Document:

EX-10.4

 Exhibit 10.4 

REGISTRATION RIGHTS AGREEMENT 

THIS REGISTRATION RIGHTS AGREEMENT (this “Agreement”) is entered into as of the 11th day of January, 2021, by and
among Adit EdTech Acquisition Corp., a Delaware corporation (the “Company”), and the undersigned parties listed under Investors on the signature page hereto (each, an “Investor” and collectively,
the “Investors”). 
 WHEREAS, the Investors and the Company desire to enter into this Agreement to provide
the Investors with certain rights relating to the registration of the securities held by them as of the date hereof. 
 NOW,
THEREFORE, in consideration of the mutual covenants and agreements set forth herein, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree as follows: 

1. DEFINITIONS. The following capitalized terms used herein have the following meanings: 

“Agreement” is defined in the Preamble to this Agreement. 

“Business Combination” means the acquisition of direct or indirect ownership through a merger, stock exchange, asset
acquisition, stock purchase, recapitalization, reorganization or other similar type of transaction, of one or more businesses or entities. 

“Commission” means the Securities and Exchange Commission, or any other Federal agency then administering the
Securities Act or the Exchange Act. 
 “Common Stock” means the common stock, par value $0.0001 per share, of
the Company. 
 “Company” is defined in the preamble to this Agreement. 

“Demand Registration” is defined in Section 2.1.1. 

“Demanding Holder” is defined in Section 2.1.1. 

“Exchange Act” means the Securities Exchange Act of 1934, as amended, and the rules and regulations of the Commission
promulgated thereunder, all as the same shall be in effect at the time. 
 “Form
S-3” is defined in Section 2.3. 
 “Founder
Shares” means the 6,900,000 shares of Common Stock of the Company issued to its sponsor prior to the Company’s initial public offering. 

“Indemnified Party” is defined in Section 4.3. 

“Indemnifying Party” is defined in Section 4.3. 

“Investor” is defined in the preamble to this Agreement. 

“Investor Indemnified Party” is defined in Section 4.1. 

“Maximum Number of Shares” is defined in Section 2.1.4. 

“Notices” is defined in Section 6.3. 

 “Piggy-Back Registration” is defined in
Section 2.2.1. 
 “Private Warrants” means the Warrants certain of the Investors are
privately purchasing simultaneously with the consummation of the Company’s initial public offering. 
 “Pro
Rata” is defined in Section 2.1.4. 
 “Register,”
“Registered” and “Registration” mean a registration effected by preparing and filing a registration statement or similar document in compliance with the requirements of the Securities Act, and the
applicable rules and regulations promulgated thereunder, and such registration statement becoming effective. 
 “Registrable
Securities” means (i) the Founder Shares, (ii) the Private Warrants, if any (including any securities issued or issuable upon the exercise of any such Private Warrants) and (iii) the Working Capital Warrants, if any
(including any securities issued or issuable upon the exercise of any such Private Warrants). Registrable Securities include any warrants, shares of capital stock or other securities of the Company issued as a dividend or other distribution with
respect to or in exchange for or in replacement of such Founder Shares, Private Warrants (including any securities issued or issuable upon the exercise of any such Private Warrants) and Working Capital Warrants (including any securities issued or
issuable upon the exercise of any such Private Warrants). As to any particular Registrable Securities, such securities shall cease to be Registrable Securities when: (a) a Registration Statement with respect to the sale of such securities shall
have become effective under the Securities Act and such securities shall have been sold, transferred, disposed of or exchanged in accordance with such Registration Statement; (b) such securities shall have been otherwise transferred, new
certificates for them not bearing a legend restricting further transfer shall have been delivered by the Company, and subsequent public distribution of them shall not require registration under the Securities Act; (c) such securities shall have
ceased to be outstanding, or (d) the Registrable Securities are freely saleable under Rule 144 under the Securities Act without limitation on the amount of securities sold or the manner of sale and without compliance with the current public
reporting requirements set forth under Rule 144(i)(2). 
 “Registration Statement” means a registration statement
filed by the Company with the Commission in compliance with the Securities Act and the rules and regulations promulgated thereunder for a public offering and sale of equity securities, or securities or other obligations exercisable or exchangeable
for, or convertible into, equity securities (other than a registration statement on Form S-4 or Form S-8, or their successors, or any registration statement covering
only securities proposed to be issued in exchange for securities or assets of another entity). 
 “Release Date”
means the date on which the Founder Shares are no longer subject to the transfer restrictions as set forth in Section 5 of that certain Letter Agreement, dated as of January 11, 2021, by and among the Company and the holders of Founder
Shares. 
 “Representative” means EarlyBirdCapital, Inc. 

“Securities Act” means the Securities Act of 1933, as amended, and the rules and regulations of the Commission
promulgated thereunder, all as the same shall be in effect at the time. 
 “Underwriter” means a securities dealer
who purchases any Registrable Securities as principal in an underwritten offering and not as part of such dealer’s market-making activities. 

“Units” means the units of the Company, each comprised of one share of Common Stock and
one-half of one Warrant, each whole Warrant entitling the holder to purchase one share of Common Stock. 

  
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 “Warrants” means the warrants of the Company with each whole warrant
entitling the holder to purchase one share of Common Stock. 
 “Working Capital Warrants” means any Warrants held by
Investors or certain of the Company’s initial stockholders, officers, directors, industry advisors or any of their respective affiliates which may be issued upon conversion of working capital loans made to the Company. 

2. REGISTRATION RIGHTS. 
 2.1
Demand Registration. 
 2.1.1 Request for Registration. At any time and from time to time on or after (i) the date that
the Company consummates a Business Combination with respect to the Private Warrants and Working Capital Warrants, or (ii) three (3) months prior to the Release Date with respect to all other Registrable Securities, the holders of a majority-in-interest of such Founder Shares, Private Warrants (or underlying securities), Working Capital Warrants (or underlying securities) or other Registrable Securities,
as the case may be, held by the Investors, officers or directors of the Company or their affiliates, or the transferees of the Investors may make a written demand for registration under the Securities Act of all or part of their Founder Shares,
Private Warrants, Working Capital Warrants or other Registrable Securities, as the case may be (a “Demand Registration”). Any demand for a Demand Registration shall specify the number of shares of Registrable Securities
proposed to be sold and the intended method(s) of distribution thereof. The Company will notify all holders of Registrable Securities of the demand, and each holder of Registrable Securities who wishes to include all or a portion of such
holder’s Registrable Securities in the Demand Registration (each such holder including shares of Registrable Securities in such registration, a “Demanding Holder”) shall so notify the
Company within fifteen (15) days after the receipt by the holder of the notice from the Company. Upon any such request, the Demanding Holders shall be entitled to have their Registrable Securities included in the Demand Registration, subject to
Section 2.1.4 and the provisos set forth in Section 3.1.1. The Company shall not be obligated to effect more than an aggregate of three (3) Demand Registrations under this
Section 2.1.1 in respect of all Registrable Securities. 
 2.1.2 Effective Registration. A registration will
not count as a Demand Registration until the Registration Statement filed with the Commission with respect to such Demand Registration has been declared effective and the Company has complied with all of its obligations under this Agreement with
respect thereto; provided, however, that if, after such Registration Statement has been declared effective, the offering of Registrable Securities pursuant to a Demand Registration is interfered with by any stop order or injunction of
the Commission or any other governmental agency or court, the Registration Statement with respect to such Demand Registration will be deemed not to have been declared effective, unless and until, (i) such stop order or injunction is removed,
rescinded or otherwise terminated, and (ii) a majority-in-interest of the Demanding Holders thereafter elect to continue the offering; provided,
further, that the Company shall not be obligated to file a second Registration Statement until a Registration Statement that has been filed is counted as a Demand Registration or is terminated. 

