will serve until the next annual meeting of stockholdersand until his successor is duly elected and qualified, or his earlier death, resignation, or removal. In connection with his appointment, Dr. Philipson was also appointed to serve as a member of the Audit Committee and theCompensation Committee of the Board, in each case effective on the same date as his appointment to the Board. Dr. Philipson, age 64, is a health care economist with experience across academia, government, and the private sector. Since June2020, Dr. Philipson has been self-employed through his consulting firm, TJP Economic Consulting Inc., where he advises seniorexecutives at biopharmaceutical and health care companies on economic and policy matters. Dr. Philipson currently serves asManaging Partner of MEDA Ventures since 2023. Dr. Philipson serves on the advisory boards of Diagnos Inc. since 2025, GATCHealth Corp. (Medical Advisory Board) since 2022, iRemedy Healthcare Companies, Inc. since 2021, Epigenetix, Inc. since 2021,Nested Knowledge, Inc. since 2022, and M2i Global, Inc. since 2024. He is also a member of the Anthropic Economic AdvisoryCouncil since 2025. Dr. Philipson co-founded Precision Health Economics LLC in 2007 and served as Managing Partner until itsacquisition in 2015. Dr. Philipson previously served in senior roles in the U.S. federal government, including as Acting Chairman ofthe White House Council of Economic Advisers from June 2019 to June 2020 and as a member of the Council of Economic Advisersfrom 2017 to 2020. Earlier in his career, he served as a senior economic advisor to the leadership of the U.S. Food and DrugAdministration and the Centers for Medicare & Medicaid Services in 2003 and 2004. He was appointed to the Key IndicatorCommission of the U.S. Congress in 2012 and has served as a scientific advisor to the House of Representatives’ 21st Century Curesinitiative (2015) and the Biden Cancer Initiative (2017). Dr. Philipson is th