EX-10.3





 Exhibit 10.3 

REGISTRATION RIGHTS AGREEMENT 

THIS REGISTRATION RIGHTS AGREEMENT (this “Agreement”), dated as of February 26, 2021, is made and entered into by
and among Hudson Executive Investment Corp. III, a Delaware corporation (the “Company”), HEC Sponsor III LLC, a Delaware limited liability company (the “Sponsor”) and the undersigned parties listed on
the signature page hereto under “Holders” (each such party, together with the Sponsor and any person or entity who hereafter becomes a party to this Agreement pursuant to Section 5.2 of this Agreement, a
“Holder” and collectively the “Holders”). 
 RECITALS 

WHEREAS, the Company has 15,093,750 shares of Class B common stock, par value $0.0001 per share (the “Founder
Shares”), issued and outstanding, up to 1,968,750 of which will be forfeited to the Company for no consideration depending on the extent to which the underwriters of the Company’s initial public offering exercise their
over-allotment option; 
 WHEREAS, the Founder Shares are convertible into shares of the Company’s Class A common stock,
par value $0.0001 per share (the “Common Stock”), on the terms and conditions provided in the Company’s amended and restated certificate of incorporation; 

WHEREAS, on February 23, 2021, the Company and the Sponsor entered into that certain Private Placement Warrants Purchase Agreement
(the “Private Placement Warrants Purchase Agreement”), pursuant to which the Sponsor agreed to purchase 8,333,333 private placement warrants (or up to 9,383,333 warrants to the extent that the over-allotment option in
connection with the Company’s initial public offering is exercised) (the “Private Placement Warrants”) in a private placement transaction occurring simultaneously with the closing of the Company’s initial public
offering; 
 WHEREAS, on February 26, 2021, the Company and HEC Master Fund LP (the “Forward Purchaser”)
entered into that certain Forward Purchase Agreement (the “Forward Purchase Agreement”), pursuant to which the Forward Purchaser agreed to purchase an aggregate of 5,000,000 forward purchase units (the “Forward
Purchase Units”) in a private placement transaction to close concurrently with the closing of the initial Business Combination (as defined below); 

WHEREAS, in order to finance the Company’s transaction costs in connection with its search for and consummation of an initial
Business Combination (as defined below), the Sponsor or an affiliate of the Sponsor or certain of the Company’s officers and directors may loan to the Company funds as the Company may require, of which up to $1,500,000 of such loans may be
convertible into private placement-equivalent warrants (“Working Capital Warrants”) at a price of $1.50 per warrant at the option of the lender; and 

WHEREAS, the Company and the Holders desire to enter into this Agreement, pursuant to which the Company shall grant the Holders certain
registration rights with respect to certain securities of the Company, as set forth in this Agreement. 












 NOW, THEREFORE, in consideration of the representations, covenants and
agreements contained herein, and certain other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto, intending to be legally bound, hereby agree as follows: 

ARTICLE I 
 DEFINITIONS

 1.1 Definitions. The terms defined in this Article I shall, for all purposes of this
Agreement, have the respective meanings set forth below: 
 “Adverse Disclosure” shall mean any public disclosure of
material non-public information, which disclosure, in the good faith judgment of the Chief Executive Officer or principal financial officer of the Company, after consultation with counsel to the Company,
(i) would be required to be made in any Registration Statement or Prospectus in order for the applicable Registration Statement or Prospectus not to contain any untrue statement of a material fact or omit to state a material fact necessary to
make the statements contained therein (in the case of any prospectus and any preliminary prospectus, in the light of the circumstances under which they were made) not misleading, (ii) would not be required to be made at such time if the
Registration Statement were not being filed, and (iii) the Company has a bona fide business purpose for not making such information public. 

“Agreement” shall have the meaning given in the Preamble. 

“Board” shall mean the Board of Directors of the Company. 

“Business Combination” shall mean any merger, capital stock exchange, asset acquisition, stock purchase,
reorganization or other similar business combination with one or more businesses, involving the Company. 

“Commission” shall mean the Securities and Exchange Commission. 

“Common Stock” shall have the meaning given in the Recitals hereto. 

“Company” shall have the meaning given in the Preamble. 

“Demand Registration” shall have the meaning given in subsection 2.1.1. 

“Demanding Holder” shall have the meaning given in subsection 2.1.1. 

“Exchange Act” shall mean the Securities Exchange Act of 1934, as it may be amended from time to time. 

“Form S-1” shall have the meaning given in subsection 2.1.1. 

“Form S-3” shall have the meaning given in subsection 2.3. 

“Forward Purchase Agreement” shall have the meaning given in the Recitals hereto. 

  
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 “Forward Purchaser” shall have the meaning given in the Recitals
hereto. 
 “Forward Purchase Units” shall have the meaning given in the Recitals hereto. 

“Founder Shares” shall have the meaning given in the Recitals hereto and shall be deemed to include the shares of
Common Stock issuable upon conversion thereof. 
 “Founder Shares Lock-up
Period” shall mean, with respect to the Founder Shares, the period ending on the earlier of (A) one year after the completion of the Company’s initial Business Combination and (B) subsequent to the Business Combination,
(x) if the closing price of the Common Stock equals or exceeds $12.00 per share (as adjusted for stock splits, stock dividends, reorganizations, recapitalizations and the like) for any 20 trading days within any
30-trading day period commencing at least 150 days after the Company’s initial Business Combination or (y) the date on which the Company completes a liquidation, merger, capital stock exchange,
reorganization or other similar transaction that results in all of the Company’s stockholders having the right to exchange their shares of Common Stock for cash, securities or other property. 

“Holders” shall have the meaning given in the Preamble. 