2.1.3 Underwritten Offering. If a majority-in-interest
of the Demanding Holders so elect and such holders so advise the Company as part of their written demand for a Demand Registration, the offering of such Registrable Securities pursuant to such Demand Registration shall be in the form of an
underwritten offering. In such event, the right of any holder to include its Registrable Securities in such registration shall be conditioned upon such holder’s participation in such underwriting and the inclusion of such holder’s
Registrable Securities in the underwriting to the extent provided herein. All Demanding Holders proposing to distribute their Registrable Securities through such underwriting shall enter into an underwriting agreement in customary form with the
Underwriter or Underwriters selected for such underwriting by a majority-in-interest of the holders initiating the Demand Registration. 

  
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 2.1.4 Reduction of Offering. If the managing Underwriter or Underwriters for a Demand
Registration that is to be an underwritten offering advises the Company and the Demanding Holders in writing that the dollar amount or number of shares of Registrable Securities which the Demanding Holders desire to sell, taken together with all
other shares of Common Stock or other securities which the Company desires to sell and the shares of Common Stock, if any, as to which registration has been requested pursuant to written contractual piggy-back registration rights held by other
stockholders of the Company who desire to sell, exceeds the maximum dollar amount or maximum number of shares that can be sold in such offering without adversely affecting the proposed offering price, the timing, the distribution method, or the
probability of success of such offering (such maximum dollar amount or maximum number of shares, as applicable, the “Maximum Number of Shares”), then the Company shall include in such registration: (i) first, the
Registrable Securities as to which Demand Registration has been requested by the Demanding Holders (pro rata in accordance with the number of shares that each such person has requested be included in such registration, regardless of the number of
shares held by each such person (such proportion is referred to herein as “Pro Rata”)) that can be sold without exceeding the Maximum Number of Shares, (ii) second, to the extent that the Maximum Number of Shares has not
been reached under the foregoing clause (i), the shares of Common Stock or other securities that the Company desires to sell that can be sold without exceeding the Maximum Number of Shares, (iii) third, to the extent that the Maximum Number of
Shares has not been reached under the foregoing clauses (i) and (ii), the shares of Common Stock or other securities for the account of other persons that the Company is obligated to register pursuant to written contractual arrangements with
such persons and that can be sold without exceeding the Maximum Number of Shares. 
 2.1.5 Withdrawal. If a majority-in-interest of the Demanding Holders disapprove of the terms of any underwriting or are not entitled to include all of their Registrable Securities in any offering,
such majority-in-interest of the Demanding Holders may elect to withdraw from such offering by giving written notice to the Company and the Underwriter or Underwriters
of their request to withdraw prior to the effectiveness of the Registration Statement filed with the Commission with respect to such Demand Registration. If the
majority-in-interest of the Demanding Holders withdraws from a proposed offering relating to a Demand Registration, then such registration shall not count as a Demand
Registration provided for in Section 2.1. 
 2.2 Piggy-Back Registration. 

2.2.1 Piggy-Back Rights. If at any time on or after the date the Company consummates a Business Combination the Company proposes to file
a Registration Statement under the Securities Act with respect to an offering of equity securities, or securities or other obligations exercisable or exchangeable for, or convertible into, equity securities, by the Company for its own account or for
stockholders of the Company for their account (or by the Company and by stockholders of the Company including, without limitation, pursuant to Section 2.1), other than a Registration Statement (i) filed in connection
with any employee stock option or other benefit plan, (ii) for an exchange offer or offering of securities solely to the Company’s existing stockholders, (iii) for an offering of debt that is convertible into equity securities of the
Company, or (iv) for a dividend reinvestment plan, then the Company shall (x) give written notice of such proposed filing to the holders of Registrable Securities as soon as practicable but in no event less than ten (10) days before
the anticipated filing date, which notice shall describe the amount and type of securities to be included in such offering, the intended method(s) of distribution, and the name of the proposed managing Underwriter or Underwriters, if any, of the
offering, and (y) offer to the holders of Registrable Securities in such notice the opportunity to register the sale of such number of shares of Registrable Securities as such holders may request in writing within five (5) days following
receipt of such notice (a “Piggy-Back Registration”). The Company shall cause such Registrable Securities to be included in such registration and shall use its best efforts to cause the managing Underwriter or Underwriters of
a proposed underwritten offering to permit the Registrable Securities requested to be included in a Piggy-Back Registration on the 

  
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same terms and conditions as any similar securities of the Company and to permit the sale or other disposition of such Registrable Securities in accordance with the intended method(s) of
distribution thereof. All holders of Registrable Securities proposing to distribute their securities through a Piggy-Back Registration that involves an Underwriter or Underwriters shall enter into an underwriting agreement in customary form with the
Underwriter or Underwriters selected for such Piggy-Back Registration. 
 2.2.2 Reduction of Offering. If the managing Underwriter or
Underwriters for a Piggy-Back Registration that is to be an underwritten offering advises the Company and the holders of Registrable Securities in writing that the dollar amount or number of shares of Common Stock which the Company desires to sell,
taken together with shares of Common Stock, if any, as to which registration has been demanded pursuant to separate written contractual arrangements with persons or entities other than the holders of Registrable Securities hereunder, the Registrable
Securities as to which registration has been requested under this Section 2.2, and the shares of Common Stock, if any, as to which registration has been requested pursuant to the written contractual piggy-back registration
rights of other stockholders of the Company, exceeds the Maximum Number of Shares, then the Company shall include in any such registration: 

(a) If the registration is undertaken for the Company’s account: (A) the shares of Common Stock or other securities
that the Company desires to sell that can be sold without exceeding the Maximum Number of Shares, (B) to the extent that the Maximum Number of Shares has not been reached under the foregoing clause (A), the shares of Common Stock or other
securities, if any, comprised of Registrable Securities, as to which registration has been requested pursuant to the applicable written contractual piggy-back registration rights of such security holders, Pro Rata, that can be sold without exceeding
the Maximum Number of Shares, and (C) to the extent that the Maximum Number of Shares has not been reached under the foregoing clauses (A) and (B), the shares of Common Stock or other securities for the account of other persons that the
Company is obligated to register pursuant to written contractual piggy-back registration rights with such persons and that can be sold without exceeding the Maximum Number of Shares; and 

(b) If the registration is a “demand” registration undertaken at the demand of persons other than the holders of
Registrable Securities, (A) first, the shares of Common Stock or other securities for the account of the demanding persons that can be sold without exceeding the Maximum Number of Shares, (B) second, to the extent that the Maximum Number
of Shares has not been reached under the foregoing clause (A), the shares of Common Stock or other securities that the Company desires to sell that can be sold without exceeding the Maximum Number of Shares, (C) third, to the extent that the
Maximum Number of Shares has not been reached under the foregoing clauses (A) and (B), collectively, the shares of Common Stock or other securities comprised of Registrable Securities, Pro Rata, as to which registration has been requested
pursuant to the terms hereof, that can be sold without exceeding the Maximum Number of Shares, and (D) fourth, to the extent that the Maximum Number of Shares has not been reached under the foregoing clauses (A), (B) and (C), the shares of
Common Stock or other securities for the account of other persons that the Company is obligated to register pursuant to written contractual arrangements with such persons, that can be sold without exceeding the Maximum Number of Shares. 

2.2.3 Withdrawal. Any holder of Registrable Securities may elect to withdraw such holder’s request for inclusion of Registrable
Securities in any Piggy-Back Registration by giving written notice to the Company of such request to withdraw prior to the effectiveness of the Registration Statement. The Company (whether on its own determination or as the result of a withdrawal by
persons making a demand pursuant to written contractual obligations) may withdraw a Registration Statement at any time prior to the effectiveness of such Registration Statement. Notwithstanding any such withdrawal, the Company shall pay all expenses
incurred by the holders of Registrable Securities in connection with such Piggy-Back Registration as provided in Section 3.3. 

  
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 2.2.4 Unlimited Piggyback Registration Rights. For purposes of clarity, any
Registration effected pursuant to Section 2.2 shall not be counted as a Registration pursuant to a Demand Registration effected under Section 2.1. 

