Exhibit 10.4

REGISTRATION RIGHTS AGREEMENT

THIS REGISTRATION RIGHTS AGREEMENT (this “Agreement”), dated as of [•], 2025 is made and entered into by and among CH4 Natural Solutions Corporation, a Cayman Islands exempted company (the “Company”), CH4 Natural Solutions Acquisition Sponsor LLC, a Cayman Islands limited liability company (the “Sponsor”), [CH4 Natural Solutions Unit Holdings, LLC, a Delaware limited liability company (the “Unit Holder Sponsor” and, together with the Sponsor, the “Sponsor Entities”),] and the undersigned parties listed under Holder on the signature pages hereto (each such party, together with the Sponsor Entities 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 Sponsor, Jean Rogers, Jeffrey Tepper and Nate Zwald own an aggregate of 7,187,500 of the Company’s Class B ordinary shares, par value $0.0001 per share (the “Founder Shares”);

WHEREAS, the Founder Shares will automatically convert into the Company’s Class A ordinary shares, par value $0.0001 per share (the “Ordinary Shares”), at the time of the Company’s initial Business Combination (as defined below) on a one-for-one basis, subject to adjustment, on the terms and conditions provided in the Company’s amended and restated memorandum and articles of association, as may be further amended from time to time;

WHEREAS, on [•], 2025, the Company, the Unit Holder Sponsor, [•], [•] and [•] (collectively, the “Purchasers”) entered into that certain Private Placement Units Purchase Agreement, pursuant to which the Unit Holder Sponsor and the Purchasers agreed to purchase an aggregate of 750,000 private placement units (or 825,000 private placement units if the over-allotment option in connection with the Company’s initial public offering is exercised in full) (the “Private Placement Units”), each unit consisting of one Ordinary Share and one-third of one warrant (the “Private Placement Warrant”), in a private placement transaction occurring in connection with the closing of the Company’s initial public offering; 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 1

DEFINITIONS

1.1 Definitions. The terms defined in this Article 1 shall, for all purposes of this Agreement, have the respective meanings set forth below:

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

“Block Trade” shall have the meaning given to it in subsection 2.3.1 of this Agreement.

“Board” shall mean the board of directors of the Company.

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

“Commission” shall mean the U.S. Securities and Exchange Commission.

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

“Demanding Holder” shall mean any Holder or group of Holders, that together elects to dispose of Registrable Securities having an aggregate value of at least $25 million, at the time of the Underwritten Demand, under a Registration Statement pursuant to an Underwritten Offering.

“Effectiveness Period” shall have the meaning given in subsection 3.1.1 of this Agreement.

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

“Financial Counterparty” shall have the meaning given in subsection 2.3.1 of this Agreement.

“Founder Shares” shall have the meaning given in the Recitals hereto.

“Holder Indemnified Persons” shall have the meaning given in subsection 4.1.1 of this Agreement.

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

“Maximum Number of Securities” shall have the meaning given in subsection 2.1.4 of this Agreement.

“Misstatement” shall mean, in the case of a Registration Statement, an untrue statement of a material fact or an omission to state a material fact required to be stated therein, or necessary to make the statements therein not misleading, and in the case of a Prospectus, an untrue statement of a material fact or an omission to state a material fact necessary in order to make the statements therein, in the light of the circumstances under which they were made, not misleading.

“Ordinary Shares” shall have the meaning given in the Recitals hereto.

“Other Coordinated Offering” shall have the meaning given to it in subsection 2.3.1 of this Agreement.

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

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

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

“Pro Rata” shall have the meaning given in subsection 2.1.4 of this Agreement.

“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 Ordinary Shares issued or issuable upon the conversion of any Founder Shares, (b) the Private Placement Units (including the underlying Ordinary Shares, Private Placement Warrants and the Ordinary Shares issuable upon exercise of the Private Placement Warrants), (c) any outstanding Ordinary Shares or any other equity security (including the Ordinary Shares 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 or acquired prior to or in connection with the Business Combination, which, for the avoidance of doubt, shall include any Ordinary Shares received by a Holder on or after the date hereof as a distribution from the Sponsor Entities in connection with its liquidation and dissolution, (d) any equity securities (including the Ordinary Shares 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 and (e) any other equity security of the Company issued or issuable with respect to any such Ordinary Shares by way of a share capitalization or share sub-division or in connection with a combination of shares, merger, consolidation or reorganization; provided, however, that, as to any particular Registrable Securities, such securities shall cease to be Registrable Securities when: (i) 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; (ii) 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; (iii) such securities shall have ceased to be outstanding; or (iv) 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).