“Insider Letter” shall mean that certain letter agreement, dated as of February 23, 2021, by and among the
Company, the Sponsor and each of the Company’s officers, directors and director nominees. 
 “Maximum Number of
Securities” shall have the meaning given in subsection 2.1.4. 
 “Misstatement” shall mean an
untrue statement of a material fact or an omission to state a material fact required to be stated in a Registration Statement or Prospectus, or necessary to make the statements in a Registration Statement or Prospectus (in the light of the
circumstances under which they were made) not misleading. 
 “Permitted Transferees” shall mean any person or entity
to whom a Holder of Registrable Securities is permitted to transfer such Registrable Securities prior to the expiration of the Founder Shares Lock-up Period, Private Placement
Lock-up Period or any other lock-up period, as the case may be, under the Insider Letter, the Private Placement Warrants Purchase Agreement, the Forward Purchase
Agreement this Agreement and any other applicable agreement between such Holder and the Company, and to any transferee thereafter. 

“Piggyback Registration” shall have the meaning given in subsection 2.2.1. 

“Private Placement Lock-up Period” shall mean, with respect to Private
Placement Warrants that are held by the initial purchasers of such Private Placement Warrants or their Permitted Transferees, the Private Placement Warrants and shares of Common Stock issuable upon the exercise or conversion of the Private Placement
Warrants, and that are held by the initial purchasers of the Private Placement Warrants or their Permitted Transferees, the period ending 30 days after the completion of the Company’s initial Business Combination. 

“Private Placement Warrants” shall have the meaning given in the Recitals hereto. 

  
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 “Private Placement Warrants Purchase Agreement” shall have the
meaning given in the Recitals hereto. 
 “Pro Rata” shall have the meaning given in subsection 2.1.4. 

“Prospectus” shall mean the prospectus included in any Registration Statement, as supplemented by any and all
prospectus supplements and as amended by any and all post-effective amendments and including all material incorporated by reference in such prospectus. 

“Registrable Security” shall mean (a) the Founder Shares and the shares of Common Stock issued or issuable upon
the conversion of the Founder Shares, (b) the Private Placement Warrants (including any shares of Common Stock issued or issuable upon the exercise of the Private Placement Warrants), (c) the Forward Purchase Units (including any shares of
Common Stock and private placement warrants included in such Forward Purchase Units and any shares of Common Stock issued or issuable upon the exercise of the private placement warrants underlying the Forward Purchase Units), (d) any outstanding
shares of Common Stock or any other equity security (including the shares of Common Stock issued or issuable upon the exercise of any other equity security) of the Company held by a Holder as of the date of this Agreement, (e) any equity
securities (including the shares of Common Stock issued or issuable upon the exercise of any such equity security) of the Company issuable upon conversion of any working capital loans in an amount up to $1,500,000 made to the Company by a Holder
(including the Working Capital Warrants and shares of Common Stock issued or issuable upon the exercise of the Working Capital Warrants) and (f) any other equity security of the Company issued or issuable with respect to any such share of
Common Stock by way of a stock dividend or stock split or in connection with a combination of shares, recapitalization, merger, consolidation or reorganization; provided, however, that, as to any particular Registrable Security, 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 such securities not bearing a legend restricting further transfer shall have been delivered
by the Company and subsequent public distribution of such securities shall not require registration under the Securities Act; (C) such securities shall have ceased to be outstanding; (D) such securities may be sold without registration
pursuant to Rule 144 promulgated under the Securities Act (or any successor rule promulgated thereafter by the Commission) (but with no volume or other restrictions or limitations); or (E) such securities have been sold to, or through, a
broker, dealer or underwriter in a public distribution or other public securities transaction. 
 “Registration”
shall 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. 
 “Registration Expenses” shall mean the out-of-pocket expenses of a Registration, including, without limitation, the following: 

  
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 (A) all registration and filing fees (including fees with respect to filings required to be
made with the Financial Industry Regulatory Authority, Inc.) and any securities exchange on which the Common Stock is then listed; 
 (B)
fees and expenses of compliance with securities or blue sky laws (including reasonable fees and disbursements of counsel for the Underwriters in connection with blue sky qualifications of Registrable Securities); 

(C) printing, messenger, telephone and delivery expenses; 

(D) reasonable fees and disbursements of counsel for the Company; 

(E) reasonable fees and disbursements of all independent registered public accountants of the Company incurred specifically in connection with
such Registration; and 
 (F) reasonable fees and expenses of one (1) legal counsel selected by the majority-in-interest of the Demanding Holders initiating a Demand Registration to be registered for offer and sale in the applicable Registration. 

“Registration Statement” shall mean any registration statement that covers the Registrable Securities pursuant to the
provisions of this Agreement, including the Prospectus included in such registration statement, amendments (including post-effective amendments) and supplements to such registration statement, and all exhibits to and all material incorporated by
reference in such registration statement. 
 “Requesting Holder” shall have the meaning given in subsection
2.1.1. 
 “Securities Act” shall mean the Securities Act of 1933, as amended from time to time. 

“Sponsor” shall have the meaning given in the Recitals hereto. 

“Underwriter” shall mean 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. 
 “Underwritten Registration” or
“Underwritten Offering” shall mean a Registration in which securities of the Company are sold to an Underwriter in a firm commitment underwriting for distribution to the public. 

“Working Capital Warrants” shall have the meaning given in the Recitals hereto. 