2.3 Registrations on Form S-3. The holders of Registrable Securities may at any time, and from
time to time, request in writing that the Company, pursuant to Rule 415 under the Securities Act (or any successor rule promulgated thereafter by the Commission), register the resale of any or all of such Registrable Securities on Form S-3 or any similar short-form registration which may be available at such time (“Form S-3”); provided, however, that the Company shall
not be obligated to effect such request through an underwritten offering. Upon receipt of such written request, the Company will promptly give written notice of the proposed registration to all other holders of Registrable Securities, and, as soon
as practicable thereafter, effect the registration of all or such portion of such holder’s or holders’ Registrable Securities as are specified in such request, together with all or such portion of the Registrable Securities or other
securities of the Company, if any, of any other holder or holders joining in such request as are specified in a written request given within fifteen (15) days after receipt of such written notice from the Company; provided,
however, that the Company shall not be obligated to effect any such registration pursuant to this Section 2.3: (i) if Form S-3 is not available for such offering, or
(ii) if the holders of the Registrable Securities, together with the holders of any other securities of the Company entitled to inclusion in such registration, propose to sell Registrable Securities and such other securities (if any) at any
aggregate price to the public of less than $500,000. Registrations effected pursuant to this Section 2.3 shall not be counted as Registration pursuant to Demand Registrations effected pursuant to
Section 2.1. 
 3. REGISTRATION PROCEDURES. 

3.1 Filings; Information. Whenever the Company is required to effect the registration of any Registrable Securities pursuant to
Article 2, the Company shall use its best efforts to effect the registration and sale of such Registrable Securities in accordance with the intended method(s) of distribution thereof as expeditiously as practicable, and in
connection with any such request: 
 3.1.1 Filing Registration Statement. The Company shall use its best efforts to, as expeditiously
as possible after receipt of a request for a Demand Registration pursuant to Section 2.1, prepare and file with the Commission a Registration Statement on any form for which the Company then qualifies or which counsel for
the Company shall deem appropriate and which form shall be available for the sale of all Registrable Securities to be registered thereunder in accordance with the intended method(s) of distribution thereof, and shall use its best efforts to cause
such Registration Statement to become effective and use its best efforts to keep it effective for the period required by Section 3.1.3; provided, however, that the Company shall have the right to defer any
Demand Registration for up to thirty (30) days, and any Piggy-Back Registration for such period as may be applicable to deferment of any demand registration to which such Piggy-Back Registration relates, in each case if the Company shall
furnish to the holders a certificate signed by the President or Chairman of the Company stating that, in the good faith judgment of the Board of Directors of the Company, it would be materially detrimental to the Company and its stockholders for
such Registration Statement to be effected at such time; provided, further, however, that the Company shall not have the right to exercise the right set forth in the immediately preceding proviso more than once in any 365-day period in respect of a Demand Registration hereunder. 

  
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 3.1.2 Copies. The Company shall, prior to filing a Registration Statement or
prospectus, or any amendment or supplement thereto, furnish without charge to the holders of Registrable Securities included in such registration, and such holders’ legal counsel, copies of such Registration Statement as proposed to be filed,
each amendment and supplement to such Registration Statement (in each case including all exhibits thereto and documents incorporated by reference therein), the prospectus included in such Registration Statement (including each preliminary
prospectus), and such other documents as the holders of Registrable Securities included in such registration or legal counsel for any such holders may request in order to facilitate the disposition of the Registrable Securities owned by such
holders. 
 3.1.3 Amendments and Supplements. The Company shall prepare and file with the Commission such amendments, including
post-effective amendments, and supplements to such Registration Statement and the prospectus used in connection therewith as may be necessary to keep such Registration Statement effective and in compliance with the provisions of the Securities Act
until all Registrable Securities and other securities covered by such Registration Statement have been disposed of in accordance with the intended method(s) of distribution set forth in such Registration Statement or such securities have been
withdrawn. 
 3.1.4 Notification. After the filing of a Registration Statement, the Company shall promptly, and in no event more than
two (2) business days after such filing, notify the holders of Registrable Securities included in such Registration Statement of such filing, and shall further notify such holders promptly and confirm such advice in writing in all events within
two (2) business days of the occurrence of any of the following: (i) when such Registration Statement becomes effective, (ii) when any post-effective amendment to such Registration Statement becomes effective, (iii) the issuance
or threatened issuance by the Commission of any stop order (and the Company shall take all actions required to prevent the entry of such stop order or to remove it if entered), and (iv) any request by the Commission for any amendment or
supplement to such Registration Statement or any prospectus relating thereto or for additional information or of the occurrence of an event requiring the preparation of a supplement or amendment to such prospectus so that, as thereafter delivered to
the purchasers of the securities covered by such Registration Statement, such prospectus will not contain an untrue statement of a material fact or omit to state any material fact required to be stated therein or necessary to make the statements
therein not misleading, and promptly make available to the holders of Registrable Securities included in such Registration Statement any such supplement or amendment; except that before filing with the Commission a Registration Statement or
prospectus or any amendment or supplement thereto, including documents incorporated by reference, the Company shall furnish to the holders of Registrable Securities included in such Registration Statement and to the legal counsel for any such
holders, copies of all such documents proposed to be filed sufficiently in advance of filing to provide such holders and legal counsel with a reasonable opportunity to review such documents and comment thereon, and the Company shall not file any
Registration Statement or prospectus or amendment or supplement thereto, including documents incorporated by reference, to which such holders or their legal counsel shall object. 

3.1.5 State Securities Laws Compliance. The Company shall use its best efforts to (i) register or qualify the Registrable
Securities covered by the Registration Statement under such securities or “blue sky” laws of such jurisdictions in the United States as the holders of Registrable Securities included in such Registration Statement (in light of their
intended plan of distribution) may request and (ii) take such action necessary to cause such Registrable Securities covered by the Registration Statement to be registered with or approved by such other governmental authorities as may be
necessary by virtue of the business and operations of the Company and do any and all other acts and things that may be necessary or advisable to enable the holders of Registrable Securities included in such Registration Statement to consummate the
disposition of such Registrable Securities in such jurisdictions; provided, however, that the Company shall not be required to qualify generally to do business in any jurisdiction where it would not otherwise be required to qualify but
for this paragraph or subject itself to taxation in any such jurisdiction. 
  

  
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 3.1.6 Agreements for Disposition. The Company shall enter into customary agreements
(including, if applicable, an underwriting agreement in customary form) and take such other actions as are reasonably required in order to expedite or facilitate the disposition of such Registrable Securities. The representations, warranties and
covenants of the Company in any underwriting agreement which are made to or for the benefit of any Underwriters, to the extent applicable, shall also be made to and for the benefit of the holders of Registrable Securities included in such
registration statement. No holder of Registrable Securities included in such registration statement shall be required to make any representations or warranties in the underwriting agreement except, if applicable, with respect to such holder’s
organization, good standing, authority, title to Registrable Securities, lack of conflict of such sale with such holder’s material agreements and organizational documents, and with respect to written information relating to such holder that
such holder has furnished in writing expressly for inclusion in such Registration Statement. 
 3.1.7 Cooperation. The principal
executive officer of the Company, the principal financial officer of the Company, the principal accounting officer of the Company and all other officers and members of the management of the Company shall cooperate fully in any offering of
Registrable Securities hereunder, which cooperation shall include, without limitation, the preparation of the Registration Statement with respect to such offering and all other offering materials and related documents, and participation in meetings
with Underwriters, attorneys, accountants and potential investors. 
 3.1.8 Records. The Company shall make available for inspection
by the holders of Registrable Securities included in such Registration Statement, any Underwriter participating in any disposition pursuant to such registration statement and any attorney, accountant or other professional retained by any holder of
Registrable Securities included in such Registration Statement or any Underwriter, all financial and other records, pertinent corporate documents and properties of the Company, as shall be necessary to enable them to exercise their due diligence
responsibility, and cause the Company’s officers, directors and employees to supply all information requested by any of them in connection with such Registration Statement. 