“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 any such registration statement having become effective by the Commission.

“Registration Expenses” shall mean the out-of-pocket expenses of a Registration, including, without limitation, the following:

(a) all registration and filing fees (including fees with respect to filings required to be made with the Financial Industry Regulatory Authority and any securities exchange on which the Ordinary Shares are 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);

(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 or Underwritten Offering;

(f) the fees and expenses incurred in connection with the listing of any Registrable Securities on each securities exchange or automated quotation system on which similar securities issued by the Company are then listed;

(g) the fees and expenses incurred by the Company in connection with any road show for any Underwritten Offerings; and

(h) reasonable fees and expenses of one (1) legal counsel selected jointly by the Demanding Holders initiating an Underwritten Demand, the Requesting Holders participating in an Underwritten Offering and the Holders participating in a Piggyback Registration, as applicable.

“Registration Statement” shall mean any registration statement under the Securities Act 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 2.1.3 of this Agreement.

“Securities Act” shall mean the Securities Act of 1933, as amended from time to time.

“Shelf Registration” shall have the meaning given in subsection 2.1.1 of this Agreement.

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

“Sponsor Entities” shall have the meaning given in the Preamble.

“Suspension Event” shall have the meaning given in Section 3.4 of this Agreement.

“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 Demand” shall have the meaning given in subsection 2.1.3 of this Agreement.

“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.

“Unit Holder Sponsor” shall have the meaning given in the Preamble.

ARTICLE 2

REGISTRATIONS

2.1 Registration.

2.1.1 Shelf Registration. The Company agrees that, within fifteen (15) business days after the consummation of the Business Combination, the Company will use commercially reasonable efforts to file with the Commission (at the Company’s sole cost and expense) a Registration Statement registering the resale or other disposition of the Registrable Securities (a “Shelf Registration”).

2.1.2 Effective Registration. The Company shall use commercially reasonable efforts to cause such Registration Statement to become effective by the Commission as soon as reasonably practicable after the initial filing of the Registration Statement. Subject to the limitations contained in this Agreement, the Company shall effect any Shelf Registration on such appropriate registration form of the Commission (a) as shall be selected by the Company and (b) as shall permit the resale or other disposition of the Registrable Securities by the Holders. If at any time a Registration Statement filed with the Commission pursuant to Section 2.1.1 is effective and a Holder provides written notice to the Company that it intends to effect an offering of all or part of the Registrable Securities included on such Registration Statement, the Company will use commercially reasonable efforts to amend or supplement such Registration Statement as may be necessary in order to enable such offering to take place in accordance with the terms of this Agreement.

2.1.3 Underwritten Offering. Subject to the provisions of subsection 2.1.4 and Sections 2.4 and 3.4 hereof, any Demanding Holder may make a written demand for an Underwritten Offering pursuant to a Registration Statement filed with the Commission in accordance with Section 2.1.1 (an “Underwritten Demand”). The Company shall, within ten (10) days of the Company’s receipt of the Underwritten Demand, notify, in writing, all other Holders of such demand, and each Holder who thereafter requests to include all or a portion of such Holder’s Registrable Securities in such Underwritten Offering pursuant to such Underwritten Demand (each such Holder that requests to include all or a portion of such Holder’s Registrable Securities in such Underwritten Offering, a “Requesting Holder”) shall so notify the Company, in writing, within two (2) days (one (1) day if such offering is an overnight

or bought Underwritten Offering) 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), such Requesting Holder(s) shall be entitled to have their Registrable Securities included in such Underwritten Offering pursuant to such Underwritten Demand. All such Holders proposing to distribute their Registrable Securities through such 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 Demanding Holders initiating such Underwritten Offering. Notwithstanding the foregoing, the Company is not obligated to effect more than an aggregate of three (3) Underwritten Offerings pursuant to this subsection 2.1.3 and is not obligated to effect an Underwritten Offering pursuant to this subsection 2.1.3 within ninety (90) days after the closing of an Underwritten Offering.

