Amended and Restated Warrant Agreement, dated as of December 23, 2021, by and between Adit EdTech Acquisition Corp. and Continental Stock Transfer & Trust Company

Exhibit 4.1

AMENDED AND RESTATED WARRANT AGREEMENT

THIS AMENDED AND RESTATED WARRANT AGREEMENT (this “Agreement”), dated as of December 23, 2021, is entered into by and between Adit EdTech Acquisition Corp., a Delaware corporation (the “Company”), and Continental Stock Transfer & Trust Company, a New York corporation (the “Warrant Agent”).

WHEREAS, the Company consummated a public offering (the “Public Offering”) of 27,600,000 units (after the underwriters’ over-allotment option was exercised in full), each unit (a “Unit”) comprised of one share of common stock of the Company, par value $0.0001 per share (“Common Stock”), and one-half of one warrant (a “Public Warrant”), with each whole Public Warrant entitling the holder to purchase one share of Common Stock at a price of $11.50 per share, subject to adjustment as described herein, and, in connection therewith, issued and delivered 13,800,000 Public Warrants to the investors in the Public Offering;

WHEREAS, the Company filed with the Securities and Exchange Commission a Registration Statement on Form S-1, No: 333-251641, as amended (the “Registration Statement”), for the registration, under the Securities Act of 1933, as amended (the “Act”) of, among other securities, the Public Warrants;

WHEREAS, Adit EdTech Sponsor, LLC purchased an aggregate of 7,270,000 warrants (the “Private Warrants”), with each whole Private Warrant entitling the holder to purchase one share of Common Stock at a price of $11.50 per share, subject to adjustment as described herein, concurrent with the Public Offering;

WHEREAS, the Company may issue up to an additional 2,000,000 warrants (“Working Capital Warrants,” and together with the Public Warrants and Private Warrants, the “Warrants”), with each whole Working Capital Warrant entitling the holder to purchase one share of Common Stock at a price of $11.50 per share, subject to adjustment as described herein in satisfaction of certain working capital loans made by the Company’s officers, directors, initial stockholders and affiliates;

WHEREAS, the Company desires the Warrant Agent to act on behalf of the Company, and the Warrant Agent is willing to so act, in connection with the issuance, registration, transfer, exchange, redemption and exercise of the Warrants;

WHEREAS, the Company and the Warrant Agent entered into that certain Warrant Agreement, dated as of January 11, 2021 (the “Original Agreement”), to provide for the form and provisions of the Warrants, the terms upon which they shall be issued and exercised, and the respective rights, limitation of rights, and immunities of the Company, the Warrant Agent, and the holders of the Warrants;

WHEREAS, all acts and things have been done and performed which are necessary to make the Warrants, when executed on behalf of the Company and countersigned by or on behalf of the Warrant Agent, as provided herein, the valid, binding and legal obligations of the Company, and to authorize the execution and delivery of the Original Agreement and this Agreement; and

WHEREAS, the Company and the Warrant Agent desire to amend the Original Agreement pursuant to Section 9.8 thereof to cure and correct certain ambiguities and defective provisions contained therein to conform with applicable disclosure contained in the Registration Statement.

NOW, THEREFORE, in consideration of the mutual agreements herein contained, the parties hereto agree that the Original Agreement is hereby amended and restated in its entirety by this Agreement and further agree as follows:

1. Appointment of Warrant Agent. The Company hereby appoints the Warrant Agent to act as agent for the Company for the Warrants, and the Warrant Agent hereby accepts such appointment and agrees to perform the same in accordance with the terms and conditions set forth in this Agreement.

2. Warrants.

2.1. Form of Warrant. Each Warrant shall be (a) issued in registered form only, (b) in substantially the form of Exhibit A hereto, the provisions of which are incorporated herein, and (c) signed by, or bear the facsimile signature of, the Chairman of the Board of Directors or the President and the Treasurer or the Secretary of the Company. In the event the person whose facsimile signature has been placed upon any Warrant shall have ceased to serve in the capacity in which such person signed the Warrant before such Warrant is issued, it may be issued with the same effect as if he or she had not ceased to be such at the date of issuance.

2.2. Uncertificated Warrants. Notwithstanding anything herein to the contrary, any Warrant, or portion thereof, may be issued as part of, and be represented by, a Unit, and any Warrant may be issued in uncertificated or book-entry form through the Warrant Agent and/or the facilities of The Depository Trust Company or other book-entry depositary system, in each case as determined by the Board of Directors of the Company or by an authorized committee thereof. Any Warrant so issued shall have the same terms, force and effect as a certificated Warrant that has been duly countersigned by the Warrant Agent in accordance with the terms of this Agreement.

2.3. Effect of Countersignature. Except with respect to uncertificated Warrants as described above, for which no Warrant Agent countersignature shall be required, unless and until countersigned by the Warrant Agent pursuant to this Agreement, a Warrant shall be invalid and of no effect and may not be exercised by the holder thereof.

2.4. Registration.

2.4.1. Warrant Register. The Warrant Agent shall maintain books (the “Warrant Register”) for the registration of the original issuance and transfers of the Warrants. Upon the initial issuance of the Warrants, the Warrant Agent shall issue and register the Warrants in the names of the respective holders thereof in such denominations and otherwise in accordance with instructions delivered to the Warrant Agent by the Company.

2.4.2. Registered Holder. Prior to due presentment for registration of transfer of any Warrant, the Company and the Warrant Agent may deem and treat the person in whose name such Warrant shall be registered upon the Warrant Register (the “registered holder”), as the absolute owner of such Warrant and of each Warrant represented thereby (notwithstanding any notation of ownership or other writing on the warrant certificate made by anyone other than the Company or the Warrant Agent), for the purpose of any exercise thereof, and for all other purposes, and neither the Company nor the Warrant Agent shall be affected by any notice to the contrary.