3.1.9 Opinions and Comfort Letters. The Company shall furnish to each holder of Registrable Securities included in any Registration
Statement a signed counterpart, addressed to such holder, of (i) any opinion of counsel to the Company delivered to any Underwriter, and (ii) any comfort letter from the Company’s independent public accountants delivered to any
Underwriter. In the event no legal opinion is delivered to any Underwriter, the Company shall furnish to each holder of Registrable Securities included in such Registration Statement, at any time that such holder elects to use a prospectus, an
opinion of counsel to the Company to the effect that the Registration Statement containing such prospectus has been declared effective and that no stop order is in effect. 

3.1.10 Earnings Statement. The Company shall comply with all applicable rules and regulations of the Commission and the Securities Act,
and make available to its stockholders, as soon as practicable, an earnings statement covering a period of twelve (12) months, which earnings statement shall satisfy the provisions of Section 11(a) of the Securities Act and Rule 158
thereunder. 
 3.1.11 Listing. The Company shall use its best efforts to cause all Registrable Securities included in any registration
to be listed on such exchanges or otherwise designated for trading in the same manner as similar securities issued by the Company are then listed or designated or, if no such similar securities are then listed or designated, in a manner satisfactory
to the holders of a majority of the Registrable Securities included in such registration. 
 3.1.12 Road Show. If the registration
involves the registration of Registrable Securities involving gross proceeds in excess of $25,000,000, the Company shall use its reasonable efforts to make available senior executives of the Company to participate in customary “road show”
presentations that may be reasonably requested by the Underwriter in any underwritten offering. 

  
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 3.2 Obligation to Suspend Distribution. Upon receipt of any notice from the Company
of the happening of any event of the kind described in Section 3.1.4(iv), or, in the case of a resale registration on Form S-3 pursuant to Section 2.3
hereof, upon any suspension by the Company, pursuant to a written insider trading compliance program adopted by the Company’s Board of Directors, of the ability of all “insiders” covered by such program to transact in the
Company’s securities because of the existence of material non-public information, each holder of Registrable Securities included in any registration shall immediately discontinue disposition of such
Registrable Securities pursuant to the Registration Statement covering such Registrable Securities until such holder receives the supplemented or amended prospectus contemplated by Section 3.1.4(iv) or the restriction on
the ability of “insiders” to transact in the Company’s securities is removed, as applicable, and, if so directed by the Company, each such holder will deliver to the Company all written copies, other than permanent file copies then in
such holder’s possession, of the most recent prospectus covering such Registrable Securities at the time of receipt of such notice. 

3.3 Registration Expenses. The Company shall bear all costs and expenses incurred in connection with any Demand Registration pursuant to
Section 2.1, any Piggy-Back Registration pursuant to Section 2.2, and any registration on Form S-3 effected pursuant to
Section 2.3, and all expenses incurred in performing or complying with its other obligations under this Agreement, whether or not the Registration Statement becomes effective, including, without limitation: (i) all
registration and filing fees, (ii) fees and expenses of compliance with securities or “blue sky” laws (including fees and disbursements of counsel in connection with blue sky qualifications of the Registrable Securities),
(iii) printing expenses, (iv) the Company’s internal expenses (including, without limitation, all salaries and expenses of its officers and employees), (v) the fees and expenses incurred in connection with the listing of the
Registrable Securities as required by Section 3.1.11, (vi) Financial Industry Regulatory Authority fees, (vii) fees and disbursements of counsel for the Company and fees and expenses for independent certified
public accountants retained by the Company (including the expenses or costs associated with the delivery of any opinions or comfort letters requested pursuant to Section 3.1.9), (viii) the fees and expenses of any
special experts retained by the Company in connection with such registration, and (ix) the fees and expenses of one legal counsel selected by the holders of a
majority-in-interest of the Registrable Securities included in such registration. The Company shall have no obligation to pay any underwriting discounts or selling
commissions attributable to the Registrable Securities being sold by the holders thereof, which underwriting discounts or selling commissions shall be borne by such holders. Additionally, in an underwritten offering, all selling stockholders and the
Company shall bear the expenses of the Underwriter pro rata in proportion to the respective amount of shares each is selling in such offering. 

3.4 Information. The holders of Registrable Securities shall provide such information as may reasonably be requested by the Company, or
the managing Underwriter, if any, in connection with the preparation of any Registration Statement, including amendments and supplements thereto, in order to effect the registration of any Registrable Securities under the Securities Act pursuant to
Article 2 and in connection with the Company’s obligation to comply with federal and applicable state securities laws. 

4. INDEMNIFICATION AND CONTRIBUTION. 

4.1 Indemnification by the Company. The Company agrees to indemnify and hold harmless each Investor and each other holder of Registrable
Securities, and each of their respective officers, employees, affiliates, directors, partners, members, attorneys and agents, and each person, if any, who controls an Investor and each other holder of Registrable Securities (within the meaning of
Section 15 of the Securities Act or Section 20 of the Exchange Act) (each, an “Investor Indemnified Party”), from and against any expenses, losses, judgments, claims, damages or
liabilities, whether joint or several, arising out of or based upon any untrue statement (or allegedly untrue statement) of a material fact contained in any Registration Statement under which the sale of such Registrable Securities was registered
under the Securities Act, any preliminary prospectus, final prospectus or summary prospectus contained in the 

  
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Registration Statement, or any amendment or supplement to such Registration Statement, or arising out of or based upon any omission (or alleged omission) to state a material fact required to be
stated therein or necessary to make the statements therein not misleading, or any violation by the Company of the Securities Act or any rule or regulation promulgated thereunder applicable to the Company and relating to action or inaction required
of the Company in connection with any such registration; and the Company shall promptly reimburse the Investor Indemnified Party for any legal and any other expenses reasonably incurred by such Investor Indemnified Party in connection with
investigating and defending any such expense, loss, judgment, claim, damage, liability or action whether or not any such person is a party to any such claim or action and including any and all legal and other expenses incurred in giving testimony or
furnishing documents in response to a subpoena or otherwise; provided, however, that the Company will not be liable in any such case to the extent that any such expense, loss, claim, damage or liability arises out of or is based upon
any untrue statement or allegedly untrue statement or omission or alleged omission made in such Registration Statement, preliminary prospectus, final prospectus, or summary prospectus, or any such amendment or supplement, in reliance upon and in
conformity with information furnished to the Company, in writing, by such selling holder expressly for use therein. The Company also shall indemnify any Underwriter of the Registrable Securities, their officers, affiliates, directors, partners,
members and agents and each person who controls such Underwriter on substantially the same basis as that of the indemnification provided above in this Section 4.1. 

4.2 Indemnification by Holders of Registrable Securities. Subject to the limitations set forth in
Section 4.4.3 hereof, each selling holder of Registrable Securities will, in the event that any registration is being effected under the Securities Act pursuant to this Agreement of any Registrable Securities held by such
selling holder, indemnify and hold harmless the Company, each of its directors and officers and each Underwriter (if any), and each other selling holder and each other person, if any, who controls another selling holder or such Underwriter within
the meaning of the Securities Act, against any losses, claims, judgments, damages or liabilities, whether joint or several, insofar as such losses, claims, judgments, damages or liabilities (or actions in respect thereof) arise out of or are based
upon any untrue statement or allegedly untrue statement of a material fact contained in any Registration Statement under which the sale of such Registrable Securities was registered under the Securities Act, any preliminary prospectus, final
prospectus or summary prospectus contained in the Registration Statement, or any amendment or supplement to the Registration Statement, or arise out of or are based upon any omission or the alleged omission to state a material fact required to be
stated therein or necessary to make the statement therein not misleading, if the statement or omission was made in reliance upon and in conformity with information furnished in writing to the Company by such selling holder expressly for use therein,
and shall reimburse the Company, its directors and officers, and each other selling holder or controlling person for any legal or other expenses reasonably incurred by any of them in connection with investigation or defending any such loss, claim,
damage, liability or action. Each selling holder’s indemnification obligations hereunder shall be several and not joint and shall be limited to the amount of any net proceeds actually received by such selling holder. 