ARTICLE II 

REGISTRATIONS 
 2.1
Demand Registration. 
 2.1.1 Request for Registration. Subject to the provisions of subsection 2.1.4 and
Section 2.4 hereof, at any time and from time to time on or after the date the Company consummates the Business Combination, the Holders of at least fifteen percent (15%) of the 

  
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then-outstanding number of Registrable Securities (the “Demanding Holders”) may make a written demand for Registration of all or part of their Registrable Securities,
which written demand shall describe the amount and type of securities to be included in such Registration and the intended method(s) of distribution thereof (such written demand a “Demand Registration”). The Company shall,
within ten (10) days of the Company’s receipt of the Demand Registration, notify, in writing, all other Holders of Registrable Securities of such demand, and each Holder of Registrable Securities who thereafter wishes to include all or a
portion of such Holder’s Registrable Securities in a Registration pursuant to a Demand Registration (each such Holder that includes all or a portion of such Holder’s Registrable Securities in such Registration, a “Requesting
Holder”) shall so notify the Company, in writing, within five (5) days after the receipt by the Holder of the notice from the Company. Upon receipt by the Company of any such written notification from a Requesting Holder(s) to the
Company, such Requesting Holder(s) shall be entitled to have their Registrable Securities included in a Registration pursuant to a Demand Registration and the Company shall effect, as soon thereafter as practicable, but not more than forty-five
(45) days immediately after the Company’s receipt of the Demand Registration, the Registration of all Registrable Securities requested by the Demanding Holders and Requesting Holders pursuant to such Demand Registration. Under no
circumstances shall the Company be obligated to effect more than an aggregate of three (3) Registrations pursuant to a Demand Registration under this subsection 2.1.1 with respect to any or all Registrable Securities; provided,
however, that a Registration shall not be counted for such purposes unless a Form S-1 or any similar long-form registration statement that may be available at such time (“Form S-1”) has become effective and all of the Registrable Securities requested by the Requesting Holders to be registered on behalf of the Requesting Holders in such Form
S-1 Registration have been sold, in accordance with Section 3.1 of this Agreement. 

2.1.2 Effective Registration. Notwithstanding the provisions of subsection 2.1.1 above or any other part of this Agreement, a
Registration pursuant to a Demand Registration shall not count as a Registration unless and until (i) the Registration Statement filed with the Commission with respect to a Registration pursuant to a Demand Registration has been declared
effective by the Commission and (ii) the Company has complied with all of its obligations under this Agreement with respect thereto; provided, further, that if, after such Registration Statement has been declared effective, an
offering of Registrable Securities in a Registration pursuant to a Demand Registration is subsequently interfered with by any stop order or injunction of the Commission, federal or state court or any other governmental agency the Registration
Statement with respect to such Registration shall 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 initiating such Demand Registration thereafter affirmatively elect to continue with such Registration and accordingly
notify the Company in writing, but in no event later than five (5) days, of such election; and provided, further, that the Company shall not be obligated or required to file another Registration Statement until the Registration Statement
that has been previously filed with respect to a Registration pursuant to a Demand Registration becomes effective or is subsequently terminated. 

2.1.3 Underwritten Offering. Subject to the provisions of subsection 2.1.4 and Section 2.4 hereof, if
a majority-in-interest of the Demanding Holders so advise the Company as part of their Demand Registration that the offering of the Registrable Securities pursuant to
such Demand Registration shall be in the form of an Underwritten Offering, then the right of such 

  
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Demanding Holder or Requesting Holder (if any) to include its Registrable Securities in such Registration shall be conditioned upon such Holder’s participation in such Underwritten Offering
and the inclusion of such Holder’s Registrable Securities in such Underwritten Offering to the extent provided herein. All such Holders proposing to distribute their Registrable Securities through an Underwritten Offering under this
subsection 2.1.3 shall enter into an underwriting agreement in customary form with the Underwriter(s) selected for such Underwritten Offering by the
majority-in-interest of the Demanding Holders initiating the Demand Registration. 

2.1.4 Reduction of Underwritten Offering. If the managing Underwriter or Underwriters in an Underwritten Registration pursuant to a
Demand Registration, in good faith, advises the Company, the Demanding Holders and the Requesting Holders (if any) in writing that the dollar amount or number of Registrable Securities that the Demanding Holders and the Requesting Holders (if any)
desire to sell, taken together with all other Common Stock or other equity securities that the Company desires to sell and the Common Stock, if any, as to which a Registration has been requested pursuant to separate written contractual piggy-back
registration rights held by any other stockholders who desire to sell, exceeds the maximum dollar amount or maximum number of equity securities that can be sold in the Underwritten 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 such securities, as applicable, the “Maximum Number of Securities”), then the Company shall
include in such Underwritten Offering, as follows: (i) first, the Registrable Securities of the Demanding Holders and the Requesting Holders (if any) (pro rata based on the respective number of Registrable Securities that each Demanding Holder
and Requesting Holder (if any) has requested be included in such Underwritten Registration and the aggregate number of Registrable Securities that the Demanding Holders and Requesting Holders have requested be included in such Underwritten
Registration (such proportion is referred to herein as “Pro Rata”)) that can be sold without exceeding the Maximum Number of Securities; (ii) second, to the extent that the Maximum Number of Securities has not been
reached under the foregoing clause (i), the Registrable Securities of Holders (Pro Rata, based on the respective number of Registrable Securities that each Holder has so requested) exercising their rights to register their Registrable Securities
pursuant to subsection 2.2.1 hereof, without exceeding the Maximum Number of Securities; and (iii) third, to the extent that the Maximum Number of Securities has not been reached under the foregoing clauses (i) and (ii), the Common
Stock or other equity securities that the Company desires to sell, which can be sold without exceeding the Maximum Number of Securities; and (iv) fourth, to the extent that the Maximum Number of Securities has not been reached under the
foregoing clauses (i), (ii) and (iii), the Common Stock or other equity securities of other persons or entities that the Company is obligated to register in a Registration pursuant to separate written contractual arrangements with such persons and
that can be sold without exceeding the Maximum Number of Securities. 
 2.1.5 Demand Registration Withdrawal. A majority-in-interest of the Demanding Holders initiating a Demand Registration or a
majority-in- interest of the Requesting Holders (if any), pursuant to a Registration under subsection 2.1.1 shall have the right to withdraw from a Registration
pursuant to such Demand Registration for any or no reason whatsoever upon written notification to the Company and the Underwriter or Underwriters (if any) of their intention to withdraw from such Registration prior to the effectiveness of the
Registration Statement filed with the Commission with respect to the Registration of their Registrable Securities pursuant to 

  
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such Demand Registration. Notwithstanding anything to the contrary in this Agreement, the Company shall be responsible for the Registration Expenses incurred in connection with a Registration
pursuant to a Demand Registration prior to its withdrawal under this subsection 2.1.5. 
 2.2 Piggyback Registration. 