2.1.4 Reduction of Underwritten Offering. If the managing Underwriter or Underwriters in an Underwritten Offering pursuant to an Underwritten Demand, in good faith, advises the Company, the Demanding Holders, the Requesting Holders and other persons or entities holding Ordinary Shares or other equity securities of the Company that the Company is obligated to include pursuant to separate written contractual arrangements with such persons or entities (if any) in writing that the dollar amount or number of Registrable Securities or other equity securities of the Company requested to be included in such Underwritten Offering exceeds the maximum dollar amount or maximum number of equity securities of the Company 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: (a) first, the Registrable Securities of the Demanding Holders (pro rata based on the respective number of Registrable Securities that each Demanding Holder has requested be included in such Underwritten Offering and the aggregate number of Registrable Securities that the Demanding Holders have requested be included in such Underwritten Offering (such proportion is referred to herein as “Pro Rata”)) that 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 the Requesting Holders, Pro Rata, 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), Ordinary Shares or other equity securities of the Company that the Company desires to sell and that 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), Ordinary Shares or other equity securities of the Company held by other persons or entities that the Company is obligated to include pursuant to separate written contractual arrangements with such persons or entities and that can be sold without exceeding the Maximum Number of Securities.

2.2 Piggyback Registration.

2.2.1 Piggyback Rights. Subject to the provisions of subsection 2.2.2 and Sections 2.4 and 3.4 hereof, if, at any time on or after the date the Company consummates a Business Combination, the Company proposes to consummate an Underwritten Offering for its own account or for the account of shareholders of the Company, then the

Company shall give written notice of such proposed action to all of the Holders as soon as practicable, which notice shall (a) describe the amount and type of securities to be included, the intended method(s) of distribution and the name of the proposed managing Underwriter or Underwriters, if any, and (b) offer to all of the Holders the opportunity to include of such number of Registrable Securities as such Holders may request in writing within two (2) days (unless such offering is an overnight or bought Underwritten Offering, then one (1) day), in each case 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 reasonable 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 Piggyback Registration and to permit the resale or other disposition of such Registrable Securities in accordance with the intended method(s) of distribution thereof. All such Holders proposing to include Registrable Securities in 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 Offering 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 shares or equity securities of the Company that the Company desires to sell, taken together with (a) the shares or equity securities of the Company, if any, as to which the Underwritten Offering has been demanded pursuant to separate written contractual arrangements with persons or entities other than the Holders of Registrable Securities hereunder, (b) the Registrable Securities as to which a Piggyback Registration has been requested pursuant to this Section 2.2 and (c) the shares or equity securities of the Company, if any, as to which inclusion in the Underwritten Offering has been requested pursuant to separate written contractual piggyback registration rights of other shareholders of the Company, exceeds the Maximum Number of Securities, then:

(i) If the Underwritten Offering is undertaken for the Company’s account, the Company shall include in any such Underwritten Offering (A) first, the Ordinary Shares or other equity securities of the Company 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 requesting a Piggyback Registration pursuant to subsection 2.2.1, Pro Rata, 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), Ordinary Shares or other equity securities of the Company, if any, as to which inclusion in the Underwritten Offering has been requested pursuant to written contractual piggyback registration rights of other shareholders of the Company, which can be sold without exceeding the Maximum Number of Securities; or

(ii) If the Underwritten Offering is pursuant to a request by persons or entities other than the Holders of Registrable Securities, then the Company shall include in any such Underwritten Offering (A) first, Ordinary Shares or other equity securities of the Company,

if any, of such requesting persons or entities, other than the Holders, 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 requesting a Piggyback Registration pursuant to subsection 2.2.1, Pro Rata, 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), Ordinary Shares or other equity securities of the Company 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), Ordinary Shares or other equity securities of the Company 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 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 commencement of the Underwritten Offering. 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.