2.5. Detachability of Warrants. The Common Stock and Warrants comprising the Units will not be separately transferable until the 52^nd day following the date of the prospectus relating to the Public Offering, or, if such 52^nd day is not on a day, other than Saturday, Sunday or federal holiday, on which banks in New York City are generally open for normal business (a “Business Day”), then on the immediately succeeding Business Day following such date, or such earlier date as EarlyBirdCapital, Inc. (the “Representative”) may consent; provided, however, that in no event will the Representative allow separate trading of the Common Stock and the Warrants comprising the Units until (i) the Company has filed a Current Report on Form 8-K which includes an audited balance sheet reflecting the receipt by the

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Company of the gross proceeds of the Public Offering including the gross proceeds received by the Company from the exercise of the underwriters’ over-allotment option in the Public Offering, if the over-allotment option is exercised prior to the filing of the Form 8-K, and (ii) the Company has issued a press release and has filed a Current Report on Form 8-K announcing when such separate trading shall begin (the “Detachment Date”).

2.6. Private Warrant and Working Capital Warrant Attributes. For so long as a Private Warrant or a Working Capital Warrant is held by its initial holder or a permitted transferee of such holder under Section 5.6 hereof, such Private Warrant or Working Capital Warrant shall be identical to a Public Warrant except that such Private Warrant or Working Capital Warrant (i) shall not be redeemable at the option of the Company and (ii) may be exercised for cash or on a cashless basis at the holder’s option. Once a Private Warrant or Working Capital Warrant is transferred to a holder other a permitted transferee under Section 5.6 hereof, it shall be treated as a Public Warrant hereunder for all purposes.

3. Terms and Exercise of Warrants.

3.1. Warrant Price. Each Warrant shall, when countersigned by the Warrant Agent, entitle the registered holder thereof, subject to the provisions of such Warrant, as the case may be, and of this Agreement, to purchase from the Company the number of shares of Common Stock stated therein, at the price of $11.50 per whole share, subject to the adjustments provided in Section 4 hereof and in the last sentence of this Section 3.1. The term “Warrant Price” as used in this Agreement refers to the price per share at which Common Stock may be purchased at the time a Warrant is exercised. The Company, in its sole discretion, may lower the Warrant Price at any time prior to the Expiration Date (as defined below).

3.2. Duration of Warrants. A Warrant may be exercised only during the period (the “Exercise Period”) commencing thirty (30) days following the consummation by the Company of a merger, capital stock exchange, asset acquisition, stock purchase, reorganization or other similar business combination, as described more fully in the Company’s Registration Statement (a “Business Combination”), and terminating at 5:00 p.m., New York City time on the earlier to occur of (x) the five (5) year anniversary of the closing of an initial Business Combination or (y) the date fixed for redemption of the Warrants as provided in Section 6 of this Agreement (the “Expiration Date”). Except with respect to the right to receive the Redemption Price (as set forth in Section 6 hereunder), each Warrant not exercised on or before the Expiration Date shall become void, and all rights thereunder and all rights in respect thereof under this Agreement shall cease at the close of business on the Expiration Date. The Company, in its sole discretion, may extend the duration of the Warrants by delaying the Expiration Date.

3.3. Exercise of Warrants.

3.3.1. Payment. Subject to the provisions of the Warrant and this Agreement, a Warrant, when countersigned by the Warrant Agent, may be exercised by the registered holder thereof by surrendering it, at the office of the Warrant Agent, or at the office of its successor as Warrant Agent, in the Borough of Manhattan, City and State of New York, with the subscription form, as set forth in the Warrant, duly executed, and by paying in full the Warrant Price for each full share of Common Stock as to which the Warrant is exercised and any and all applicable taxes due in connection with the exercise of the Warrant, as follows:

(a) by certified check payable to the order of the Warrant Agent or wire transfer,

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(b) in the event of redemption pursuant to Section 6 hereof in which the Company’s management has elected to force all holders of Warrants to exercise such Warrants on a “cashless basis,” by surrendering the Warrants for that number of shares of Common Stock equal to the quotient obtained by dividing (x) the product of the number of shares of Common Stock underlying the Warrants, multiplied by the difference between the applicable Warrant Price and the Fair Market Value (as defined below) by (y) the Fair Market Value. Solely for purposes of this Section 3.3.1(b), “Fair Market Value” shall mean the average reported last sale price of the Common Stock for the ten (10) trading days ending on the third trading day prior to the date on which the notice of redemption is sent to holders of Warrants pursuant to Section 6 hereof; or

(c) with respect to any Private Warrants or Working Capital Warrants, for so long as such Private Warrants or Working Capital Warrants are held by the initial purchasers or their permitted transferees, by surrendering such Private Warrants or Working Capital Warrants for that number of shares of Common Stock equal to the quotient obtained by dividing (x) the product of (A) the number of shares of Common Stock underlying such Warrants and (B) the difference between the exercise price of such Warrants and the Fair Market Value (as defined below) by (y) the Fair Market Value; provided, however, that no cashless exercise shall be permitted unless the Fair Market Value is equal to or higher than the exercise price. Solely for purposes of this Section 3.3.1(c), the “Fair Market Value” shall mean the average reported last sale price of the Common Stock for the ten (10) trading days ending on the third trading day prior to the date of exercise.