2.2.1 Piggyback 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, for its own account or for the
account of stockholders of the Company (or by the Company and by the stockholders of the Company including, without limitation, pursuant to Section 2.1 hereof), 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 give written notice of such proposed filing to all of the Holders of Registrable Securities as soon as practicable but not less than ten (10) days
before the anticipated filing date of such Registration Statement, which notice shall (A) 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, in such offering, and (B) offer to all of the Holders of Registrable Securities the opportunity to register the sale of such number of Registrable Securities as such Holders may request in writing within
five (5) days after receipt of such written notice (such Registration a “Piggyback Registration”). The Company shall, in good faith, cause such Registrable Securities to be included in such Piggyback 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 by the Holders pursuant to this subsection 2.2.1 to be included in a Piggyback
Registration on the same terms and conditions as any similar securities of the Company included in such Registration and to permit the sale or other disposition of such Registrable Securities in accordance with the intended method(s) of distribution
thereof. All such Holders proposing to distribute their Registrable Securities through an Underwritten Offering under this subsection 2.2.1 shall enter into an underwriting agreement in customary form with the Underwriter(s) selected for such
Underwritten Offering by the Company. 
 2.2.2 Reduction of Piggyback Registration. If the managing Underwriter or Underwriters in an
Underwritten Registration that is to be a Piggyback Registration, in good faith, advises the Company and the Holders of Registrable Securities participating in the Piggyback Registration in writing that the dollar amount or number of the shares of
Common Stock that the Company desires to sell, taken together with (i) the 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 (ii) the Registrable Securities as to which registration has been requested pursuant to Section 2.2 hereof, and (iii) the shares of Common Stock, if any, as to which
Registration has been requested pursuant to separate written contractual piggy-back registration rights of other stockholders of the Company, exceeds the Maximum Number of Securities, then: 

  
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 (a) If the Registration is undertaken for the Company’s account, the Company shall
include in any such Registration (A) first, the Common Stock or other equity securities that the Company desires to sell, which can be sold without exceeding the Maximum Number of Securities; (B) second, to the extent that the Maximum
Number of Securities has not been reached under the foregoing clause (A), the Registrable Securities of Holders exercising their rights to register their Registrable Securities pursuant to subsection 2.2.1 hereof (pro rata based on the
respective number of Registrable Securities that such Holder has requested be included in such Registration), which can be sold without exceeding the Maximum Number of Securities; and (C) third, to the extent that the Maximum Number of
Securities has not been reached under the foregoing clauses (A) and (B), the Common Stock, if any, as to which Registration has been requested pursuant to written contractual piggy-back registration rights of other stockholders of the Company,
which can be sold without exceeding the Maximum Number of Securities; 
 (b) If the Registration is pursuant to a request by persons or
entities other than the Holders of Registrable Securities, then the Company shall include in any such Registration (A) first, the Common Stock or other equity securities, if any, of such requesting persons or entities, other than the Holders of
Registrable Securities, which can be sold without exceeding the Maximum Number of Securities; (B) second, to the extent that the Maximum Number of Securities has not been reached under the foregoing clause (A), the Registrable Securities of
Holders exercising their rights to register their Registrable Securities pursuant to subsection 2.2.1, pro rata based on the number of Registrable Securities that each Holder has requested be included in such Registration and the aggregate
number of Registrable Securities that the Holders have requested to be included in such Registration, which can be sold without exceeding the Maximum Number of Securities; (C) third, to the extent that the Maximum Number of Securities has not
been reached under the foregoing clauses (A) and (B), the Common Stock or other equity securities that the Company desires to sell, which can be sold without exceeding the Maximum Number of Securities; and (D) fourth, to the extent that
the Maximum Number of Securities has not been reached under the foregoing clauses (A), (B) and (C), the Common Stock or other equity securities for the account of other persons or entities that the Company is obligated to register pursuant to
separate written contractual arrangements with such persons or entities, which can be sold without exceeding the Maximum Number of Securities. 

2.2.3 Piggyback Registration Withdrawal. Any Holder of Registrable Securities shall have the right to withdraw from a Piggyback
Registration for any or no reason whatsoever upon written notification to the Company and the Underwriter or Underwriters (if any) of his, her or its intention to withdraw from such Piggyback Registration prior to the effectiveness of the
Registration Statement filed with the Commission with respect to such Piggyback Registration. The Company (whether on its own good faith determination or as the result of a request for withdrawal by persons pursuant to separate written contractual
obligations) may withdraw a Registration Statement filed with the Commission in connection with a Piggyback Registration at any time prior to the effectiveness of such Registration Statement. Notwithstanding anything to the contrary in this
Agreement, the Company shall be responsible for the Registration Expenses incurred in connection with the Piggyback Registration prior to its withdrawal under this subsection 2.2.3. 