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

2.3 Block Trades Other Coordinated Offerings.

2.3.1 Notwithstanding any other provision of this Article 2, but subject to Sections 2.4 and 3.4, at any time and from time to time when an effective Registration Statement is on file with the Commission, if a Demanding Holder wishes to engage in (a) an underwritten registered offering not involving a “roadshow,” an offer commonly known as a “block trade” (a “Block Trade”) or (b) an “at the market” or similar registered offering through a broker, sales agent or distribution agent, whether as agent or principal, (an “Other Coordinated Offering”), in each case, with a total offering price reasonably expected to exceed, in the aggregate, $25 million, then if such Demanding Holder requires any assistance from the Company pursuant to this Section 2.3, such Holder shall notify the Company promptly of the Block Trade or Other Coordinated Offering at least five (5) business days prior to the day such offering is to commence and the Company shall use its commercially reasonable efforts to facilitate such Block Trade or Other Coordinated Offering; provided that the Demanding Holders representing a majority of the Registrable Securities wishing to engage in the Block Trade or Other Coordinated Offering shall use commercially reasonable efforts to work with the Company and any Underwriters or brokers, sales agents or placement agents (each, a “Financial Counterparty”) prior to making such request in order to facilitate preparation of the registration statement, prospectus and other offering documentation related to the Block Trade or Other Coordinated Offering.

2.3.2 Prior to the filing of the applicable “red herring” prospectus or prospectus supplement used in connection with a Block Trade or Other Coordinated Offering, a majority-in interest of the Demanding Holders initiating such Block Trade or Other Coordinated Offering shall have the right to withdraw from such Block Trade or Other Coordinated Offering for any or no reason whatsoever upon written notification to the Company, the Underwriter or Underwriters (if any) and Financial Counterparty (if any) of their intention to withdraw from such Block Trade or Other Coordinated Offering. Notwithstanding anything to the contrary in this Agreement, the Company shall be responsible for the Registration Expenses incurred in connection with a Block Trade or Other Coordinated Offering prior to its withdrawal under this subsection 2.3.2.

2.3.3 Notwithstanding anything to the contrary in this Agreement, Section 2.2 shall not apply to a Block Trade or Other Coordinated Offering initiated by a Demanding Holder pursuant to Section 2.3 of this Agreement.

2.3.4 The Demanding Holder in a Block Trade or Other Coordinated Offering shall have the right to select the Underwriters and Financial Counterparty (if any) for such Block Trade or Other Coordinated Offering (in each case, which shall consist of one or more reputable nationally recognized investment banks).

2.3.5 A Demanding Holder in the aggregate may demand no more than four (4) Block Trades or Other Coordinated Offerings pursuant to this Section 2.3 in any twelve (12) month period. For the avoidance of doubt, any Block Trade or Other Coordinated Offering effected pursuant to this Section 2.3 shall not be counted as a demand for an Underwritten Offering pursuant to subsection 2.1.3 hereof.

2.4 Restrictions on Registration Rights. If (a) the Holders have requested an Underwritten Offering pursuant to an Underwritten Demand and the Company and the Holders are unable to obtain the commitment of underwriters to firmly underwrite the offer; or (b) the Holders have requested an Underwritten Offering pursuant to an Underwritten Demand and in the good faith judgment of the Board such Underwritten Offering would be seriously detrimental to the Company and the Board concludes as a result that it is essential to defer the undertaking of such Underwritten Offering 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 to undertake such Underwritten Offering in the near future and that it is therefore essential to defer the undertaking of such Underwritten Offering. In such event, the Company shall have the right to defer such offering 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 twelve (12)-month period.