4.3 Conduct of Indemnification Proceedings. Promptly after receipt by any person of any notice of any loss, claim, damage or liability
or any action in respect of which indemnity may be sought pursuant to Section 4.1 or Section 4.2, such person (the “Indemnified Party”) shall, if a claim in respect thereof
is to be made against any other person for indemnification hereunder, notify such other person (the “Indemnifying Party”) in writing of the loss, claim, judgment, damage, liability or action; provided,
however, that the failure by the Indemnified Party to notify the Indemnifying Party shall not relieve the Indemnifying Party from any liability which the Indemnifying Party may have to such Indemnified Party hereunder, except and solely to
the extent the Indemnifying Party is actually prejudiced by such failure. If the Indemnified Party is seeking indemnification with respect to any claim or action brought against the Indemnified Party, then the Indemnifying Party shall be entitled to
participate in such claim or action, and, 

  
 10 

 
to the extent that it wishes, jointly with all other Indemnifying Parties, to assume control of the defense thereof with counsel satisfactory to the Indemnified Party. After notice from the
Indemnifying Party to the Indemnified Party of its election to assume control of the defense of such claim or action, the Indemnifying Party shall not be liable to the Indemnified Party for any legal or other expenses subsequently incurred by the
Indemnified Party in connection with the defense thereof other than reasonable costs of investigation; provided, however, that in any action in which both the Indemnified Party and the Indemnifying Party are named as defendants, the
Indemnified Party shall have the right to employ separate counsel (but no more than one such separate counsel) to represent the Indemnified Party and its controlling persons who may be subject to liability arising out of any claim in respect of
which indemnity may be sought by the Indemnified Party against the Indemnifying Party, with the fees and expenses of such counsel to be paid by such Indemnifying Party if, based upon the written advice of counsel of such Indemnified Party,
representation of both parties by the same counsel would be inappropriate due to actual or potential differing interests between them. No Indemnifying Party shall, without the prior written consent of the Indemnified Party, consent to entry of
judgment or effect any settlement of any claim or pending or threatened proceeding in respect of which the Indemnified Party is or could have been a party and indemnity could have been sought hereunder by such Indemnified Party, unless such judgment
or settlement includes an unconditional release of such Indemnified Party from all liability arising out of such claim or proceeding. 
 4.4
Contribution. 
 4.4.1 If the indemnification provided for in the foregoing Section 4.1,
Section 4.2 and Section 4.3 is unavailable to any Indemnified Party in respect of any loss, claim, damage, liability or action referred to herein, then each such Indemnifying Party, in lieu of
indemnifying such Indemnified Party, shall contribute to the amount paid or payable by such Indemnified Party as a result of such loss, claim, damage, liability or action in such proportion as is appropriate to reflect the relative fault of the
Indemnified Parties and the Indemnifying Parties in connection with the actions or omissions which resulted in such loss, claim, damage, liability or action, as well as any other relevant equitable considerations. The relative fault of any
Indemnified Party and any Indemnifying Party shall be determined by reference to, among other things, whether the untrue or alleged untrue statement of a material fact or the omission or alleged omission to state a material fact relates to
information supplied by such Indemnified Party or such Indemnifying Party and the parties’ relative intent, knowledge, access to information and opportunity to correct or prevent such statement or omission. 

4.4.2 The parties hereto agree that it would not be just and equitable if contribution pursuant to this Section 4.4
were determined by pro rata allocation or by any other method of allocation which does not take account of the equitable considerations referred to in the immediately preceding Section 4.4.1. 

4.4.3 The amount paid or payable by an Indemnified Party as a result of any loss, claim, damage, liability or action referred to in the
immediately preceding paragraph shall be deemed to include, subject to the limitations set forth above, any legal or other expenses incurred by such Indemnified Party in connection with investigating or defending any such action or claim.
Notwithstanding the provisions of this Section 4.4, no holder of Registrable Securities shall be required to contribute any amount in excess of the dollar amount of the net proceeds (after payment of any underwriting fees,
discounts, commissions or taxes) actually received by such holder from the sale of Registrable Securities which gave rise to such contribution obligation. No person guilty of fraudulent misrepresentation (within the meaning of Section 11(f) of
the Securities Act) with respect to any action shall be entitled to contribution in such action from any person who was not guilty of such fraudulent misrepresentation. 

  
 11 

 5. UNDERWRITING AND DISTRIBUTION. 

5.1 Rule 144. The Company covenants that it shall file any reports required to be filed by it under the Securities Act and the Exchange
Act and shall take such further action as the holders of Registrable Securities may reasonably request, all to the extent required from time to time to enable such holders to sell Registrable Securities without registration under the Securities Act
within the limitation of the exemptions provided by Rule 144 under the Securities Act, as such Rules may be amended from time to time, or any similar rule or regulation hereafter adopted by the Commission. 

6. MISCELLANEOUS. 
 6.1
Other Registration Rights. The Company represents and warrants that no person, other than the holders of the Registrable Securities, has any right to require the Company to register any shares of the Company’s capital stock for sale or
to include shares of the Company’s capital stock in any registration filed by the Company for the sale of shares of capital stock for its own account or for the account of any other person. 

6.2 Assignment; No Third Party Beneficiaries. This Agreement and the rights, duties and obligations of the Company hereunder may not be
assigned or delegated by the Company in whole or in part. This Agreement and the rights, duties and obligations of the holders of Registrable Securities hereunder may be freely assigned or delegated by such holder of Registrable Securities in
conjunction with and to the extent of any transfer of Registrable Securities by any such holder. This Agreement and the provisions hereof shall be binding upon and shall inure to the benefit of each of the parties, to the permitted assigns of the
Investors or holder of Registrable Securities or of any assignee of the Investors or holder of Registrable Securities. This Agreement is not intended to confer any rights or benefits on any persons that are not party hereto other than as expressly
set forth in Article 4 and this Section 6.2. 
 6.3 Notices. All notices, demands,
requests, consents, approvals or other communications (collectively, “Notices”) required or permitted to be given hereunder or which are given with respect to this Agreement shall be in writing and shall be personally served,
delivered by reputable air courier service with charges prepaid, or transmitted by hand delivery, telegram, telex or facsimile, addressed as set forth below, or to such other address as such party shall have specified most recently by written
notice. Notice shall be deemed given on the date of service or transmission if personally served or transmitted by telegram, telex or facsimile; provided, that if such service or transmission is not on a business day or is after normal
business hours, then such notice shall be deemed given on the next business day. Notice otherwise sent as provided herein shall be deemed given on the next business day following timely delivery of such notice to a reputable air courier service with
an order for next-day delivery. 
 To the Company: 

Adit EdTech Acquisition Corp. 

1345 Avenue of Americas, 33rd Floor 

New York, NY 10105 
 Attn: David
L. Shrier, Chief Executive Officer 
 with a copy to: 

Troutman Pepper Hamilton Sanders LLP 

875 Third Avenue 
 New York, NY
10022 
 Attn: Patrick B. Costello, Esq. 

  
 12 

 To an Investor, to the address set forth below such Investor’s name on
Exhibit A hereto. 
 6.4 Severability. This Agreement shall be deemed severable, and the invalidity or
unenforceability of any term or provision hereof shall not affect the validity or enforceability of this Agreement or of any other term or provision hereof. Furthermore, in lieu of any such invalid or unenforceable term or provision, the parties
hereto intend that there shall be added as a part of this Agreement a provision as similar in terms to such invalid or unenforceable provision as may be possible that is valid and enforceable. 

6.5 Counterparts. This Agreement may be executed in multiple counterparts, each of which shall be deemed an original, and all of which
taken together shall constitute one and the same instrument. Delivery of a signed counterpart of this Agreement by facsimile or email/pdf transmission shall constitute valid and sufficient delivery thereof. 

