Filed Pursuant to Rule 424(b)(3)

File No. 333-298808

PROSPECTUS SUPPLEMENT NO. 2

(to Prospectus dated September 17, 2026)

CDT EQUITY INC.

673,023 Shares of Common Stock

This prospectus supplement supplements the prospectus dated September 17, 2026 (the “Prospectus”), which forms a part of our registration statement on Form S-1 (File No. 333-298808). This prospectus supplement is being filed to update and supplement the information in the Prospectus with the information contained in our Form 8-K filed with the Securities and Exchange Commission (“SEC”) on September 25, 2026 (the “Form 8-K”). Accordingly, we have attached the Form 8-K to this prospectus supplement.

This prospectus relates to the offer and resale of shares (the “Shares”) of our common stock, par value $0.0001 per share (the “Common Stock”) of (i) up to 14,630 shares of our common stock (the “Warrant Shares”) underlying common stock purchase warrants (the “Warrants”) issued to J.J. Astor & Co. (the “Lender”); (ii) 140,925 shares of Common Stock (the “Conversion Shares”) issuable to the Lender pursuant to the senior secured convertible promissory note, dated June 11, 2026, as amended and restated on July 31, 2026 and August 3, 2026, in $2,536,650 aggregate principal amount and an additional $541,620 senior secured convertible promissory note issued to the Lender on August 31, 2026 (collectively, the “Notes”); (iii) 1,284 shares of Common Stock issued to EX-ANIMO Ltd. (“EX-ANIMO”) on July 24, 2026 for certain consulting services; (iv) 1,000 shares of Common Stock issued to Maxim Partners LLC on July 30, 2026 as consideration for services provided to the Company; (v) 1,254 shares of Common Stock issued to Ian Burton on July 30, 2026 as consideration for services provided to the Company; (vi) 485,244 shares of Common Stock issued to shareholders of Sarborg Limited, a Cayman Islands company (“Sarborg”) pursuant to a Securities Purchase Agreement, dated July 30, 2026; (vii) 1,343 shares of Common Stock issued to NJS Foresight Bio-Advisory LLC (“NJS”) on July 31, 2026 as consideration for services provided to the Company; (viii) 1,343 shares of Common Stock issued to Thesprogen, PC (“Thesprogen”) on July 31, 2026 as consideration for services provided to the Company; and (ix) 26,000 shares of Common Stock issued to Sarborg pursuant to Amendment No. 1, dated August 31, 2026, to the Securities Purchase Agreement, dated February 19, 2026 (the “Amendment”).

We are registering the Shares on behalf of the Selling Stockholders to be offered and sold by them from time to time. We are not selling any securities under this prospectus and will not receive any proceeds from the sale of our Common Stock by the Selling Stockholders in the offering described in this prospectus. The Selling Stockholders may sell any, all or none of the Shares offered by this prospectus. For more information, see “Use of Proceeds.”

The Selling Stockholders, or their respective transferees, pledgees, donees or other successors-in-interest, may offer or sell the Shares from time to time in a number of different ways and at varying prices, including through public or private transactions at prevailing market prices, at prices related to prevailing market prices or at privately negotiated prices. See “Plan of Distribution” on page 108 of this prospectus for more information about how the Selling Stockholders may sell or dispose of the Shares being registered pursuant to this prospectus.

This prospectus describes the general manner in which the Shares may be offered and sold. When the Selling Stockholders sell Shares under this prospectus, we may, if necessary and required by law, provide a prospectus supplement that will contain specific information about the terms of that offering. Any prospectus supplement may also add to, update, modify or replace information contained in this prospectus. We urge you to read carefully this prospectus, any accompanying prospectus supplement and any documents we incorporate by reference into this prospectus and any accompanying prospectus supplement before you make your investment decision.

On September 24, 2026, the Company filed a certificate of amendment to the Company’s Second Amended and Restated Certificate of Incorporation (the “Certificate of Amendment”) with the Secretary of State of Delaware to effectuate a 1-for-25 reverse stock split (the “Reverse Stock Split”) of the outstanding shares of the Company’s Common Stock. Effective September 28, 2026 at 5:00 p.m. Eastern Time, every 25 shares of our Common Stock, either issued or outstanding, immediately prior to the filing and effectiveness of our Certificate of Amendment, was automatically combined and converted (without any further act) into one fully paid and non-assessable share of Common Stock. No fractional shares were issued as a result of the Reverse Stock Split. Stockholders of record who would otherwise be entitled to receive a fractional share of Common Stock received a cash payment in lieu thereof at a price equal to the fraction to which the stockholder would otherwise be entitled multiplied by the closing price per share of our Common Stock (as adjusted for the Reverse Stock Split) on The Nasdaq Capital Market on September 28, 2026.