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

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 their Registrable Securities on Form S-3 or any similar short form registration statement that 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. Within five (5) days of the Company’s receipt of a written request from a Holder or Holders of Registrable Securities for a Registration on Form S-3, the Company shall promptly give written notice of the proposed Registration on Form S-3 to all other Holders of Registrable Securities, and each Holder of Registrable
Securities who thereafter wishes to include all or a portion of such Holder’s Registrable Securities in such Registration on Form S-3 shall so notify the Company, in writing, within ten (10) days
after the receipt by the Holder of the notice from the Company. As soon as practicable thereafter, but not more than twelve (12) days after the Company’s initial receipt of such written request for a Registration on Form S-3, the Company shall register all or such portion of such Holder’s Registrable Securities as are specified in such written request, together with all or such portion of Registrable Securities of any other
Holder or Holders joining in such request as are specified in the written notification given by such Holder or Holders; provided, however, that the Company shall not be obligated to effect any such Registration pursuant to
Section 2.3 hereof if (i) a Form S-3 is not available for such offering; or (ii) the Holders of Registrable Securities, together with the Holders of any other equity
securities of the Company entitled to inclusion in such Registration, propose to sell the Registrable Securities and such other equity securities (if any) at any aggregate price to the public of less than $10,000,000. 

2.4 Restrictions on Registration Rights. If (A) during the period starting with the date sixty (60) days prior to the
Company’s good faith estimate of the date of the filing of, and ending on a date one hundred and twenty (120) days after the effective date of, a Company initiated Registration and provided that the Company has delivered written notice to
the Holders prior to receipt of a Demand Registration pursuant to subsection 2.1.1 and it continues to actively employ, in good faith, all reasonable efforts to cause the applicable Registration Statement to become effective; (B) the
Holders have requested an Underwritten Registration and the Company and the Holders are unable to obtain the commitment of underwriters to firmly underwrite the offer; or (C) in the good faith judgment of the Board such Registration would be
seriously detrimental to the Company and the Board concludes as a result that it is essential to defer the filing of such Registration Statement at such time, then in each case the Company shall furnish to such Holders a certificate signed by the
Chairman of the Board stating that in the good faith judgment of the Board it would be seriously detrimental to the Company for such Registration Statement to be filed in the near future and that it is therefore essential to defer the filing of such
Registration Statement. In such event, the Company shall have the right to defer such filing for a period of not more than thirty (30) days; provided, however, that the Company shall not defer its obligation in this manner more
than once in any 12-month period. 

  
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 ARTICLE III 

COMPANY PROCEDURES 
 3.1
General Procedures. If at any time on or after the date the Company consummates a Business Combination the Company is required to effect the Registration of Registrable Securities, the Company shall use its best efforts to effect such
Registration to permit the sale of such Registrable Securities in accordance with the intended plan of distribution thereof, and pursuant thereto the Company shall, as expeditiously as possible: 

3.1.1 prepare and file with the Commission as soon as practicable a Registration Statement with respect to such Registrable Securities and use
its reasonable best efforts to cause such Registration Statement to become effective and remain effective until all Registrable Securities covered by such Registration Statement have been sold; 

3.1.2 prepare and file with the Commission such amendments and post-effective amendments to the Registration Statement, and such supplements
to the Prospectus, as may be requested by the Holders or any Underwriter of Registrable Securities or as may be required by the rules, regulations or instructions applicable to the registration form used by the Company or by the Securities Act or
rules and regulations thereunder to keep the Registration Statement effective until all Registrable Securities covered by such Registration Statement are sold in accordance with the intended plan of distribution set forth in such Registration
Statement or supplement to the Prospectus; 
 3.1.3 prior to filing a Registration Statement or prospectus, or any amendment or supplement
thereto, furnish without charge to the Underwriters, if any, and 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 Underwriters and the Holders of Registrable Securities included in such Registration or the legal counsel for any such Holders may request in order to facilitate the disposition of the Registrable Securities owned by such
Holders; 
 3.1.4 prior to any public offering of Registrable Securities, 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 or
take any action to which it would be subject to general service of process or taxation in any such jurisdiction where it is not then otherwise so subject; 

  
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 3.1.5 cause all such Registrable Securities to be listed on each securities exchange or
automated quotation system on which similar securities issued by the Company are then listed; 
 3.1.6 provide a transfer agent or warrant
agent, as applicable, and registrar for all such Registrable Securities no later than the effective date of such Registration Statement; 

3.1.7 advise each seller of such Registrable Securities, promptly after it shall receive notice or obtain knowledge thereof, of the issuance
of any stop order by the Commission suspending the effectiveness of such Registration Statement or the initiation or threatening of any proceeding for such purpose and promptly use its reasonable best efforts to prevent the issuance of any stop
order or to obtain its withdrawal if such stop order should be issued; 
 3.1.8 at least five (5) days prior to the filing of any
Registration Statement or Prospectus or any amendment or supplement to such Registration Statement furnish a copy thereof to each seller of such Registrable Securities and its counsel, including, without limitation, providing copies promptly upon
receipt of any comment letters received with respect to any such Registration Statement or Prospectus; 
 3.1.9 notify the Holders at any
time when a Prospectus relating to such Registration Statement is required to be delivered under the Securities Act, of the happening of any event as a result of which the Prospectus included in such Registration Statement, as then in effect,
includes a Misstatement, and then to correct such Misstatement as set forth in Section 3.4 hereof; 
 3.1.10
permit a representative of the Holders (such representative to be selected by a majority of the participating Holders), the Underwriters, if any, and any attorney or accountant retained by such Holders or Underwriter to participate, at each such
person’s own expense, in the preparation of the Registration Statement, and cause the Company’s officers, directors and employees to supply all information reasonably requested by any such representative, Underwriter, attorney or
accountant in connection with the Registration; provided, however, that such representatives or Underwriters enter into a confidentiality agreement, in form and substance reasonably satisfactory to the Company, prior to the release or
disclosure of any such information; and provided further, the Company may not include the name of any Holder or Underwriter or any information regarding any Holder or Underwriter in any Registration Statement or Prospectus, any amendment or
supplement to such Registration Statement or Prospectus, any document that is to be incorporated by reference into such Registration Statement or Prospectus, or any response to any comment letter, without the prior written consent of such Holder or
Underwriter and providing each such Holder or Underwriter a reasonable amount of time to review and comment on such applicable document, which comments the Company shall include unless contrary to applicable law; 