3.3.2. Issuance of Shares of Common Stock. As soon as practicable after the exercise of any Warrant and the clearance of the funds in payment of the Warrant Price (if any), the Company shall issue to the registered holder of such Warrant a certificate or certificates, or book entry position, for the number of shares of Common Stock to which he, she or it is entitled, registered in such name or names as may be directed by him, her or it, and if such Warrant shall not have been exercised in full, a new countersigned Warrant, or book entry position, for the number of shares as to which such Warrant shall not have been exercised. Notwithstanding the foregoing, the Company shall not be obligated to deliver any securities pursuant to the exercise of a Warrant unless (a) a registration statement under the Act with respect to the Common Stock issuable upon exercise of such Warrants is effective and a current prospectus relating to the shares of Common Stock issuable upon exercise of the Warrants is available for delivery to the Warrant holders or (b) in the opinion of counsel to the Company, the exercise of the Warrants is exempt from the registration requirements of the Act and such securities are qualified for sale or exempt from qualification under applicable securities laws of the states or other jurisdictions in which the registered holder resides. Warrants may not be exercised by, or securities issued to, any registered holder in any state in which such exercise or issuance would be unlawful. In the event that a registration statement under the Act with respect to the Common Stock underlying the Warrants is not effective or a current prospectus is not available, or because such exercise would be unlawful with respect to a registered holder in any state, the registered holder shall not be entitled to exercise such Warrants and such Warrants may have no value and expire worthless. In no event will the Company be required to “net cash settle” the warrant exercise.

3.3.3. Valid Issuance. All shares of Common Stock issued upon the proper exercise of a Warrant in conformity with this Agreement shall be validly issued, fully paid and nonassessable.

3.3.4. Date of Issuance. Each person in whose name any book entry position or certificate for shares of Common Stock is issued shall for all purposes be deemed to have become the holder of record of such shares on the date on which the Warrant, or book entry position representing such Warrant, was surrendered and payment of the Warrant Price was made, irrespective of the date of delivery of such certificate, except that, if the date of such surrender and payment is a date when the stock transfer books of the Company or book entry system of the Warrant Agent are closed, such person shall be deemed to have become the holder of such shares at the close of business on the next succeeding date on which the stock transfer books or book entry system are open.

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3.3.5. Maximum Percentage. A holder of a Warrant may, by notification to the Company in writing, elect to be subject to a prohibition on exercises of Warrants by such holder that would result in such holder beneficially owning in excess of 9.8% (the “Maximum Percentage”) of the shares of Common Stock outstanding immediately after giving effect to such exercise. No holder of a Warrant shall be subject to this Section 3.3.5 unless he, she or it makes such election. If such election is made by a holder, the Warrant Agent shall not effect any exercise of such holder’s Warrant, and such holder shall not have the right to exercise any such Warrant, to the extent that after giving effect to such exercise, such holder (together with such holder’s affiliates), to the Warrant Agent’s actual knowledge, would beneficially own in excess of the Maximum Percentage of the shares of Common Stock outstanding immediately after giving effect to such exercise. For purposes of the foregoing sentences, the aggregate number of shares of Common Stock beneficially owned by such person and its affiliates shall include the number of shares of Common Stock issuable upon exercise of the Warrant with respect to which the determination of such sentence is being made, but shall exclude shares of Common Stock that would be issuable upon (x) exercise of the remaining, unexercised portion of the Warrant beneficially owned by such person and its affiliates and (y) exercise or conversion of the unexercised or unconverted portion of any other securities of the Company beneficially owned by such person and its affiliates (including, without limitation, any convertible notes or convertible preferred stock or warrants) subject to a limitation on conversion or exercise analogous to the limitation contained herein. Except as set forth in the preceding sentence, for purposes of this Section 3.3.5, beneficial ownership shall be calculated in accordance with Section 13(d) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”). For purposes of the Warrant, in determining the number of outstanding shares of Common Stock, the Warrant Agent may rely on the number of outstanding shares of Common Stock as reflected in (1) the Company’s most recent annual report on Form 10-K, quarterly report on Form 10-Q, current report on Form 8-K or other public filing with the SEC setting forth the number of outstanding shares of Common Stock, (2) a more recent written public announcement by the Company or (3) any other notice by the Company setting forth the number of shares of Common Stock outstanding. For any reason at any time, upon the written request of the holder of the Warrant, the Company shall, within two (2) Business Days, confirm orally and in writing to such holder the number of shares of Common Stock then outstanding. In any case, the number of outstanding shares of Common Stock used to determine the number of shares of Common Stock constituting the Maximum Percentage shall be determined after giving effect to the conversion or exercise of equity securities of the Company by the holder and its affiliates since the date as of which such number of outstanding shares of Common Stock was reported. By written notice to the Company, the holder of a Warrant may from time to time increase or decrease the Maximum Percentage applicable to such holder to any other percentage specified in such notice; provided, however, that any such increase shall not be effective until the sixty-first (61st) day after such notice is delivered to the Company.

4. Adjustments.

4.1. Stock Dividends—Split-Ups. If, after the date hereof, and subject to the provisions of Section 4.6 below, the number of outstanding shares of Common Stock is increased by a stock dividend payable in shares of Common Stock, or by a split-up of shares of Common Stock, or other similar event, then, on the effective date of such stock dividend, split-up or similar event, the number of shares of Common Stock issuable on exercise of each Warrant shall be increased in proportion to such increase in outstanding shares of Common Stock.

4.2. Aggregation of Shares. If, after the date hereof, and subject to the provisions of Section 4.6, the number of outstanding shares of Common Stock is decreased by a consolidation, combination, reverse stock split or reclassification of shares of Common Stock or other similar event, then, on the effective date of such consolidation, combination, reverse stock split, reclassification or similar event, the number of shares of Common Stock issuable on exercise of each Warrant shall be decreased in proportion to such decrease in outstanding shares of Common Stock.