6.6 Entire Agreement. This Agreement (including all agreements entered into pursuant hereto and all certificates and instruments
delivered pursuant hereto and thereto) constitute the entire agreement of the parties with respect to the subject matter hereof and supersede all prior and contemporaneous agreements, representations, understandings, negotiations and discussions
between the parties, whether oral or written. 
 6.7 Modifications and Amendments. No amendment, modification or termination of this
Agreement shall be binding upon any party unless executed in writing by such party. 
 6.8 Titles and Headings. Titles and headings of
sections of this Agreement are for convenience only and shall not affect the construction of any provision of this Agreement. 
 6.9
Waivers and Extensions. Any party to this Agreement may waive any right, breach or default which such party has the right to waive, provided, that such waiver will not be effective against the waiving party unless it is in writing, is
signed by such party, and specifically refers to this Agreement. Waivers may be made in advance or after the right waived has arisen or the breach or default waived has occurred. Any waiver may be conditional. No waiver of any breach of any
agreement or provision herein contained shall be deemed a waiver of any preceding or succeeding breach thereof nor of any other agreement or provision herein contained. No waiver or extension of time for performance of any obligations or acts shall
be deemed a waiver or extension of the time for performance of any other obligations or acts. 
 6.10 Remedies Cumulative. In the
event that the Company fails to observe or perform any covenant or agreement to be observed or performed under this Agreement, the Investor or any other holder of Registrable Securities may proceed to protect and enforce its rights by suit in equity
or action at law, whether for specific performance of any term contained in this Agreement or for an injunction against the breach of any such term or in aid of the exercise of any power granted in this Agreement or to enforce any other legal or
equitable right, or to take any one or more of such actions, without being required to post a bond. None of the rights, powers or remedies conferred under this Agreement shall be mutually exclusive, and each such right, power or remedy shall be
cumulative and in addition to any other right, power or remedy, whether conferred by this Agreement or now or hereafter available at law, in equity, by statute or otherwise. 

  
 13 

 6.11 Governing Law. This Agreement shall be governed by, interpreted under, and
construed in accordance with the internal laws of the State of New York applicable to agreements made and to be performed within the State of New York, without giving effect to any
choice-of-law provisions thereof that would compel the application of the substantive laws of any other jurisdiction. The Company irrevocably submits to the nonexclusive
jurisdiction of any New York State or United States Federal court sitting in The City of New York, Borough of Manhattan, over any suit, action or proceeding arising out of or relating to this Agreement. The Company irrevocably waives, to the fullest
extent permitted by law, any objection that they may now or hereafter have to the laying of venue of any such suit, action or proceeding brought in such a court and any claim that any such suit, action or proceeding brought in such a court has been
brought in an inconvenient forum. 
 6.12 Waiver of Trial by Jury. EACH PARTY HEREBY IRREVOCABLY AND UNCONDITIONALLY WAIVES THE RIGHT
TO A TRIAL BY JURY IN ANY ACTION, SUIT, COUNTERCLAIM OR OTHER PROCEEDING (WHETHER BASED ON CONTRACT, TORT OR OTHERWISE) ARISING OUT OF, CONNECTED WITH OR RELATING TO THIS AGREEMENT, THE TRANSACTIONS CONTEMPLATED HEREBY, OR THE ACTIONS OF THE
INVESTOR IN THE NEGOTIATION, ADMINISTRATION, PERFORMANCE OR ENFORCEMENT HEREOF. 
 [Remainder of Page Intentionally Left Blank;
Signature Page Follows] 

  
 14 

 IN WITNESS WHEREOF, the parties have caused this Registration Rights Agreement to be
executed and delivered by their duly authorized representatives as of the date first written above. 
  

			
		 	COMPANY:
		
		 	ADIT EDTECH ACQUISITION CORP.
		
	By:	 	 /s/ David L. Shrier

		 	Name: David L. Shrier
		 	Title: Chief Executive Officer
		
		 	INVESTORS:
		
		 	ADIT EDTECH SPONSOR, LLC
		
	By:	 	 /s/ Eric Munson

		 	Name: Eric Munson
		 	Title: Chairman of the Board
		
		 	 /s/ Jacob Cohen

		 	JACOB COHEN
		
		 	 /s/ Sharmila Kassam

		 	SHARMILA KASSAM
		
		 	 /s/ Sheldon H. Levy

		 	SHELDON H. LEVY
		
		 	 /s/ Vuk Jeremic

		 	VUK JEREMIC
		
		 	 /s/ Eva Kaili

		 	EVA KAILI
		
		 	 /s/ William Bennett

		 	WILLIAM BENNETT

 [Signature Page to Registration Rights Agreement] 

 EXHIBIT A 

 

			
	 NAME OF INVESTOR
	  	 ADDRESS OF INVESTOR

	Adit EdTech Sponsor, LLC	  	 1345 Avenue of Americas, 33rd Floor
 New York,
NY 10105

		
	Jacob Cohen	  	 613 Pleasant Street
 Belmont, MA 02478
USA

		
	Sharmila Kassam	  	 4103 Idlewild Road
 Austin, TX
78731

		
	Sheldon H. Levy	  	 704 Balliol Street
 Toronto, Canada M4S
1E7

		
	Vuk Jeremic	  	 Brane Crnceviva 5/5
 Belgrade, Serbia
11000

		
	Eva Kaili	  	 Giasemon 1, Psychiko
 Athens, Greece
15452

		
	William Bennett	  	 29 East Beach Drive
 Bald Head Island, NC
28461

  

  
 A-1EX-10.5

 Exhibit 10.5 

Execution Version 
 PRIVATE
PLACEMENT WARRANTS PURCHASE AGREEMENT 
 THIS PRIVATE PLACEMENT WARRANTS PURCHASE AGREEMENT (as it may from time to time be amended and
including all exhibits referenced herein, this “Agreement”), dated as of January 11, 2021, is entered into by and between Adit EdTech Acquisition Corp., a Delaware corporation
(the “Company”), and Adit EdTech Sponsor, LLC, a Delaware limited liability company (the “Purchaser”). 

WHEREAS, the Company intends to consummate an initial public offering of the Company’s units (the “Public
Offering”), each unit consisting of one share of common stock of the Company, par value $0.0001 per share (each, a “Share”), and one-half of one warrant, each whole warrant
entitling the holder to purchase one Share at an exercise price of $11.50 per Share, as set forth in the Company’s Registration Statement on Form S-1, filed with the U.S. Securities and Exchange
Commission (the “SEC”) (the “Registration Statement”), under the Securities Act of 1933, as amended (the “Securities Act”); and 

WHEREAS, the Purchaser has agreed to purchase an aggregate of 6,550,000 warrants (and up to 720,000 additional warrants if the
underwriters (the “Underwriters”) in the Public Offering exercise their option to purchase additional units in full) (the “Private Placement Warrants”), each Private Placement Warrant entitling the
holder to purchase one Share at an exercise price of $11.50 per Share, at a price of $1.00 per Warrant. 
 NOW THEREFORE, in
consideration of the mutual promises contained in this Agreement and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties to this Agreement hereby, intending legally to be bound, agree as
follows: 
 AGREEMENT 

Section 1. Authorization, Purchase and Sale; Terms of the Private Placement Warrants. 

