Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We hereby consent to the use in the Prospectus constituting a part of this Registration Statement on Form S-1 of our report dated August 27, 2025, relating to the financial statements of Bitcoin Infrastructure Acquisition Corp Ltd. as of July 18, 2025, and for the period from June 9, 2025 (inception) through July 18, 2025, which is contained in that Prospectus. We also consent to the reference to our firm under the caption “Experts” in the Prospectus.

/s/ WithumSmith+Brown, PC

New York, New York

August 27, 2025