All financial information, share numbers, option numbers, warrant numbers, other derivative security numbers and exercise prices appearing in this registration statement have been adjusted to give effect to the Reverse Stock Split, except where otherwise stated.

Our Common Stock is traded on The Nasdaq Capital Market under the trading symbol “CDT.” On October 1, 2026, the last reported sale price of our Common Stock on The Nasdaq Capital Market was $1.25.

We are an “emerging growth company,” as defined under the federal securities laws, and, as such, may elect to comply with certain reduced public company reporting requirements for future filings.

Investing in our securities involves a high degree of risk. Before buying any securities, you should carefully read the discussion of the risks of investing in our securities in the section entitled “Risk Factors” beginning on page 8 of the Prospectus, and under similar headings in any amendments or supplements to the Prospectus.

You should rely only on the information contained in this Prospectus or any prospectus supplement or amendment hereto. We have not authorized anyone to provide you with different information.

Neither the Securities and Exchange Commission nor any state securities commission has approved or disapproved of these securities or determined if this Prospectus or this prospectus supplement is truthful or complete. Any representation to the contrary is a criminal offense.

The date of this prospectus supplement is October 2, 2026

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, DC 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): September 24, 2026

CDT Equity Inc.

(Exact name of registrant as specified in its charter)

(646) 491-9132

(Registrant’s telephone number, including area code)

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 (see General Instruction A.2. below):

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 3.03 Material Modification to Rights of Security Holders.

To the extent required by Item 3.03 of Form 8-K, the information contained in Item 5.03 of this Current Report on Form 8-K (the “Current Report”) is incorporated herein by reference.

Item 5.03. Amendments to Articles of Incorporation or Bylaws; Change in Fiscal Year.

On September 24, 2026, CDT Equity Inc. (the “Company”) filed a certificate of amendment to the Company’s Second Amended and Restated Certificate of Incorporation (the “Amendment”) with the Secretary of State of the State of Delaware to effectuate a 1-for-25 reverse stock split (the “Reverse Stock Split”) of the outstanding shares of the Company’s common stock, par value $0.0001 per share (“Common Stock”). The Company’s stockholders previously approved future reverse stock splits and granted the board of directors the authority to determine the exact split ratios and when to proceed with any such reverse stock splits.

The Reverse Stock Split will become effective on September 28, 2026, at 5:00 p.m., Eastern Time (the “Effective Time”) and the Common Stock is expected to begin trading on The Nasdaq Capital Market on a Reverse Stock Split-adjusted basis on September 29, 2026, at market open under the existing ticker symbol, “CDT.” As of the Effective Time, every 25 shares of the Company’s issued and outstanding Common Stock will be combined into one share of Common Stock.

The par value and other terms of the Common Stock will not be affected by the Reverse Stock Split. The Company’s post-Reverse Stock Split Common Stock CUSIP number will be 20678X700.

No fractional shares will be issued as a result of the Reverse Stock Split. Stockholders of record who would otherwise be entitled to receive a fractional share of Common Stock will receive a cash payment in lieu thereof at a price equal to the fraction to which the stockholder would otherwise be entitled multiplied by the closing price per share of the Common Stock (as adjusted for the Reverse Stock Split) on the Nasdaq Capital Market on September 28, 2026.

The foregoing description of the Amendment is qualified in its entirety by reference to the Amendment, a copy of which is filed as Exhibit 3.1 to this Current Report and is incorporated herein by reference.

Item 7.01. Regulation FD Disclosure.

On September 25, 2026, the Company issued a press release announcing the Reverse Stock Split. The press release is furnished as Exhibit 99.1 and incorporated by reference herein.

The information in this Item 7.01, including Exhibit 99.1 attached hereto, is being furnished and shall not be deemed “filed” for purposes of Section 18 of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), or otherwise subject to the liabilities of that section. Such information shall not be incorporated by reference into any filing under the Securities Act of 1933, as amended (the “Securities Act”), whether made before or after the date hereof, except as expressly set forth by specific reference in such filing. The furnishing of this information will not be deemed an admission as to the materiality of any information contained therein.