A. Authorization of the Private Placement Warrants. The Company has duly authorized the issuance and sale of the Private Placement
Warrants to the Purchaser. 
 B. Purchase and Sale of the Private Placement Warrants. 

a) On the date of the consummation of the Public Offering (the “IPO Closing Date”), the Company shall issue and sell to
the Purchaser, and the Purchaser shall purchase from the Company, 6,550,000 Private Placement Warrants at a price of $1.00 per Warrant for an aggregate purchase price of $6,550,000 (the “Purchase Price”). On the IPO Closing
Date, subject to the receipt of funds pursuant to Section 1.B.d) below, the Company, at its option, shall deliver a certificate evidencing the Private Placement Warrants purchased on such date duly registered in the Purchaser’s name to the
Purchaser or effect such delivery in book-entry form. 
 b) On the date of the closing (the “Option Closing”) of the
option to purchase additional units, if any, in connection with the Public Offering or on such earlier time and date as may be mutually agreed by the Purchaser and the Company (the “Option Closing Date”, and each Option
Closing Date (if any) and the IPO Closing Date, a “Closing Date”), the Company shall issue and sell to the Purchaser, and the Purchaser shall purchase from the Company, up to 720,000 Private Placement Warrants (or, to the
extent the option to purchase additional units is not exercised in full, a lesser number of Private Placement Warrants in proportion to the portion of the option that is exercised) at a price of $1.00 per

 
warrant for an aggregate purchase price of up to $720,000 (the “Option Purchase Price”). On the Option Closing Date, subject to the receipt of funds pursuant to
Section 1.B.e) below, the Company shall, at its option, deliver a certificate evidencing the Private Placement Warrants purchased on such date duly registered in the Purchaser’s name to the Purchaser or effect such delivery in book-entry
form. 
 c) At least twenty-four (24) hours prior to the effective date of the Registration Statement, the undersigned will cause the
Purchase Price and the maximum amount of the Option Purchase Price (i.e., $720,000) to be delivered to Continental Stock Transfer and Trust Company (“CST”), escrow agent for the Company, by wire transfer as set forth in the
instructions to be provided to it by the Company to hold in a non-interest bearing account (the “Escrow Account”) until the Company consummates the Public Offering. 

d) Simultaneously with the consummation of the Public Offering, the Purchaser shall cause CST to deposit on behalf of the Purchaser the
Purchase Price, without interest or deduction, by wire transfer of immediately available funds from the Escrow Account as follows: (i) $1,750,000 to the Company at a financial institution to be chosen by the Company, and (ii) $4,800,000 to the trust
account maintained by CST, acting as trustee (the “Trust Account”), in each case in accordance with the Company’s wiring instructions. If the Company does not complete the Public Offering within ten (10) days from
the date of this Agreement, the Purchase Price (without interest or deduction) in the Escrow Account will be returned to the Purchaser. 
 e)
Simultaneously with the Option Closing, the Purchaser shall cause CST to deposit on behalf of the Purchaser the Option Purchase Price, without interest or deduction, by wire transfer of immediately available funds from the Escrow Account to the
Trust Account, in accordance with the Company’s wiring instructions. If the Option Closing does not occur, or if the Option Closing occurs but the Option Purchase Price is less than $720,000, the balance of the Option Purchase Price in the
Escrow Account will promptly be returned to the Purchaser. 
 f) Each of the Company and the Purchaser acknowledges and agrees that CST is
serving hereunder solely as a convenience to the parties to facilitate the purchase of the Private Placement Warrants, and CST’s sole obligation with respect to this Agreement is to hold and disburse the Purchase Price and the Option Purchase
Price for the Private Placement Warrants, as described above. CST shall not be liable to the Company, the Underwriters or the Purchaser or any other person or entity in respect of any act or failure to act hereunder or otherwise in connection with
performing its services hereunder unless CST has acted in a manner constituting gross negligence or willful misconduct. The Company shall indemnify CST against any claim made against it (including reasonable attorney’s fees) by reason of it
acting or failing to act in connection with this Agreement except as a result of its gross negligence or willful misconduct. CST may rely and shall be protected in acting or refraining from acting upon any written notice, instruction or request
furnished to it hereunder and believed by it to be genuine and to have been signed or presented by the proper party or parties. 
 C.
Terms of the Private Placement Warrants. 
 a) Each Private Placement Warrant shall have the terms set forth in a warrant agreement to
be entered into by the Company and a warrant agent on the IPO Closing Date, in connection with the Public Offering (the “Warrant Agreement”). 

  
 2 

 b) On the IPO Closing Date, the Company and the Purchaser shall enter into a registration
rights agreement (the “Registration Rights Agreement”) pursuant to which the Company will grant certain registration rights to the Purchaser relating to the Private Placement Warrants and the Shares underlying the Private
Placement Warrants. 
 Section 2. Representations and Warranties of the Company. As a material inducement to
the Purchaser to enter into this Agreement and purchase the Private Placement Warrants, the Company hereby represents and warrants to the Purchaser (which representations and warranties shall survive each Closing Date) that: 

A. Incorporation and Corporate Power. The Company is a corporation duly incorporated, validly existing and in good standing under the
laws of the State of Delaware and is qualified to do business in every jurisdiction in which the failure to so qualify would reasonably be expected to have a material adverse effect on the financial condition, operating results or assets of the
Company. The Company possesses all requisite corporate power and authority necessary to carry out the transactions contemplated by this Agreement and the Warrant Agreement. 

B. Authorization; No Breach. 

a) The execution, delivery and performance of this Agreement and the Private Placement Warrants have been duly authorized by the Company as of
the Closing Date. This Agreement constitutes the valid and binding obligation of the Company, enforceable in accordance with its terms, subject to bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other laws of general
applicability relating to or affecting creditors’ rights and to general equitable principles (whether considered in a proceeding in equity or law). Upon issuance in accordance with, and payment pursuant to, the terms of the Warrant Agreement
and this Agreement, the Private Placement Warrants will constitute valid and binding obligations of the Company, enforceable in accordance with their terms as of the Closing Date. 

b) The execution and delivery by the Company of this Agreement and the Private Placement Warrants, the issuance and sale of the Private
Placement Warrants, the issuance of the Shares upon exercise of the Private Placement Warrants and the fulfillment of and compliance with the respective terms hereof and thereof by the Company, do not and will not as of the Closing Date
(i) conflict with or result in a breach of the terms, conditions or provisions of, (ii) constitute a default under, (iii) result in the creation of any lien, security interest, charge or encumbrance upon the Company’s share
capital or assets under, (iv) result in a violation of, or (v) require any authorization, consent, approval, exemption or other action by or notice or declaration to, or filing with, any court or administrative or governmental body or
agency pursuant to the memorandum and articles of association of the company (in effect on the date hereof or as may be amended prior to completion of the Public Offering) or any material law, statute, rule or regulation to which the Company is
subject, or any agreement, order, judgment or decree to which the Company is subject, except for any filings required after the date hereof under federal or state securities laws. 

C. Title to Securities. Upon issuance in accordance with, and payment pursuant to, the terms hereof and the Warrant Agreement, the
Shares issuable upon exercise of the Private Placement Warrants will be duly and validly issued, fully paid and nonassessable. On the date of issuance of the Private Placement Warrants, the Shares issuable upon exercise of the Private Placement
Warrants shall have been reserved for issuance. Upon issuance in accordance with, and payment pursuant to, the terms hereof and 

  
 3 

 
the Warrant Agreement, the Purchaser will have good title to the Private Placement Warrants purchased by it and the Shares issuable upon exercise of such Private Placement Warrants, free and
clear of all liens, claims and encumbrances of any kind, other than (i) transfer restrictions hereunder and under the other agreements contemplated hereby, (ii) transfer restrictions under federal and state securities laws, and
(iii) liens, claims or encumbrances imposed due to the actions of the Purchaser. 
 D. Governmental Consents. No permit, consent,
approval or authorization of, or declaration to or filing with, any governmental authority is required in connection with the execution, delivery and performance by the Company of this Agreement or the consummation by the Company of any other
transactions contemplated hereby. 
 E. Regulation D Qualification. Neither the Company nor, to its actual knowledge, any of its
affiliates, officers, directors or beneficial stockholders of 20% or more of its outstanding securities, has experienced a disqualifying event as enumerated pursuant to Rule 506(d) of Regulation D under the Securities Act. 

Section 3. Representations and Warranties of the Purchaser. As a material inducement to the Company to enter
into this Agreement and issue and sell the Private Placement Warrants to the Purchaser, the Purchaser hereby represents and warrants to the Company (which representations and warranties shall survive each Closing Date) that: 

A. Organization and Requisite Authority. The Purchaser possesses all requisite power and authority necessary to carry out the
transactions contemplated by this Agreement. 
 B. Authorization; No Breach. 

a) This Agreement constitutes a valid and binding obligation of the Purchaser, enforceable in accordance with its terms, subject to bankruptcy,
insolvency, fraudulent conveyance, reorganization, moratorium and other laws of general applicability relating to or affecting creditors’ rights and to general equitable principles (whether considered in a proceeding in equity or law). 

b) The execution and delivery by the Purchaser of this Agreement and the fulfillment of and compliance with the terms hereof by the Purchaser
does not and shall not as of each Closing Date (i) conflict with or result in a breach by the Purchaser of the terms, conditions or provisions of, (ii) constitute a default under, (iii) result in the creation of any lien, security
interest, charge or encumbrance upon the Purchaser’s equity or assets under, (iv) result in a violation of, or (v) require authorization, consent, approval, exemption or other action by or notice or declaration to, or filing with, any
court or administrative or governmental body or agency pursuant to the Purchaser’s organizational documents in effect on the date hereof or as may be amended prior to completion of the contemplated Public Offering, or any material law, statute,
rule or regulation to which the Purchaser is subject, or any agreement, instrument, order, judgment or decree to which the Purchaser is subject, except for any filings required after the date hereof under federal or state securities laws. 