3.1.11 obtain a “cold comfort” letter from the Company’s independent registered public accountants in the event of an
Underwritten Registration which the participating Holders may rely on, in customary form and covering such matters of the type customarily covered by “cold comfort” letters as the managing Underwriter may reasonably request, and reasonably
satisfactory to a majority-in-interest of the participating Holders; 

  
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 3.1.12 on the date the Registrable Securities are delivered for sale pursuant to such
Registration, obtain an opinion, dated such date, of counsel representing the Company for the purposes of such Registration, addressed to the Holders, the placement agent or sales agent, if any, and the Underwriters, if any, covering such legal
matters with respect to the Registration in respect of which such opinion is being given as the Holders, placement agent, sales agent, or Underwriter may reasonably request and as are customarily included in such opinions and negative assurance
letters, and reasonably satisfactory to a majority in interest of the participating Holders; 
 3.1.13 in the event of any Underwritten
Offering, enter into and perform its obligations under an underwriting agreement, in usual and customary form, with the managing Underwriter of such offering; 

3.1.14 make available to its security holders, as soon as reasonably practicable, an earnings statement covering the period of at least twelve
(12) months beginning with the first day of the Company’s first full calendar quarter after the effective date of the Registration Statement which satisfies the provisions of Section 11(a) of the Securities Act
and Rule 158 thereunder (or any successor rule promulgated thereafter by the Commission); 
 3.1.15 if the Registration involves the
Registration of Registrable Securities involving gross proceeds in excess of $25,000,000, 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; and 
 3.1.16 otherwise, in good faith, cooperate reasonably with, and
take such customary actions as may reasonably be requested by the Holders, in connection with such Registration. 
 3.2 Registration
Expenses. The Registration Expenses of all Registrations shall be borne by the Company. It is acknowledged by the Holders that the Holders shall bear all incremental selling expenses relating to the sale of Registrable Securities, such as
Underwriters’ commissions and discounts, brokerage fees, Underwriter marketing costs and, other than as set forth in the definition of “Registration Expenses,” all reasonable fees and expenses of any legal counsel representing the
Holders. 
 3.3 Requirements for Participation in Underwritten Offerings. No person may participate in any Underwritten Offering for
equity securities of the Company pursuant to a Registration initiated by the Company hereunder unless such person (i) agrees to sell such person’s securities on the basis provided in any underwriting arrangements approved by the Company
and (ii) completes and executes all customary questionnaires, powers of attorney, indemnities, lock-up agreements, underwriting agreements and other customary documents as may be reasonably required under
the terms of such underwriting arrangements. 

  
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 3.4 Suspension of Sales; Adverse Disclosure. Upon receipt of written notice from the
Company that a Registration Statement or Prospectus contains a Misstatement, each of the Holders shall forthwith discontinue disposition of Registrable Securities until he, she or it has received copies of a supplemented or amended Prospectus
correcting the Misstatement (it being understood that the Company hereby covenants to prepare and file such supplement or amendment as soon as practicable after the time of such notice), or until he, she or it is advised in writing by the Company
that the use of the Prospectus may be resumed. If the filing, initial effectiveness or continued use of a Registration Statement in respect of any Registration at any time would require the Company to make an Adverse Disclosure or would require the
inclusion in such Registration Statement of financial statements that are unavailable to the Company for reasons beyond the Company’s control, the Company may, upon giving prompt written notice of such action to the Holders, delay the filing or
initial effectiveness of, or suspend use of, such Registration Statement for the shortest period of time, but in no event more than thirty (30) days, determined in good faith by the Company to be necessary for such purpose. In the event the
Company exercises its rights under the preceding sentence, the Holders agree to suspend, immediately upon their receipt of the notice referred to above, their use of the Prospectus relating to any Registration in connection with any sale or offer to
sell Registrable Securities. The Company shall immediately notify the Holders of the expiration of any period during which it exercised its rights under this Section 3.4. 

3.5 Reporting Obligations. As long as any Holder shall own Registrable Securities, the Company, at all times while it shall be a
reporting company under the Exchange Act, covenants to file timely (or obtain extensions in respect thereof and file within the applicable grace period) all reports required to be filed by the Company after the date hereof pursuant to Sections
13(a) or 15(d) of the Exchange Act and to promptly furnish the Holders with true and complete copies of all such filings. The Company further covenants that it shall take such further action as any Holder may reasonably request, all to
the extent required from time to time to enable such Holder to sell shares of Common Stock held by such Holder without registration under the Securities Act within the limitation of the exemptions provided by Rule 144 promulgated under the
Securities Act (or any successor rule promulgated thereafter by the Commission), including providing any legal opinions. Upon the request of any Holder, the Company shall deliver to such Holder a written certification of a duly authorized officer as
to whether it has complied with such requirements. 
 ARTICLE IV 

INDEMNIFICATION AND CONTRIBUTION 

4.1 Indemnification. 

4.1.1 The Company agrees to indemnify, to the extent permitted by law, each Holder of Registrable Securities, its officers and directors and
each person who controls such Holder (within the meaning of the Securities Act) against all losses, claims, damages, liabilities and expenses (including attorneys’ fees) caused by any untrue or alleged untrue statement of material fact
contained in any Registration Statement, Prospectus or preliminary Prospectus or any amendment thereof or supplement thereto or any omission or alleged omission of a material fact required to be stated therein or necessary to make the statements
therein not misleading, except insofar as the same are caused by or contained in any information furnished in writing to the Company by such Holder expressly for use therein. The Company shall indemnify the Underwriters, their officers and directors
and each person who controls such Underwriters (within the meaning of the Securities Act) to the same extent as provided in the foregoing with respect to the indemnification of the Holder. 