Forward-Looking Statements

This Current Report includes forward-looking statements. These statements are made under the “safe harbor” provisions of the U.S. Private Securities Litigation Reform Act of 1995. These statements may be identified by words such as “will,” “would,” “expected,” or the negative of such terms, or other comparable terminology, and include statements about the Reverse Stock Split and the impacts, if any, on the Company’s Common Stock. Forward-Looking statements are statements that are not historical facts. Such forward-looking statements are not guarantees of future performance and are subject to risks and uncertainties, which could cause actual results to differ materially from the forward-looking statements contained herein due to many factors. These forward-looking statements and such risks, uncertainties and other factors speak only as of the date of this Current Report, and the Company expressly disclaims any obligation or undertaking to update or revise and forward-looking statement contained herein, or to reflect any change in our expectations with regard thereto or any other change in events, conditions, or circumstances on which any such statement is based, except to the extent otherwise required by applicable law.

Item 9.01. Financial Statements and Exhibits.

(d) Exhibits.

SIGNATURES

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.

Exhibit 3.1

CERTIFICATE OF AMENDMENT

OF

SECOND AMENDED AND RESTATED CERTIFICATE OF INCORPORATION

OF

CDT EQUITY INC.

(Pursuant to Section 242 of the General Corporation Law of the State of Delaware)

CDT Equity Inc., a corporation organized and existing under and by virtue of the General Corporation Law of the State of Delaware (the “Corporation”), does hereby certify as follows:

“Section 4.1 Authorized Capital Stock. The total number of shares of all classes of capital stock, each with a par value of $0.0001 per share, which the Corporation is authorized to issue is 251,000,000 shares, consisting of (a) 250,000,000 shares of common stock (the “Common Stock”), and (b) 1,000,000 shares of preferred stock (the “Preferred Stock”). The number of authorized shares of Common Stock may be increased or decreased (but not below the number of shares thereof then outstanding) by the affirmative vote of the holders of a majority in voting power of the stock of the Corporation with the power to vote thereon irrespective of the provisions of Section 242(b)(2) of the DGCL or any successor provision thereof, and no vote of the holders of any of the Common Stock or Preferred Stock voting separately as a class shall be required therefor.

Effective September 28, 2026 at 5:00pm Eastern Time (the “Reverse Stock Split Effective Time”), a one-for-twenty-five reverse stock split of the Corporation’s Common Stock shall become effective, pursuant to which each 25 shares of Common Stock issued and outstanding and held of record by each stockholder of the Corporation or issued and held by the Corporation in treasury immediately prior to the Reverse Stock Split Effective Time shall be reclassified and combined into one (1) validly issued, fully paid and nonassessable share of Common Stock automatically and without any action by the holder thereof upon the Reverse Stock Split Effective Time, with no corresponding reduction in the number of authorized shares of Common Stock (such reclassification and combination of shares, the “Reverse Stock Split”). No fractional shares of Common Stock will be issued in connection with the Reverse Stock Split. If, upon aggregating all of the shares of Common Stock held by a holder of Common Stock immediately following the Reverse Stock Split such holder would otherwise be entitled to a fractional share of Common Stock, the Corporation shall pay in cash (without interest) to each such holder an amount equal to such fraction multiplied by the closing price of the Common Stock on The Nasdaq Capital Market on the last trading day immediately preceding the Reverse Stock Split Effective Time (with such closing price proportionately adjusted to give effect to the Reverse Stock Split).

Each stock certificate that, immediately prior to the Reverse Stock Split Effective Time, represented shares of Common Stock that were issued and outstanding immediately prior to the Reverse Stock Split Effective Time shall, from and after the Reverse Stock Split Effective Time, automatically and without the necessity of presenting the same for exchange, represent that number of whole shares of Common Stock after the Reverse Stock Split Effective Time into which the shares formerly represented by such certificate have been reclassified as well the right to receive cash in lieu of fractional shares of Common Stock to which such holder may be entitled; provided, however, that each person of record holding a certificate that represented shares of Common Stock that were issued and outstanding immediately prior to the Reverse Stock Split Effective Time shall receive, upon surrender of such certificate, a new certificate evidencing and representing the number of whole shares of Common Stock after the Reverse Stock Split Effective Time into which the shares of Common Stock formerly represented by such certificate shall have been reclassified as well as the right to receive cash in lieu of fractional shares of Common Stock to which such holder may be entitled.”

IN WITNESS WHEREOF, this Certificate of Amendment has been executed by a duly authorized officer of the Corporation on this 24th day of September, 2026.

Exhibit 99.1

CDT Equity Inc. Announces Reverse Stock Split

NAPLES, Fla. and CAMBRIDGE, United Kingdom, September 25, 2026 (GLOBE NEWSWIRE) — CDT Equity Inc. (Nasdaq: CDT) (“CDT” or the “Company”), announces that its board of directors has approved a 1-for-25 reverse stock split of the Company’s common stock, to ensure continued compliance with the Nasdaq bid-price rule. The Company’s stockholders approved future reverse stock splits, their timing, and granted the board of directors authority to determine future exact split ratios.