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4.3. Extraordinary Dividends. If the Company, at any time while any Warrant is outstanding and unexpired, shall pay a dividend or make a distribution in cash, securities or other assets to the holders of the shares of Common Stock or other shares of the Company’s capital stock into which the Warrants are convertible (an “Extraordinary Dividend”), then the Warrant Price shall be decreased, effective immediately after the effective date of such Extraordinary Dividend, by the amount of cash and the fair market value (as determined by the Company’s Board of Directors, in good faith) of any securities or other assets paid in respect of such Extraordinary Dividend divided by all outstanding shares of Common Stock of the Company at such time (whether or not any shareholders waived their right to receive such dividend); provided, however, that none of the following shall be deemed an Extraordinary Dividend for purposes of this provision: (a) any adjustment described in Section 4.1 above, (b) any cash dividends or cash distributions which, when combined on a per share basis with all other cash dividends and cash distributions paid on the Common Stock during the 365-day period ending on the date of declaration of such dividend or distribution do not exceed $0.50 per share (taking into account all of the outstanding shares of Common Stock of the Company at such time (whether or not any shareholders waived their right to receive such dividend) and as adjusted to appropriately reflect any of the events referred to in other subsections of this Section 4 and excluding cash dividends or cash distributions that resulted in an adjustment to the Warrant Price or to the number of shares of Common Stock issuable on exercise of each Warrant) but only with respect to the amount of the aggregate cash dividends or cash distributions equal to or less than $0.50, (c) any payment to satisfy the conversion rights of the holders of the shares of Common Stock in connection with a proposed initial Business Combination or certain amendments to the Company’s Amended and Restated Certificate of Incorporation (as described in the Registration Statement) or (d) any payment in connection with the Company’s liquidation and the distribution of its assets upon its failure to consummate a Business Combination. Solely for purposes of illustration, if the Company, at a time while the Warrants are outstanding and unexpired, pays a cash dividend of $0.35 and previously paid an aggregate of $0.40 of cash dividends and cash distributions on the Common Stock during the 365-day period ending on the date of declaration of such $0.35 dividend, then the Warrant Price will be decreased, effectively immediately after the effective date of such $0.35 dividend, by $0.25 (the absolute value of the difference between $0.75 (the aggregate amount of all cash dividends and cash distributions paid or made in such 365-day period, including such $0.35 dividend) and $0.50 (the greater of (x) $0.50 and (y) the aggregate amount of all cash dividends and cash distributions paid or made in such 365-day period prior to such $0.35 dividend)). Furthermore, solely for the purposes of illustration, if following the closing of the Company’s initial Business Combination, there were total shares outstanding of 100,000,000 and the Company paid a $1.00 dividend to 17,500,000 of such shares (with the remaining 82,500,000 shares waiving their right to receive such dividend), then no adjustment to the Warrant Price would occur as a $17.5 million dividend payment divided by 100,000,000 shares equals $0.175 per share which is less than $0.50 per share.

4.4. Adjustments in Exercise Price. Whenever the number of shares of Common Stock purchasable upon the exercise of the Warrants is adjusted, as provided in Section 4.1 and Section 4.2 above, the Warrant Price shall be adjusted (to the nearest cent) by multiplying such Warrant Price immediately prior to such adjustment by a fraction (x) the numerator of which shall be the number of shares of Common Stock purchasable upon the exercise of the Warrants immediately prior to such adjustment, and (y) the denominator of which shall be the number of shares of Common Stock so purchasable immediately thereafter.

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4.5. Replacement of Securities upon Reorganization, etc. In case of any reclassification or reorganization of the outstanding shares of Common Stock (other than a change covered by Section 4.1 and Section 4.2 hereof or one that solely affects the par value of such shares of Common Stock), or, in the case of any merger or consolidation of the Company with or into another corporation (other than a consolidation or merger in which the Company is the continuing corporation and that does not result in any reclassification or reorganization of the outstanding shares of Common Stock), or, in the case of any sale or conveyance to another corporation or entity of the assets or other property of the Company as an entirety or substantially as an entirety, in connection with which the Company is dissolved, the Warrant holders shall thereafter have the right to purchase and receive, upon the basis and upon the terms and conditions specified in the Warrants and in lieu of the shares of Common Stock of the Company immediately theretofore purchasable and receivable upon the exercise of the rights represented thereby, the kind and amount of shares of stock or other securities or property (including cash) receivable upon such reclassification, reorganization, merger or consolidation, or upon a dissolution following any such sale or transfer, that the Warrant holder would have received if such Warrant holder had exercised his, her or its Warrant(s) immediately prior to such event; provided that if less than 70% of the consideration receivable by the holders of the Common Stock in the applicable event is payable in the form of common stock in the successor entity that is listed for trading on a national securities exchange or is quoted in an established over-the-counter market, or is to be so listed for trading or quoted immediately following such event, and if the registered holder properly exercises the Warrant within thirty (30) days following the public disclosure of the consummation of such applicable event by the Company pursuant to a Current Report on Form 8-K filed with the Commission, the Warrant Price shall be reduced by an amount (in dollars) equal to the difference between (i) the Warrant Price in effect prior to such reduction and (ii) the difference between (A) the Per Share Consideration (as defined below) and (B) the Black-Scholes Warrant Value (as defined below). The “Black-Scholes Warrant Value” means the value of a Warrant immediately prior to the consummation of the applicable event based on the Black-Scholes Warrant Model for a Capped American Call on Bloomberg Financial Markets (“Bloomberg”). For purposes of calculating such amount, (1) any adjustments pursuant to Section 6 of this Agreement shall accounted for, (2) the price of each share of Common Stock shall be the volume weighted average price of the Common Stock as reported during the ten (10) trading day period ending on the trading day prior to the effective date of the applicable event, (3) the assumed volatility shall be the 90-day volatility obtained from the HVT function on Bloomberg determined as of the trading day immediately prior to the day of the announcement of the applicable event, and (4) the assumed risk-free interest rate shall correspond to the U.S. Treasury rate for a period equal to the remaining term of the Warrant. “Per Share Consideration” means (a) if the consideration paid to holders of the Common Stock consists exclusively of cash, the amount of such cash per share of Common Stock, and (b) in all other cases, the amount of cash per share of Common Stock, if any, plus the volume weighted average price of the Common Stock as reported during the ten (10) trading day period ending on the trading day prior to the effective date of the applicable event. If any reclassification also results in a change in shares of Common Stock covered by Section 4.1 or Section 4.2, then such adjustment shall be made pursuant to Section 4.1, Section 4.2, Section 4.4 and this Section 4.5. The provisions of this Section 4.5 shall similarly apply to successive reclassifications, reorganizations, mergers or consolidations, sales or other transfers. In no event will the Warrant Price be reduced to less than the par value per share issuable upon exercise of the Warrant.