C. Investment Representations. 

a) The Purchaser is acquiring the Private Placement Warrants and, upon exercise of the Private Placement Warrants, the Shares issuable upon
such exercise (collectively, the “Securities”) for its own account, for investment purposes only and not with a view towards, or for resale in connection with, any public sale or distribution thereof. 

  
 4 

 b) The Purchaser is an “accredited investor” as such term is defined
in Rule 501(a)(3) of Regulation D, and the Purchaser has not experienced a disqualifying event as enumerated pursuant to Rule 506(d) of Regulation D under the Securities Act. 

c) The Purchaser understands that the Securities are being offered and will be sold to it in reliance on specific exemptions from the
registration requirements of the United States federal and state securities laws and that the Company is relying upon the truth and accuracy of, and the Purchaser’s compliance with, the representations and warranties of the Purchaser set forth
herein in order to determine the availability of such exemptions and the eligibility of the Purchaser to acquire such Securities. 
 d) The
Purchaser did not decide to enter into this Agreement as a result of any general solicitation or general advertising within the meaning of Rule 502(c) under the Securities Act. 

e) The Purchaser has been furnished with all materials relating to the business, finances and operations of the Company and materials relating
to the offer and sale of the Securities which have been requested by the Purchaser. The Purchaser has been afforded the opportunity to ask questions of the executive officers and directors of the Company. The Purchaser understands that its
investment in the Securities involves a high degree of risk and it has sought such accounting, legal and tax advice as it has considered necessary to make an informed investment decision with respect to the acquisition of the Securities. 

f) The Purchaser understands that no United States federal or state agency or any other government or governmental agency has passed on or made
any recommendation or endorsement of the Securities or the fairness or suitability of the investment in the Securities by the Purchaser nor have such authorities passed upon or endorsed the merits of the offering of the Securities. 

g) The Purchaser understands that: (i) the Securities have not been and are not being registered under the Securities Act or any state
securities laws, and may not be offered for sale, sold, assigned or transferred unless (1) subsequently registered thereunder or (2) sold in reliance on an exemption therefrom, and (ii) except as specifically set forth in the
Registration Rights Agreement, neither the Company nor any other person is under any obligation to register the Securities under the Securities Act or any state securities laws or to comply with the terms and conditions of any exemption thereunder.
In this regard, the Purchaser understands that the SEC has taken the position that promoters or affiliates of a blank check company and their transferees, both before and after an initial Business Combination, are deemed to be
“underwriters” under the Securities Act when reselling the securities of a blank check company. Based on that position, Rule 144 adopted pursuant to the Securities Act would not be available for resale transactions of the
Securities despite technical compliance with the requirements of such Rule, and the Securities can be resold only through a registered offering or in reliance upon another exemption from the registration requirements of the Securities Act. 

h) The Purchaser has such knowledge and experience in financial and business matters, knowledge of the high degree of risk associated with
investments in the securities of companies in the development stage such as the Company, is capable of evaluating the merits and risks of an investment in the Securities and is able to bear the economic risk of an investment in the Securities in the
amount contemplated hereunder for an indefinite period of time. The Purchaser has adequate means of providing for its current financial needs and contingencies and will have no current or anticipated future needs for liquidity which would be
jeopardized by the investment in the Securities. The Purchaser can afford a complete loss of its investments in the Securities. 

  
 5 

 Section 4. Conditions of the Purchaser’s Obligations. The
obligations of the Purchaser to purchase and pay for the Private Placement Warrants are subject to the fulfillment, on or before each Closing Date, of each of the following conditions: 

A. Representations and Warranties. The representations and warranties of the Company contained in Section 2 shall be true and
correct at and as of the Closing Date as though then made. 
 B. Performance. The Company shall have performed and complied with all
agreements, obligations and conditions contained in this Agreement that are required to be performed or complied with by it on or before such Closing Date. 

C. No Injunction. No litigation, statute, rule, regulation, executive order, decree, ruling or injunction shall have been enacted,
entered, promulgated or endorsed by or in any court or governmental authority of competent jurisdiction or any self-regulatory organization having authority over the matters contemplated hereby, which prohibits the consummation of any of the
transactions contemplated by this Agreement or the Warrant Agreement. 
 D. Warrant Agreement and Registration Rights Agreement. The
Company shall have entered into the Warrant Agreement and the Registration Rights Agreement in each case on terms reasonably satisfactory to the Purchaser. 

Section 5. Conditions of the Company’s Obligations. The obligations of the Company to the Purchaser under this
Agreement are subject to the fulfillment, on or before each Closing Date, of each of the following conditions: 
 A. Representations and
Warranties. The representations and warranties of the Purchaser contained in Section 3 shall be true and correct at and as of such Closing Date as though then made. 

B. Performance. The Purchaser shall have performed and complied with all agreements, obligations and conditions contained in this
Agreement that are required to be performed or complied with by the Purchaser on or before such Closing Date. 
 C. No Injunction. No
litigation, statute, rule, regulation, executive order, decree, ruling or injunction shall have been enacted, entered, promulgated or endorsed by or in any court or governmental authority of competent jurisdiction or any self-regulatory organization
having authority over the matters contemplated hereby, which prohibits the consummation of any of the transactions contemplated by this Agreement or the Warrant Agreement. 

D. Warrant Agreement. The Company shall have entered into the Warrant Agreement. 

Section 6. Miscellaneous. 

A. Successors and Assigns. Except as otherwise expressly provided herein, all covenants and agreements contained in this Agreement by or
on behalf of any of the parties hereto shall bind and inure to the benefit of the respective successors of the parties hereto whether so expressed or not. Notwithstanding the foregoing or anything to the contrary herein, the parties may not assign
this Agreement, other than assignments by the Purchaser to affiliates thereof (including, without limitation one or more of its members). 

  
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 B. 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. 
 C. Counterparts. This Agreement may be executed
simultaneously in two or more counterparts, none of which need contain the signatures of more than one party, but all such counterparts taken together shall constitute one and the same agreement. Signatures to this Agreement transmitted via
facsimile or e-mail shall be valid and effective to bind the party so signing. 
 D. Descriptive
Headings; Interpretation. The descriptive headings of this Agreement are inserted for convenience only and do not constitute a substantive part of this Agreement. The use of the word “including” in this Agreement shall be by way of
example rather than by limitation. 
 E. Governing Law. This Agreement shall be deemed to be a contract made under the laws of the
State of New York and for all purposes shall be construed in accordance with the internal laws of the State of New York, without giving effect to conflicts of law principles that would result in the application of the laws of another jurisdiction.

 F. Amendments. This Agreement may not be amended, modified or waived as to any particular provision, except by a written instrument
executed by the parties hereto. 
 [Remainder of Page Intentionally Left Blank; Signature page follows] 

  
 7 

 IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of the date
first set forth above. 
  

			
	COMPANY:
	
	ADIT EDTECH ACQUISITION CORP.
		
	By:	 	 /s/ David Shrier

		 	Name: David Shrier
		 	Title: Chief Executive Officer
	
	PURCHASER:
	
	ADIT EDTECH SPONSOR, LLC
		
	By:	 	 /s/ Eric L. Munson

		 	Name: Eric L. Munson
		 	Title: Chairman

 [Signature Page to Private Placement Warrants Purchase Agreement]

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