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8,771,470 Shares of Common Stock 16,033,000 Shares of Common Stock Underlying Warrants This prospectus supplement is being filed to update and supplement the information contained in the prospectusdated May 2, 2024 (the “Prospectus”), which forms part of our registration statement on Form S-1 (No. 333-275056), as amended, as well as Supplement No. 1 to the Prospectus dated May 16, 2024, and Supplement No. 2 tothe Prospectus Dated August 19, 2024 with the information contained in our (i) Amendment to Quarterly Report onForm 10-Q for the quarter ended March 31, 2024 filed with the Securities and Exchange Commission (the “SEC”)on November 14, 2024 (the “First Quarter Amendment”); (ii) Amendment to Quarterly Report on Form 10-Q for thequarter ended June 30, 2024 filed with the SEC on November 14, 2024 (the “Second Quarter Amendment”); (iii)Form 10-Q filed with the SEC on September 16, 2024 (the “Quarterly Report,” and together with the First QuarterAmendment and the Second Quarter Amendment, the “Quarterly Reports”); and (iv) Current Reports on Form 8-Kfiled with the SEC on November 19, 2024 and November 25, 2024 (collectively, the “Current Reports”).Accordingly, we have attached the Quarterly Reports and Current Reports to this prospectus supplement. The Prospectus and this prospectus supplement relate to the offer and sale from time to time by the sellingsecurityholders named in the Prospectus of an aggregate of: (a) up to 8,771,470 shares of our common stock, parvalue $0.0001 per share (“Common Stock”), consisting of: (i) 2,000,000 shares of Common Stock issued in a privateplacement (the “PIPE Financing”) pursuant to that certain Subscription Agreement dated as of September 13, 2023(as the same may be amended from time to time, the “PIPE Subscription Agreement”); (ii) 4,015,250 shares ofCommon Stock held by Murphy Canyon Acquisition Sponsor, LLC (the “Sponsor”); (iii) 1,300,000 shares ofCommon Stock issued to A.G.P./Alliance Global Partners (“A.G.P.”) upon the completion of the BusinessCombination (as defined below); (iv) 395,460 shares of Common Stock issued to Cizzle Biotechnology HoldingsPLC (“Cizzle”) pursuant to its exercise of an option that it held; (v) 1,015,760 shares of Common Stock issued toVela Technologies Plc pursuant to its exercise of an option that it held; and (vi) 45,000 shares of Common Stockheld by one of our current directors and certain of our former directors; and (b) up to 16,033,000 shares of CommonStock, consisting of (i) 2,000,000 shares of Common Stock issuable upon the exercise of certain warrants (the “PIPEWarrants”) issued in the PIPE Financing and having an exercise price of $11.50 per share; (ii) 54,000 shares ofCommon Stock issuable upon the exercise of certain warrants (the “A.G.P. Warrants”) issued to A.G.P. upon thecompletion of the Business Combination and having an exercise price of $11.00 per share; (iii) 754,000 shares ofCommon Stock issuable upon the exercise of certain warrants (the “Private Warrants”) held by the Sponsor andhaving an exercise price of $11.50 per share; and (iv) 13,225,000 shares of Common Stock issuable upon exercise ofcertain public warrants (the “Public Warrants”) having an exercise price of $11.50 that were issued in connectionwith Murphy Canyon Acquisition Corp.’s initial public offering. This prospectus supplement updates and supplements the information in the Prospectus and is not complete without,and may not be delivered or utilized except in combination with, the Prospectus, including all amendments andsupplements thereto. This prospectus supplement should be read in conjunction with the Prospectus and if there isany inconsistency between the information in the Prospectus and this prospectus supplement, you should rely on theinformation in this prospectus supplement. Terms used in this prospectus supplement but not defined herein shallhave the meanings given to such terms in the Prospectus. You should read the Prospectus, this prospectus supplement and all additional prospectus supplements andamendments carefully before you invest in our securities. Our Common Stock and the Public Warrants are listed onThe Nasdaq Global Market and The Nasdaq Capital Market, respectively, of The Nasdaq Stock Market LLC(“Nasdaq”) under the symbol “CDT” and “CDTTW”, respectively. On December 13, 2024, the last quoted saleprice for our Common Stock as reported on Nasdaq was $0.082 per share. We are an “emerging growth company,” as defined under the federal securities laws, and, as such, may electto comply with certain reduced public company reporting requirements for future filings. INVESTING IN OUR SECURITIES INVOLVES RISKS. SEE THE“RISK FACTORS”ON PAGE 6 OFTHISPROSPECTUS AND ANY SIMILAR SECTION CONTAINED IN THE APPLICABLEPROSPECTUSSUPPLEMENT AND IN THE DOCUMENTS INCORPORATED BY REFERENCEHEREIN AND THEREIN CONCERNING FACTORS YOU SHOULD CONSIDER BEFORE INVESTINGIN OUR SECURITIES. Neither the U.S. Securities and Exchange Commission nor any state securit