ARTICLE 3

COMPANY PROCEDURES

3.1 General Procedures. The Company shall use its reasonable best efforts to effect such Registration or Underwritten Offering to permit the resale or other disposition of such Registrable Securities in accordance with the intended plan of distribution thereof, and pursuant thereto the Company shall, as expeditiously as possible and to the extent applicable:

3.1.1 prepare and file with the Commission after the consummation of the Business Combination a Registration Statement with respect to such Registrable Securities and use commercially reasonable efforts to cause such Registration Statement to become effective in accordance with Section 2.1 hereof and remain effective, including filing a replacement Registration Statement, if necessary, until all Registrable Securities covered by such Registration Statement have been sold or are no longer outstanding (such period, the “Effectiveness Period”);

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 reasonably requested by the Holders or any Underwriter 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 or are no longer outstanding;

3.1.3 prior to filing a Registration Statement or Prospectus, or any amendment or supplement thereto, furnish without charge to the Underwriters or Financial Counterparty, if any, and the Holders of Registrable Securities included in such Registration or Underwritten Offering or Block Trade, 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 (including each preliminary Prospectus) and such other documents as the Underwriters and the Holders of Registrable Securities included in such Registration or Underwritten Offering or the legal counsel for any such Holders may reasonably request in order to facilitate the disposition of the Registrable Securities owned by such Holders; provided, that the Company will not have any obligation to provide any document pursuant to this clause that is available on the Commission’s EDGAR system;

3.1.4 prior to any Underwritten Offering of Registrable Securities, use commercially reasonable efforts to (a) 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 (b) 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;

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 or Underwritten Offering;

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 during the Effectiveness Period, furnish a conformed copy of each filing of any Registration Statement or Prospectus or any amendment or supplement to such Registration Statement or Prospectus or any document that is to be incorporated by reference into such Registration Statement or Prospectus, promptly after such filing of such documents with the Commission to each seller of such Registrable Securities or its counsel; provided, that the Company will not have any obligation to provide any document pursuant to this clause that is available on the Commission’s EDGAR system;

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;

3.1.10 subject to the provisions of this Agreement, notify the Holders of the happening of any event as a result of which a Misstatement exists, and then to correct such Misstatement as set forth in Section 3.4 hereof;

3.1.11 in the event of an Underwritten Offering, a Block Trade, an Other Coordinated Offering, or sale by a Financial Counterparty pursuant to such Registration, permit a representative of the Holders, the Underwriters or other Financial Counterparty facilitating such Underwritten Offering, Block Trade, Other Coordinated Offering or other sale pursuant to such Registration, 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 or the Prospectus, and cause the Company’s officers, directors and employees to supply all information reasonably requested by any such representative, Underwriter, Financial Counterparty, attorney or accountant in connection with the Registration; provided, however, that such representatives or Underwriters or Financial Counterparty enter into confidentiality agreements, in form and substance reasonably satisfactory to the Company, prior to the release or disclosure of any such information;

3.1.12 obtain a comfort letter from the Company’s independent registered public accountants in the event of an Underwritten Offering, a Block Trade, an Other Coordinated Offering, or sale by a Financial Counterparty pursuant to such Registration (subject to such Financial Counterparty providing such certification or representation reasonably requested by the Company’s independent registered public accountants and the Company’s counsel), in

customary form and covering such matters of the type customarily covered by comfort letters as the managing Underwriter may reasonably request, and reasonably satisfactory to a majority-in-interest of the participating Holders;

3.1.13 in the event of an Underwritten Offering, a Block Trade, an Other Coordinated Offering, or sale by a Financial Counterparty pursuant to such Registration, 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 participating Holders or the Financial Counterparty, 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 participating Holders, Financial Counterparty or Underwriter may reasonably request and as are customarily included in such opinions and negative assurance letters, and reasonably satisfactory to such participating Holders, Financial Counterparty or Underwriter;

3.1.14 in the event of an Underwritten Offering or a Block Trade, or an Other Coordinated Offering or sale by a Financial Counterparty pursuant to such Registration to which the Company has consented, to the extent reasonably requested by such Financial Counterparty in order to engage in such offering, allow the Underwriters or Financial Counterparty to conduct customary “underwriter’s due diligence” with respect to the Company;

3.1.15 in the event of any Underwritten Offering, a Block Trade, an Other Coordinated Offering or sale by a Financial Counterparty pursuant to such Registration, enter into and perform its obligations under an underwriting agreement or other purchase or sales agreement, in usual and customary form, with the managing Underwriter or the Financial Counterparty of such offering or sale;

3.1.16 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 (1st) 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);

3.1.17 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

3.1.18 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.