4.6. Issuance in Connection with a Business Combination. If, in connection with a Business Combination, (a) the Company issues, for capital-raising purposes, additional shares of Common Stock or equity-linked securities at an issue price or effective issue price of less than $9.20 per share (with such issue price or effective issue price as determined by the Company’s Board of Directors, in good faith, and in the case of any such issuance to Adit EdTech Sponsor, LLC, the initial stockholders, or their affiliates, without taking into account any founders’ shares held by them prior to such issuance) (such price, the “Newly Issued Price”), (b) the aggregate gross proceeds from such issuances represent more than 60% of the total equity proceeds, and interest thereon, available for the funding of the Business Combination on the date of the consummation of such Business Combination (net of redemptions), and (c) the Fair Market Value (as defined below) is below $9.20 per share, the exercise price of the warrants will be adjusted (to the nearest

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cent) to be equal to 115% of the greater of (i) the Fair Market Value or (ii) the price at which the Company issues the Common Stock or equity-linked securities and the Redemption Trigger Price (as defined below) shall be adjusted to be equal to 180% of the greater of the Fair Market Value and the Newly Issued Price. Solely for purposes of this Section 4.6, the “Fair Market Value” shall mean the volume weighted average reported trading price of the Common Stock for the ten (10) trading days starting on the trading day prior to the date of the consummation of the Business Combination.

4.7. Notices of Changes in Warrant. Upon every adjustment of the Warrant Price or the number of shares issuable upon exercise of a Warrant, the Company shall give written notice thereof to the Warrant Agent, which notice shall state the Warrant Price resulting from such adjustment and the increase or decrease, if any, in the number of shares purchasable at such price upon the exercise of a Warrant, setting forth in reasonable detail the method of calculation and the facts upon which such calculation is based. Upon the occurrence of any event specified in Section 4.1, Section 4.2, Section 4.3, Section 4.4, Section 4.5 or Section 4.6 then, in any such event, the Company shall give written notice to each Warrant holder, at the last address set forth for such holder in the Warrant Register, of the record date or the effective date of the event. Failure to give such notice, or any defect therein, shall not affect the legality or validity of such event.

4.8. No Fractional Shares. Notwithstanding any provision contained in this Agreement to the contrary, the Company shall not issue fractional shares upon exercise of Warrants. If, by reason of any adjustment made pursuant to this Section 4, the holder of any Warrant would be entitled, upon the exercise of such Warrant, to receive a fractional interest in a share, the Company shall, upon such exercise, round up to the nearest whole number of shares of Common Stock to be issued to the Warrant holder.

4.9. Form of Warrant. The form of Warrant need not be changed because of any adjustment pursuant to this Section 4, and Warrants issued after such adjustment may state the same Warrant Price and the same number of shares as is stated in the Warrants initially issued pursuant to this Agreement. However, the Company may, at any time, in its sole discretion, make any change in the form of Warrant that the Company may deem appropriate and that does not affect the substance thereof, and any Warrant thereafter issued or countersigned, whether in exchange or substitution for an outstanding Warrant or otherwise, may be in the form as so changed.

5. Transfer and Exchange of Warrants.

5.1. Registration of Transfer. The Warrant Agent shall register the transfer, from time to time, of any outstanding Warrant in the Warrant Register, upon surrender of such Warrant for transfer, in the case of certificated Warrants, properly endorsed with signatures properly medallion guaranteed and accompanied by appropriate instructions for transfer. Upon any such transfer, a new Warrant representing an equal aggregate number of Warrants shall be issued and the old Warrant shall be cancelled by the Warrant Agent. In the case of certificated Warrants, the Warrants so cancelled shall be delivered by the Warrant Agent to the Company from time to time upon request.

5.2. Procedure for Surrender of Warrants. Warrants may be surrendered to the Warrant Agent, either in certificated form or in book entry position, together with a written request for exchange or transfer, and thereupon the Warrant Agent shall issue in exchange therefor one or more new Warrants, or book entry positions, as requested by the registered holder of the Warrants so surrendered, representing an equal aggregate number of Warrants; provided, however, that in the event that a Warrant surrendered for transfer bears a restrictive legend, the Warrant Agent shall not cancel such Warrant and issue new Warrants in exchange therefor until the Warrant Agent has received an opinion of counsel for the Company stating that such transfer is exempt from registration under the Act and indicating whether the new Warrants must also bear a restrictive legend.

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5.3. Fractional Warrants. The Warrant Agent shall not be required to effect any registration of transfer or exchange which will result in the issuance of a Warrant certificate or book-entry position for a fraction of a Warrant.

5.4. Service Charges. No service charge shall be made for any exchange or registration of transfer of Warrants.

5.5. Warrant Execution and Countersignature. The Warrant Agent is hereby authorized to countersign and to deliver, in accordance with the terms of this Agreement, the Warrants required to be issued pursuant to the provisions of this Section 5, and the Company, whenever required by the Warrant Agent, will supply the Warrant Agent with Warrants duly executed on behalf of the Company for such purpose.