The reverse stock split will become effective on September 28, 2026, at 5:00 pm, Eastern Time (the “Effective Time”), and the Company’s common stock is expected to begin trading on a reverse stock split-adjusted basis on The Nasdaq Capital Market (“Nasdaq”) at market open under the existing ticker symbol, “CDT” on September 29, 2026, the date which has been approved by Nasdaq for the effectiveness of such split.

As of the Effective Time, every 25 shares of the Company’s issued and outstanding common stock will be combined into one share of common stock. The par value per share of the Company’s common stock will remain unchanged at $0.0001. Proportional adjustments will be made to the number of shares of common stock issuable upon the exercise of the Company’s equity awards, convertible securities and warrants, as well as the applicable exercise price, and the number of shares authorized and reserved for issuance pursuant to the Company’s equity incentive plans.

The Company’s common stock will continue to trade on Nasdaq under the symbol “CDT” following the reverse stock split, with a new CUSIP number of 20678X700. After the effectiveness of the reverse stock split, the number of outstanding shares of common stock will be reduced to approximately 1,124,515. No fractional shares will be issued in connection with the reverse stock split, and stockholders who would otherwise be entitled to a fractional share will receive a proportional cash payment.

The Company’s transfer agent, Continental Stock Transfer & Trust Co., will serve as the exchange agent for the reverse stock split. Registered stockholders holding pre-reverse stock split shares of common stock electronically in book-entry form are not required to take any action to receive post-reverse stock split shares. Those stockholders who hold their shares in brokerage accounts or in “street name” will have their positions automatically adjusted to reflect the reverse stock split, subject to each broker’s particular processes, and will not be required to take any action in connection with the reverse stock split.

About CDT Equity Inc.

CDT Equity Inc. (NASDAQ: CDT) is a data-driven biopharmaceutical development company focused on identifying, enhancing, and advancing high-potential therapeutic assets through scientific innovation and strategic partnerships. Originally established as Conduit Pharmaceuticals, the company has evolved into a broader, more agile platform that leverages artificial intelligence, solid-form chemistry, and efficient asset repositioning to accelerate the development of novel treatments. Looking ahead, CDT is committed to creating shareholder value through licensing, strategic M&A, and positioning the company as a platform for transformative innovation.

Cautionary Statement Regarding Forward-Looking Statements

This press release contains certain forward-looking statements within the meaning of the federal securities laws. All statements other than statements of historical facts contained in this press release, including statements regarding the reverse stock split, CDT’s future results of operations and financial position, CDT’s business strategy, prospective product candidates, product approvals, research and development costs, timing and likelihood of success, plans and objectives of management for future operations, future results of current and anticipated studies and business endeavors with third parties, and future results of current and anticipated product candidates, are forward-looking statements. These forward-looking statements generally are identified by the words “believe,” “project,” “expect,” “anticipate,” “estimate,” “intend,” “strategy,” “future,” “opportunity,” “plan,” “may,” “should,” “will,” “would,” “will be,” “will continue,” “will likely result,” and similar expressions. These forward-looking statements are subject to a number of risks, uncertainties and assumptions, including, but not limited to; the effect that the reverse stock split may have on the price of the Company’s common stock; the ability or inability to maintain the listing of CDT’s securities on Nasdaq; the ability to recognize the anticipated benefits of the business combination completed in September 2023, which may be affected by, among other things, competition; the ability of the combined company to grow and manage growth economically and hire and retain key employees; the risks that CDT’s product candidates in development fail clinical trials or are not approved by the U.S. Food and Drug Administration or other applicable authorities on a timely basis or at all; changes in applicable laws or regulations; the possibility that CDT may be adversely affected by other economic, business, and/or competitive factors; and other risks and uncertainties identified in other filings made by CDT with the U.S. Securities and Exchange Commission. Moreover, CDT operates in a very competitive and rapidly changing environment. Because forward-looking statements are inherently subject to risks and uncertainties, some of which cannot be predicted or quantified and some of which are beyond CDT’s control, you should not rely on these forward-looking statements as predictions of future events. Forward-looking statements speak only as of the date they are made. Readers are cautioned not to put undue reliance on forward-looking statements, and except as required by law, CDT assumes no obligation and does not intend to update or revise these forward-looking statements, whether as a result of new information, future events, or otherwise. CDT gives no assurance that it will achieve its expectations.

Investors

CDT Equity Inc.

Info@cdtequity.com