Exhibit 3.1

FORM OF AMENDMENT TO

THE SECOND AMENDED AND RESTATED MEMORANDUM AND ARTICLES

OF
ASSOCIATION

OF

BLACK HAWK ACQUISITION CORP

July 8, 2025

RESOLVED, as a special resolution, that:

(i) Article 36.2 of the Second Amended and Restated Memorandum and Articles of Association of the Company as adopted by special resolution passed on March 20, 2024 (the Existing Memorandum and Articles) be deleted in its entirety and replaced as follows:

36.2 The Company has until June 22, 2025 — 15 months from the consummation of the IPO to consummate a Business Combination, provided however that if the Board of Directors anticipates that the Company may not be able to consummate a Business Combination within 15 months of the consummation of the IPO, the Company may, by Resolution of Directors, at the request of the Sponsor, extend the period of time to consummate a Business Combination up to eighteen (18) times, each by an additional one (1) month, for a total of up to eighteen (18) months from June 22, 2025 to December 22, 2026 (i.e. for a total of up to thirty-three (33) months after the consummation of the IPO) to complete a Business Combination). In the event that the Company does not consummate a Business Combination by December 22, 2026 (subject in the latter case to valid extensions having been made in each case) or such later time as the Members of the Company may approve in accordance with these Articles, the Company shall:

(a) cease all operations except for the purpose of winding up;

(b) as promptly as reasonably possible but not more than ten business days thereafter, redeem the Public Shares, at a per-Share price, payable in cash, equal to the aggregate amount then on deposit in the Trust Account, including interest earned on the funds held in the Trust Account and not previously released to the Company to pay income taxes, if any, divided by the number of the Public Shares then in issue, which redemption will completely extinguish public Members’ rights as Members (including the right to receive further liquidation distributions, if any); and

(c) as promptly as reasonably possible following such redemption, subject to the approval of the Company’s remaining Members and the directors, dissolve and liquidate, subject in each case, to its obligations under Cayman Islands law to provide for claims of creditors and in all cases subject to the other requirements of Applicable Law. If the Company shall wind up for any other reason prior to the consummation of a Business Combination, the Company shall, as promptly as reasonably possible but not more than ten business days thereafter, follow the foregoing procedures set out in this Article with respect to the liquidation of the Trust Account, subject to its obligations under Cayman Islands law to provide for claims of creditors and in all cases subject to the other requirements of Applicable Law.