5.6. Private Warrants and Working Capital Warrants. The Warrant Agent shall not register any transfer of Private Warrants or Working Capital Warrants until after the consummation by the Company of an initial Business Combination, except for transfers (a) to the Company’s initial stockholders, officers or directors, any affiliates or family members of any of the Company’s initial stockholders, officers or directors, any members of the Company’s sponsor, or any affiliates of the sponsor; (b) in the case of an individual, by gift to a member of one of the members of the individual’s immediate family or to a trust, the beneficiary of which is a member of one of the individual’s immediate family, an affiliate of such person or to a charitable organization; (c) in the case of an individual, by virtue of laws of descent and distribution upon death of the individual; (d) in the case of an individual, pursuant to a qualified domestic relations order; (e) by private sales or transfers made in connection with the consummation of a Business Combination at prices no greater than the price at which the Private Warrants were originally purchased; (f) in the event of the Company’s liquidation prior to completion of an initial Business Combination; (g) by virtue of the laws of Delaware or Adit EdTech Sponsor, LLC’s limited liability company agreement upon dissolution of Adit EdTech Sponsor, LLC; or (h) in the event of the Company’s completion of a liquidation, merger, stock exchange or other similar transaction which results in all of the Company’s stockholders having the right to exchange their shares of common stock for cash, securities or other property subsequent to the Company’s completion of an initial Business Combination, in each case (except for clauses (f) through (h) or with the Company’s prior written consent) on the condition that prior to such registration for transfer, the Warrant Agent shall be presented with written documentation pursuant to which each transferee or the trustee or legal guardian for such transferee agrees to be bound by the transfer restrictions contained in this section and any other applicable agreement the transferor is bound by.

6. Redemption.

6.1. Redemption. Subject to Section 6.4 hereof, an amount of Public Warrants not less than all of the outstanding Public Warrants may be redeemed, at the option of the Company, at any time after they become exercisable and prior to their expiration, at the office of the Warrant Agent, upon the notice referred to in Section 6.2, (a) at the price of $0.01 per Warrant (the “Redemption Price”), provided that the last sales price of the Common Stock has been at least $18.00 per share (subject to adjustment in accordance with Section 4 hereof) (the “Redemption Trigger Price”), on each of twenty (20) trading days within any thirty (30) trading day period commencing after the Warrants become exercisable and ending on the third business day prior to the date on which notice of redemption is given and provided that there is an effective registration statement covering the shares of Common Stock issuable upon exercise of the Warrants, and a current prospectus relating thereto, available throughout the 30-day redemption period or (b) on a “cashless basis” pursuant to Section 3.3.1(b), at the Company’s election.

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6.2. Date Fixed for, and Notice of, Redemption. In the event the Company shall elect to redeem all of the Public Warrants that are subject to redemption, the Company shall fix a date for the redemption (the “Redemption Date”). Notice of redemption shall be mailed by first class mail, postage prepaid, by the Company not less than thirty (30) days prior to the Redemption Date to the registered holders of the Public Warrants to be redeemed at their last addresses as they shall appear in the Warrant Register. Any notice mailed in the manner herein provided shall be conclusively presumed to have been duly given whether or not the registered holder received such notice.

6.3. Exercise After Notice of Redemption. The Public Warrants may be exercised, for cash (or on a “cashless basis” in accordance with Section 3 of this Agreement) at any time after notice of redemption shall have been given by the Company pursuant to Section 6.2 hereof and prior to the Redemption Date. In the event the Company determines to require all holders of Public Warrants to exercise their Warrants on a “cashless basis” pursuant to Section 3.3.1(b), the notice of redemption will contain the information necessary to calculate the number of shares of Common Stock to be received upon exercise of the Warrants, including the “Fair Market Value” in such case. On and after the Redemption Date, the record holder of the Warrants shall have no further rights except to receive, upon surrender of the Warrants, the Redemption Price.

6.4. Exclusion of Certain Warrants. The Company agrees that the redemption rights provided in this Section 6 shall not apply to the Private Warrants and Working Capital Warrants if at the time of the redemption such Private Warrants or Working Capital Warrants continue to be held by the initial purchasers or their permitted transferees. However, once such Private Warrants or Working Capital Warrants are transferred (other than to permitted transferees under Section 5.6), the Company may redeem the Private Warrants and Working Capital Warrants in the same manner as the Public Warrants.

7. Other Provisions Relating to Rights of Holders of Warrants.

7.1. No Rights as Stockholder. A Warrant does not entitle the registered holder thereof to any of the rights of a stockholder of the Company, including, without limitation, the right to receive dividends, or other distributions, exercise any preemptive rights to vote or to consent or to receive notice as stockholders in respect of the meetings of stockholders or the election of directors of the Company or any other matter.

7.2. Lost, Stolen, Mutilated, or Destroyed Warrants. If any Warrant is lost, stolen, mutilated or destroyed, the Company and the Warrant Agent may, on such terms as to indemnity or otherwise as they may in their discretion impose (which terms shall, in the case of a mutilated Warrant, include the surrender thereof), issue a new Warrant of like denomination, tenor and date as the Warrant so lost, stolen, mutilated or destroyed. Any such new Warrant shall constitute a substitute contractual obligation of the Company, whether or not the allegedly lost, stolen, mutilated or destroyed Warrant shall be at any time enforceable by anyone.

7.3. Reservation of Common Stock. The Company shall at all times reserve and keep available a number of its authorized but unissued shares of Common Stock that will be sufficient to permit the exercise in full of all outstanding Warrants issued pursuant to this Agreement.