Notwithstanding the foregoing, the Company shall not be required to provide any documents or information to an Underwriter or Financial Counterparty if such Underwriter of Financial Counterparty has not then been named with respect to the applicable Underwritten Offering or other offering involving a registration as an Underwriter or Financial Counterparty, as applicable.

3.2 Registration Expenses. The Registration Expenses in respect 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 or entity may participate in any Underwritten Offering for equity securities of the Company pursuant to a Registration initiated by the Company hereunder unless such person or entity (a) agrees to sell such person’s or entity’s securities on the basis provided in any underwriting arrangements approved by the Company and (b) 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.

3.4 Suspension of Sales. Notwithstanding anything to the contrary in this Agreement, the Company shall be entitled to (A) delay or postpone the (i) initial effectiveness of any Registration Statement or (ii) launch of any Underwritten Offering, in each case, filed or requested pursuant to this Agreement, and (B) from time to time to require the Holders not to sell under any Registration Statement or Prospectus or to suspend the effectiveness thereof, if the negotiation or consummation of a transaction by the Company or its subsidiaries is pending or an event has occurred, which negotiation, consummation or event, the Board reasonably believes, upon the advice of legal counsel, would require additional disclosure by the Company in the applicable Registration Statement or Prospectus of material information that the Company has a bona fide business purpose for keeping confidential and the non-disclosure of which in the Registration Statement or Prospectus would be expected, in the reasonable determination of the Board, upon the advice of legal counsel, to cause the Registration Statement or Prospectus to fail to comply with applicable disclosure requirements (each such circumstance, a “Suspension Event”); provided, however, that the Company may not delay or suspend a Registration Statement, Prospectus or Underwritten Offering on more than two occasions, for more than sixty (60) consecutive calendar days, or more than ninety (90) total calendar days, in each case during any twelve (12)-month period. Upon receipt of any written notice from the Company of a Suspension Event while a Registration Statement filed pursuant to this Agreement is effective or if as a result of a Suspension Event a Misstatement exists, each Holder agrees that (i) it will immediately discontinue offers and sales of Registered Securities under each Registration Statement filed pursuant to this Agreement until the Holder receives copies of a supplemental or amended Prospectus (which the Company agrees to promptly prepare) that corrects the relevant misstatements or omissions and receives notice that any post-effective amendment has become effective or unless otherwise notified by the Company that it may resume such offers and sales and (ii) it will maintain the confidentiality of information included in such written notice delivered by the Company unless otherwise required by law or subpoena. If so directed by the Company, the Holders will deliver to the Company or, in Holders’ sole discretion destroy, all copies of each Prospectus covering Registrable Securities in Holders’ possession; provided, however, that this obligation to deliver or destroy shall not apply (A) to the extent the Holders are required to retain a copy of such Prospectus (x) to comply with applicable legal, regulatory, self-regulatory or professional requirements or (y) in accordance with a bona fide pre-existing

document retention policy or (B) to copies stored electronically on archival servers as a result of automatic data back-up.

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 Section 13(a) or 15(d) of the Exchange Act. 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 resell or otherwise dispose of Registrable Securities 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 4

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, directors, employees, advisors, agents, representatives, members and each person who controls such Holder (within the meaning of the Securities Act) (collectively, the “Holder Indemnified Persons”) against all losses, claims, damages, liabilities and expenses (including reasonable attorneys’ fees and inclusive of all reasonable attorneys’ fees arising out of the enforcement of each such persons’ rights under this Section 4.1) resulting from any Misstatement, except insofar as the same are caused by or contained or included in any information furnished in writing to the Company by or on behalf of such Holder Indemnified Person specifically for use therein.