  
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 4.1.2 In connection with any Registration Statement in which a Holder of Registrable
Securities is participating, such Holder shall furnish to the Company in writing such information and affidavits as the Company reasonably requests for use in connection with any such Registration Statement or Prospectus and, to the extent permitted
by law, shall indemnify the Company, its directors and officers and agents and each person who controls the Company (within the meaning of the Securities Act) against any losses, claims, damages, liabilities and expenses (including without
limitation reasonable attorneys’ fees) resulting from any untrue statement of material fact contained in the Registration Statement, Prospectus or preliminary Prospectus or any amendment thereof or supplement thereto or any omission of a
material fact required to be stated therein or necessary to make the statements therein not misleading, but only to the extent that such untrue statement or omission is contained in any information or affidavit so furnished in writing by such Holder
expressly for use therein; provided, however, that the obligation to indemnify shall be several, not joint and several, among such Holders of Registrable Securities, and the liability of each such Holder of Registrable Securities shall
be in proportion to and limited to the net proceeds received by such Holder from the sale of Registrable Securities pursuant to such Registration Statement. The Holders of Registrable Securities shall indemnify the Underwriters, their officers,
directors and each person who controls such Underwriters (within the meaning of the Securities Act) to the same extent as provided in the foregoing with respect to indemnification of the Company. 

4.1.3 Any person entitled to indemnification herein shall (i) give prompt written notice to the indemnifying party of any claim with
respect to which it seeks indemnification (provided that the failure to give prompt notice shall not impair any person’s right to indemnification hereunder to the extent such failure has not materially prejudiced the indemnifying party) and
(ii) unless in such indemnified party’s reasonable judgment a conflict of interest between such indemnified and indemnifying parties may exist with respect to such claim, permit such indemnifying party to assume the defense of such claim
with counsel reasonably satisfactory to the indemnified party. If such defense is assumed, the indemnifying party shall not be subject to any liability for any settlement made by the indemnified party without its consent (but such consent shall not
be unreasonably withheld). An indemnifying party who is not entitled to, or elects not to, assume the defense of a claim shall not be obligated to pay the fees and expenses of more than one counsel (plus local counsel) for all parties indemnified by
such indemnifying party with respect to such claim, unless in the reasonable judgment of any indemnified party a conflict of interest may exist between such indemnified party and any other of such indemnified parties with respect to such claim. No
indemnifying party shall, without the consent of the indemnified party, consent to the entry of any judgment or enter into any settlement which cannot be settled in all respects by the payment of money (and such money is so paid by the indemnifying
party pursuant to the terms of such settlement) or which settlement does not include as an unconditional term thereof the giving by the claimant or plaintiff to such indemnified party of a release from all liability in respect to such claim or
litigation. 

  
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 4.1.4 The indemnification provided for under this Agreement shall remain in full force and
effect regardless of any investigation made by or on behalf of the indemnified party or any officer, director or controlling person of such indemnified party and shall survive the transfer of securities. The Company and each Holder of Registrable
Securities participating in an offering also agrees to make such provisions as are reasonably requested by any indemnified party for contribution to such party in the event the Company’s or such Holder’s indemnification is unavailable for
any reason. 
 4.1.5 If the indemnification provided under Section 4.1 hereof from the indemnifying party is
unavailable or insufficient to hold harmless an indemnified party in respect of any losses, claims, damages, liabilities and expenses referred to herein, then the indemnifying party, in lieu of indemnifying the indemnified party, shall contribute to
the amount paid or payable by the indemnified party as a result of such losses, claims, damages, liabilities and expenses in such proportion as is appropriate to reflect the relative fault of the indemnifying party and the indemnified party, as well
as any other relevant equitable considerations. The relative fault of the indemnifying party and indemnified party shall be determined by reference to, among other things, whether any action in question, including any untrue or alleged untrue
statement of a material fact or omission or alleged omission to state a material fact, was made by, or relates to information supplied by, such indemnifying party or indemnified party, and the indemnifying party’s and indemnified party’s
relative intent, knowledge, access to information and opportunity to correct or prevent such action; provided, however, that the liability of any Holder under this subsection 4.1.5 shall be limited to the amount of the net
proceeds received by such Holder in such offering giving rise to such liability. The amount paid or payable by a party as a result of the losses or other liabilities referred to above shall be deemed to include, subject to the limitations set forth
in subsections 4.1.1, 4.1.2 and 4.1.3 above, any legal or other fees, charges or expenses reasonably incurred by such party in connection with any investigation or proceeding. The parties hereto agree that it would not be just and
equitable if contribution pursuant to this subsection 4.1.5 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 this subsection 4.1.5.
No person guilty of fraudulent misrepresentation (within the meaning of Section 11(f) of the Securities Act) shall be entitled to contribution pursuant to this subsection 4.1.5 from any person who was not guilty of
such fraudulent misrepresentation. 
 ARTICLE V 

MISCELLANEOUS 
 5.1
Notices. Any notice or communication under this Agreement must be in writing and given by (i) deposit in the United States mail, addressed to the party to be notified, postage prepaid and registered or certified with return receipt
requested, (ii) delivery in person or by courier service providing evidence of delivery, or (iii) transmission by hand delivery, electronic mail, telecopy, telegram or facsimile. Each notice or communication that is mailed, delivered, or
transmitted in the manner described above shall be deemed sufficiently given, served, sent, and received, in the case of mailed notices, on the third business day following the date on which it is mailed and, in the case of notices delivered by
courier service, hand delivery, electronic mail, telecopy, telegram or facsimile, at such time as it is delivered to the addressee (with the delivery receipt or the affidavit of messenger) or at such time as delivery is refused by the addressee upon
presentation. Any notice or communication under this Agreement must be addressed, if to the Company, to: 570 Lexington Avenue, 35th Floor, New York, NY 10022, and, if to any Holder, at such Holder’s address or contact information as set forth
in the Company’s books and records. Any party may change its address for notice at any time and from time to time by written notice to the other parties hereto, and such change of address shall become effective thirty (30) days after
delivery of such notice as provided in this Section 5.1. 