7.4. Registration of Common Stock. The Company agrees that prior to the commencement of the Exercise Period, it shall use its best efforts to file with the Securities and Exchange Commission a post-effective amendment to the Registration Statement, or a new registration statement, for the registration under the Act of the Common Stock issuable upon exercise of the Warrants, and it shall take such action as is necessary to qualify for sale, in those states in which the Warrants were initially offered by the Company, the Common Stock issuable upon exercise of the Warrants. In either case, the Company will use its best efforts to cause the same to become effective and to maintain the effectiveness of such registration statement until the expiration of the Warrants in accordance with the provisions of this Agreement. In no event will the registered holder of a Warrant be entitled to receive a “net cash settlement” in lieu of physical settlement in shares of Common Stock, regardless of whether the Company complies with this Section 7.4.

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7.5. Limitation on Monetary Damages. In no event shall the registered holder of a Warrant be entitled to receive monetary damages for failure to settle any Warrant exercise if the Common Stock issuable upon exercise of the Warrants has not been registered with the Securities and Exchange Commission pursuant to an effective registration statement or if a current prospectus is not available for delivery by the Warrant Agent, provided the Company has fulfilled its obligations under Section 7.4 to use its best efforts to effect the registration under the Act of the Common Stock issuable upon exercise of the Warrants.

8. Concerning the Warrant Agent and Other Matters.

8.1. Payment of Taxes. The Company will from time to time promptly pay all taxes and charges that may be imposed upon the Company or the Warrant Agent in respect of the issuance or delivery of shares of Common Stock upon the exercise of Warrants, but the Company shall not be obligated to pay any transfer taxes in respect of the Warrants or such shares.

8.2. Resignation, Consolidation, or Merger of Warrant Agent.

8.2.1. Appointment of Successor Warrant Agent. The Warrant Agent, or any successor to it hereafter appointed, may resign its duties and be discharged from all further duties and liabilities hereunder after giving sixty (60) days’ notice in writing to the Company. If the office of the Warrant Agent becomes vacant by resignation or incapacity to act or otherwise, the Company shall appoint in writing a successor Warrant Agent in place of the Warrant Agent. If the Company shall fail to make such appointment within a period of thirty (30) days after it has been notified in writing of such resignation or incapacity by the Warrant Agent or by the holder of the Warrant (who shall, with such notice, submit his, her or its Warrant for inspection by the Company), then the holder of any Warrant may apply to the Supreme Court of the State of New York for the County of New York for the appointment of a successor Warrant Agent at the Company’s cost. Any successor Warrant Agent, whether appointed by the Company or by such court, shall be a corporation organized and existing under the laws of the State of New York, in good standing and having its principal office in the Borough of Manhattan, City and State of New York, and authorized under such laws to exercise corporate trust powers and subject to supervision or examination by federal or state authority. After appointment, any successor Warrant Agent shall be vested with all the authority, powers, rights, immunities, duties, and obligations of its predecessor Warrant Agent with like effect as if originally named as Warrant Agent hereunder, without any further act or deed; but if for any reason it becomes necessary or appropriate, the predecessor Warrant Agent shall execute and deliver, at the expense of the Company, an instrument transferring to such successor Warrant Agent all the authority, powers, and rights of such predecessor Warrant Agent hereunder; and upon request of any successor Warrant Agent the Company shall make, execute, acknowledge, and deliver any and all instruments in writing for more fully and effectually vesting in and confirming to such successor Warrant Agent all such authority, powers, rights, immunities, duties, and obligations.

8.2.2. Notice of Successor Warrant Agent. In the event a successor Warrant Agent shall be appointed, the Company shall give notice thereof to the predecessor Warrant Agent and the transfer agent for the Common Stock not later than the effective date of any such appointment.

8.2.3. Merger or Consolidation of Warrant Agent. Any corporation into which the Warrant Agent may be merged or with which it may be consolidated or any corporation resulting from any merger or consolidation to which the Warrant Agent shall be a party shall be the successor Warrant Agent under this Agreement without any further act.

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8.3. Fees and Expenses of Warrant Agent.

8.3.1. Remuneration. The Company agrees to pay the Warrant Agent reasonable remuneration for its services as such Warrant Agent hereunder and will reimburse the Warrant Agent upon demand for all expenditures that the Warrant Agent may reasonably incur in the execution of its duties hereunder.

8.3.2. Further Assurances. The Company agrees to perform, execute, acknowledge and deliver or cause to be performed, executed, acknowledged and delivered all such further and other acts, instruments and assurances as may reasonably be required by the Warrant Agent for the carrying out or performing of the provisions of this Agreement.

8.4. Liability of Warrant Agent.

8.4.1. Reliance on Company Statement. Whenever in the performance of its duties under this Agreement the Warrant Agent shall deem it necessary or desirable that any fact or matter be proved or established by the Company prior to taking or suffering any action hereunder, such fact or matter (unless other evidence in respect thereof be herein specifically prescribed) may be deemed to be conclusively proved and established by a statement signed by the President or Chairman of the Board of the Company and delivered to the Warrant Agent. The Warrant Agent may rely upon such statement for any action taken or suffered in good faith by it pursuant to the provisions of this Agreement.

8.4.2. Indemnity. The Warrant Agent shall be liable hereunder only for its own gross negligence, willful misconduct or bad faith. The Company agrees to indemnify the Warrant Agent and save it harmless against any and all liabilities, including judgments, costs and reasonable counsel fees, for anything done or omitted by the Warrant Agent in the execution of this Agreement, except as a result of the Warrant Agent’s gross negligence, willful misconduct or bad faith.

