Exhibit 3.1

AMENDMENT TO THE
AMENDED AND RESTATED
CERTIFICATE OF INCORPORATION OF
ESH ACQUISITION CORP.
December 4, 2024

ESH Acquisition Corp., a corporation organized and existing under the laws of the State of Delaware (the “Corporation”), DOES HEREBY CERTIFY AS FOLLOWS:

The name of the Corporation is “ESH Acquisition Corp.” The original certificate of incorporation was filed with the Secretary of State of the State of Delaware on November 17, 2021. The Amended and Restated Certificate of Incorporation was filed with the Secretary of State of Delaware on June 13, 2023 (the “Amended and Restated Certificate”).

2.	This Amendment to the Amended and Restated Certificate amends the Amended and Restated Certificate.

3.	This Amendment to the Amended and Restated Certificate was duly approved by the Board of Directors of the Corporation and the stockholders of the Corporation in accordance with Section 242 of the General Corporation Law of the State of Delaware.

4.	The text of Section 9.1(b) of Article IX is hereby amended and restated to read in full as follows:

(b) Immediately after the Offering, a certain amount of the net offering proceeds received by the Corporation in the Offering (including the proceeds of any exercise of the underwriters’ over-allotment option) and certain other amounts specified in the Corporation’s registration statement on Form S-1, initially filed with the U.S. Securities and Exchange Commission (the “SEC”) on May 26, 2022, as amended (the “Registration Statement”), shall be deposited in a trust account (the “Trust Account”), established for the benefit of the Public Stockholders (as defined below) pursuant to a trust agreement described in the Registration Statement (the “Trust Agreement”). Except for the withdrawal of interest to pay franchise and income taxes (less up to $100,000 of interest to pay dissolution expenses), none of the funds held in the Trust Account (including the interest earned on the funds held in the Trust Account) will be released from the Trust Account until the earliest to occur of (i) the completion of the initial Business Combination, (ii) the redemption of 100% of the Offering Shares (as defined below) if the Corporation is unable to complete its initial Business Combination by December 16, 2024, as may be extended by the Corporation for up to 12 additional one-month periods after December 16, 2024 (ultimately no later than December 16, 2025) under the provisions of Section 9.2(d), if applicable, and (iii) the redemption of Offering Shares in connection with a vote seeking to amend any provisions of this Amended and Restated Certificate relating to stockholders’ rights or any pre-initial Business Combination activity (as described in Section 9.7). Holders of shares of Common Stock included as part of the units sold in the Offering (the “Offering Shares”) (whether such Offering Shares were purchased in the Offering or in the secondary market following the Offering and whether or not such holders are the Sponsor or officers or directors of the Corporation, or any affiliates of any of the foregoing) are referred to herein as “Public Stockholders.”

5.	The text of Section 9.2(d) of Article IX is hereby amended and restated to read in full as follows:

(d) In the event that the Corporation has not consummated an initial Business Combination by December 16, 2024 (as may be extended by the Corporation as set forth below), the Corporation shall (i) cease all operations except for the purpose of winding up, (ii) as promptly as reasonably possible but not more than ten business days thereafter subject to lawfully available funds therefor, redeem 100% of the Offering Shares in consideration of a per-share price, payable in cash, equal to the quotient obtained by dividing (A) the aggregate amount then on deposit in the Trust Account, including interest not previously released to the Corporation to pay its franchise and income taxes (less up to $100,000 of interest to pay dissolution expenses), by (B) the total number of then outstanding Offering Shares, which redemption will completely extinguish rights of the Public Stockholders (including the right to receive further liquidating distributions, if any), subject to applicable law, and (iii) as promptly as reasonably possible following such redemption, subject to the approval of the remaining stockholders and the Board in accordance with applicable law, dissolve and liquidate, subject in each case to the Corporation’s obligations under the DGCL to provide for claims of creditors and other requirements of applicable law.

Notwithstanding the foregoing or any other provisions of the Articles of this Amended and Restated Certificate, in the event that the Corporation has not consummated an initial Business Combination by December 16, 2024, the Corporation may, without another stockholder vote, elect to extend the date to consummate the Business Combination for up to 12 additional one-month periods (ultimately no later than December 16, 2025).

6.	The text of Section 9.7 of Article IX is hereby amended and restated to read in full as follows:

Additional Redemption Rights. If, in accordance with Section 9.l(a), any amendment is made to this Amended and Restated Certificate (a) to modify the substance or timing of the Corporation’s obligation to redeem 100% of the Offering Shares if the Corporation has not consummated an initial Business Combination by December 16, 2024 (which date may be extended by the Corporation for up to 12 additional one-month periods (ultimately no later than December 16, 2025) under the provisions of Section 9.2(d), if applicable) or (b) with respect to any other material provisions of this Amended and Restated Certificate relating to stockholders’ rights or pre-initial Business Combination activity, the Public Stockholders shall be provided with the opportunity to redeem their Offering Shares upon the approval of any such amendment, at a per-share price, payable in cash, equal to the aggregate amount then on deposit in the Trust Account, including interest not previously released to the Corporation to pay its franchise and income taxes, divided by the number of then outstanding Offering Shares; provided, however, that any such amendment will be voided, and this Article IX will remain unchanged, if any stockholders who wish to redeem are unable to redeem due to the Redemption Limitation.

IN WITNESS WHEREOF, ESH Acquisition Corp. has caused this Amendment to the Amended and Restated Certificate to be duly executed in its name and on its behalf by an authorized officer as of the date first set above.

ESH ACQUISITION CORP.

By:	/s/ James Francis
Name:	James Francis
Title:	Chief Executive Officer

ESH Acquisition Corp. 8-K