  
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 5.2 Assignment; No Third Party Beneficiaries. 

5.2.1 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. 
 5.2.2 Prior to the expiration of the Founder Shares Lock-up Period or the Private
Placement Lock-up Period, as the case may be, no Holder may assign or delegate such Holder’s rights, duties or obligations under this Agreement, in whole or in part, except in connection with a transfer
of Registrable Securities by such Holder to a Permitted Transferee but only if such Permitted Transferee agrees to become bound by the transfer restrictions set forth in this Agreement. 

5.2.3 This Agreement and the provisions hereof shall be binding upon and shall inure to the benefit of each of the parties and its successors
and the permitted assigns of the Holders, which shall include Permitted Transferees. 
 5.2.4 This Agreement shall not confer any rights or
benefits on any persons that are not parties hereto, other than as expressly set forth in this Agreement and Section 5.2 hereof. 

5.2.5 No assignment by any party hereto of such party’s rights, duties and obligations hereunder shall be binding upon or obligate the
Company unless and until the Company shall have received (i) written notice of such assignment as provided in Section 5.1 hereof and (ii) the written agreement of the assignee, in a form reasonably satisfactory to
the Company, to be bound by the terms and provisions of this Agreement (which may be accomplished by an addendum or certificate of joinder to this Agreement). Any transfer or assignment made other than as provided in this
Section 5.2 shall be null and void. 
 5.3 Counterparts. This Agreement may be executed in multiple
counterparts (including facsimile or PDF counterparts), each of which shall be deemed an original, and all of which together shall constitute the same instrument, but only one of which need be produced. 

5.4 Governing Law; Venue. NOTWITHSTANDING THE PLACE WHERE THIS AGREEMENT MAY BE EXECUTED BY ANY OF THE PARTIES HERETO, THE PARTIES
EXPRESSLY AGREE THAT (I) THIS AGREEMENT SHALL BE GOVERNED BY AND CONSTRUED UNDER THE LAWS OF THE STATE OF NEW YORK AS APPLIED TO AGREEMENTS AMONG NEW YORK RESIDENTS ENTERED INTO AND TO BE PERFORMED ENTIRELY WITHIN NEW YORK AND (II) THE
VENUE FOR ANY ACTION TAKEN WITH RESPECT TO THIS AGREEMENT SHALL BE ANY STATE OR FEDERAL COURT IN NEW YORK COUNTY IN THE STATE OF NEW YORK. 

5.5 Amendments and Modifications. Upon the written consent of the Company and the Holders of at least a majority in interest of the
Registrable Securities at the time in question, compliance with any of the provisions, covenants and conditions set forth in this Agreement may be waived, or any of such provisions, covenants or conditions may be amended or modified;
provided, however, that notwithstanding the foregoing, any amendment hereto or waiver hereof 

  
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that adversely affects one Holder, solely in his, her or its capacity as a holder of the shares of capital stock of the Company, in a manner that is materially different from the other Holders
(in such capacity) shall require the consent of the Holder so affected. No course of dealing between any Holder or the Company and any other party hereto or any failure or delay on the part of a Holder or the Company in exercising any rights or
remedies under this Agreement shall operate as a waiver of any rights or remedies of any Holder or the Company. No single or partial exercise of any rights or remedies under this Agreement by a party shall operate as a waiver or preclude the
exercise of any other rights or remedies hereunder or thereunder by such party. 
 5.6 Other Registration Rights. The Company
represents and warrants that no person, other than a Holder of Registrable Securities, has any right to require the Company to register any securities of the Company for sale or to include such securities of the Company in any Registration filed by
the Company for the sale of securities for its own account or for the account of any other person. Further, the Company represents and warrants that this Agreement supersedes any other registration rights agreement or agreement with similar terms
and conditions and in the event of a conflict between any such agreement or agreements and this Agreement, the terms of this Agreement shall prevail. 

5.7 Term. This Agreement shall terminate upon the earlier of (i) the tenth anniversary of the date of this Agreement or
(ii) the date as of which (A) all of the Registrable Securities have been sold pursuant to a Registration Statement (but in no event prior to the applicable period referred to in Section 4(a)(3) of the Securities Act and Rule 174
thereunder (or any successor rule promulgated thereafter by the Commission)) or (B) the Holders of all Registrable Securities are permitted to sell the Registrable Securities without registration pursuant to Rule 144 (or any similar provision)
under the Securities Act with no volume or other restrictions or limitations. The provisions of Section 3.5 and Article IV shall survive any termination. 

[Signature Page Follows] 

  
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 IN WITNESS WHEREOF, the undersigned have caused this Agreement to be executed as of the date first
written above. 
  

			
	COMPANY:
	
	HUDSON EXECUTIVE INVESTMENT CORP. III, a Delaware corporation
		
	By:	 	 /s/ Jonathan Dobres

		 	Name: Jonathan Dobres
		 	Title: Chief Financial Officer
	
	HOLDERS:
	
	HEC SPONSOR III LLC, a Delaware limited liability company
		
	By:	 	 /s/ Douglas L. Braunstein

		 	Name: Douglas L. Braunstein
		 	Title: Manager
	
	HEC MASTER FUND LP, a Cayman Islands exempted limited partnership
	
	 By: HEC Performance GP LLC, its General Partner

	
	 By: HEC Management GP LLC, its Managing Member

		
	By:	 	 /s/ Douglas L. Braunstein

		 	Name: Douglas L. Braunstein
		 	Title: Managing Member


 [Signature Page to Registration Rights Agreement]