8.4.3. Exclusions. The Warrant Agent shall have no responsibility with respect to the validity of this Agreement or with respect to the validity or execution of any Warrant (except its countersignature thereof); nor shall it be responsible for any breach by the Company of any covenant or condition contained in this Agreement or in any Warrant; nor shall it be responsible to make any adjustments required under the provisions of Section 4 hereof or responsible for the manner, method or amount of any such adjustment or the ascertaining of the existence of facts that would require any such adjustment; nor shall it by any act hereunder be deemed to make any representation or warranty as to the authorization or reservation of any shares of Common Stock to be issued pursuant to this Agreement or any Warrant or as to whether any shares of Common Stock will when issued be valid and fully paid and nonassessable.

8.5. Acceptance of Agency. The Warrant Agent hereby accepts the agency established by this Agreement and agrees to perform the same upon the terms and conditions herein set forth and, among other things, shall account promptly to the Company with respect to Warrants exercised and concurrently account for, and pay to the Company, all moneys received by the Warrant Agent for the purchase of shares of Common Stock through the exercise of Warrants.

9. Miscellaneous Provisions.

9.1. Successors. All the covenants and provisions of this Agreement by or for the benefit of the Company or the Warrant Agent shall bind and inure to the benefit of their respective successors and assigns.

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9.2. Notices. Any notice, statement or demand authorized by this Agreement to be given or made by the Warrant Agent or by the holder of any Warrant to or on the Company shall be delivered by hand or sent by registered or certified mail or overnight courier service, addressed (until another address is filed in writing by the Company with the Warrant Agent) as follows:

Adit EdTech Acquisition Corp.

1345 Avenue of the Americas, 33^rd Floor

New York, NY 10105

Attn: David L. Shrier, Chief Executive Officer

with a copy (which shall not constitute notice) to:

Troutman Pepper Hamilton Sanders LLP

875 Third Avenue

New York, NY 10022

Attn: Patrick B. Costello, Esq.

Any notice, statement or demand authorized by this Agreement to be given or made by the holder of any Warrant or by the Company to or on the Warrant Agent shall be delivered by hand or sent by registered or certified mail or overnight courier service, addressed (until another address is filed in writing by the Company with the Warrant Agent) as follows:

Continental Stock Transfer & Trust Company

1 State Street, 30 FL

New York, New York 10004

Attn: Compliance Department

Any notice, sent pursuant to this Agreement shall be effective, if delivered by hand, upon receipt thereof by the party to whom it is addressed, if sent by overnight courier, on the next business day of the delivery to the courier, and if sent by registered or certified mail on the third day after registration or certification thereof.

9.3. Applicable Law. The validity, interpretation and performance of this Agreement and of the Warrants shall be governed in all respects by the laws of the State of New York, without giving effect to conflicts of law principles that would result in the application of the substantive laws of another jurisdiction. The Company hereby agrees that any action, proceeding or claim against it arising out of or relating in any way to this Agreement shall be brought and enforced in the courts of the State of New York or the United States District Court for the Southern District of New York, and irrevocably submits to such jurisdiction. The Company hereby waives any objection that such courts represent an inconvenient forum. Any such process or summons to be served upon the Company may be served by transmitting a copy thereof by registered or certified mail, return receipt requested, postage prepaid, addressed to it at the address set forth in Section 9.2 hereof. Such mailing shall be deemed personal service and shall be legal and binding upon the Company in any action, proceeding or claim. The foregoing shall not apply to any claims brought under the Act or the Exchange Act.

9.4. Persons Having Rights under this Agreement. Nothing in this Agreement expressed and nothing that may be implied from any of the provisions hereof is intended, or shall be construed, to confer upon, or give to, any person or corporation other than the parties hereto and the registered holders of the Warrants, any right, remedy, or claim under or by reason of this Agreement or of any covenant, condition, stipulation, promise, or agreement hereof. All covenants, conditions, stipulations, promises, and agreements contained in this Agreement shall be for the sole and exclusive benefit of the parties hereto and their successors and assigns and of the registered holders of the Warrants.

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9.5. Examination of the Agreement. A copy of this Agreement shall be available at all reasonable times at the office of the Warrant Agent in the Borough of Manhattan, City and State of New York, for inspection by the registered holder of any Warrant. The Warrant Agent may require any such holder to submit his, her or its Warrant for inspection by it.

9.6. Counterparts. This Agreement may be executed in any number of original or facsimile counterparts and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument.

9.7. Effect of Headings. The section headings herein are for convenience only and are not part of this Agreement and shall not affect the interpretation thereof.

9.8. Amendments. This Agreement may be amended by the parties hereto without the consent of any registered holder for the purpose of curing any ambiguity, or curing, correcting or supplementing any defective provision contained herein or adding or changing any other provisions with respect to matters or questions arising under this Agreement as the parties may deem necessary or desirable and that the parties deem shall not adversely affect the interest of the registered holders. All other modifications or amendments, including any amendment to increase the Warrant Price or shorten the Exercise Period, shall require the written consent of the registered holders of a majority of the then outstanding Public Warrants. Notwithstanding the foregoing, the Company may lower the Warrant Price or extend the duration of the Exercise Period pursuant to Section 3.1 and Section 3.2, respectively, without the consent of the registered holders.

9.9. Severability. Whenever possible, each provision of this Agreement shall be interpreted in such manner as to be effective and valid under applicable law, but if any provision of this Agreement is held to be prohibited by or invalid under applicable law, such provision shall be ineffective only to the extent of such prohibition or invalidity, without invalidating the remainder of this Agreement.

[Remainder of Page Intentionally Left Blank; Signature Page Follows]

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IN WITNESS WHEREOF, this Agreement has been duly executed by the parties hereto as of the day and year first above written.

[Signature Page to Warrant Agreement]

EXHIBIT A

FORM OF WARRANT CERTIFICATE

[FACE]

Number

Warrants