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, severally and not jointly, indemnify the Company, its officers, directors, employees, advisors, agents, representatives and each person who controls the Company (within the meaning of the Securities Act) against any losses, claims, damages, liabilities and expenses (including reasonable attorneys’ fees and inclusive of all reasonable attorneys’ fees arising out of the enforcement of each such persons’ rights under this Section 4.1) resulting from any Misstatement, but only to the extent that the same are made in reliance on and in conformity with information relating to the Holder so furnished in writing to the Company by or on behalf of such Holder specifically for use therein. In no event shall the liability of any selling Holder hereunder be greater in amount than the net proceeds received by such Holder from the sale of Registrable Securities pursuant to such Registration Statement giving rise to such indemnification obligation.

4.1.3 Any person entitled to indemnification herein shall (a) 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 (b) 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 or there may be reasonable defenses available to the indemnified party that are different from or additional to those available to the indemnifying party, 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 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.

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, employee, advisor, agent, representative, member or controlling person of such indemnified party and shall survive the transfer of securities.

4.1.5 If the indemnification provided under this Section 4.1 is held by a court of competent jurisdiction to be unavailable to 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 to the extent permitted by law 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 a court of law by reference to, among other things, whether the Misstatement relates to information supplied by such indemnifying party or such 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 5

MISCELLANEOUS

5.1 Notices. Any notice or communication under this Agreement must be in writing and given by (a) deposit in the United States mail, addressed to the party to be notified, postage prepaid and registered or certified with return receipt requested, (b) delivery in person or by courier service or sent by overnight mail via a reputable overnight carrier, in each case providing evidence of delivery or (c) transmission by facsimile or email. 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 (3rd) business day following the date on which it is mailed, in the case of notices delivered by courier service, hand delivery or overnight mail, 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, and in the case of notices delivered by facsimile or email, at such time as it is successfully transmitted to the addressee. Any notice or communication under this Agreement must be addressed, if to the Company, or if to either of the Sponsor Entities, to: 712 Fifth Avenue, 36^th Floor, New York, NY 10019, or by email at: tsmith@riverstonellc.com, and, if to any other Holder, to the address of such Holder as it appears in the applicable register for the Registrable Securities or such other address as may be designated in writing by such Holder (including on the signature pages hereto). 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.

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 This Agreement and the provisions hereof shall be binding upon and shall inure to the benefit of each of the parties and its successors.

5.2.3 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 this Section 5.2.

5.2.4 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 (a) written notice of such assignment as provided in Section 5.1 hereof and (b) 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 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, WITHOUT REGARD TO THE CONFLICT OF LAW PROVISIONS OF SUCH JURISDICTION.

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 that adversely affects any Holder, solely in his, her or its capacity as a holder of the shares of the Company, in a manner that is materially different from the other Holders (in such capacity) shall require the consent of each such 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) a Holder of Registrable Securities, (b) the holders of the Company’s warrants pursuant to that certain Public Warrant Agreement and that certain Private Warrant Agreement, each dated as of [•], 2025, each by and between the Company and Continental Stock Transfer & Trust Company, and (c) the holders of the Private Placement Units (including the underlying Ordinary Shares and Private Placement Warrants) pursuant to that certain Private Placement Units Purchase Agreement, dated as of [•], 2025, by and among the Company and the purchasers named therein, 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 (a) the tenth (10th) anniversary of the date of this Agreement and (b) the date as of which the Holders cease to hold any Registrable Securities. The provisions of Article 4 shall survive any termination.

[Signature Page Follows]

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


COMPANY:

CH4 NATURAL SOLUTIONS CORPORATION, a Cayman Islands exempted company

By:
		Name: Thomas Smith
		Title: Chief Financial Officer, Chief
		Accounting Officer and Secretary

HOLDERS:

CH4 NATURAL SOLUTIONS ACQUISITION SPONSOR LLC, a Cayman Islands limited liability company

By:
		Name: Thomas Smith
		Title: Authorized Person

[CH4 NATURAL SOLUTIONS UNIT HOLDINGS, LLC,] a Delaware limited liability company

By:
		Name: Thomas Smith
		Title: Authorized Person

SIGNATURE PAGE TO

REGISTRATION RIGHTS AGREEMENT

HOLDERS:

Jean Rogers

Jeffrey Tepper

Nate Zwald

SIGNATURE PAGE TO

REGISTRATION RIGHTS AGREEMENT

CH4 Natural Solutions Corp S-1/A