Exhibit 3.1

CERTIFICATE OF TRUST

OF

THIRD POINT PRIVATE CAPITAL INCOME FUND

This Certificate of Trust of Third Point Private Capital Income Fund (the "Trust") is being duly executed and filed on behalf of the Trust by the undersigned, as sole trustee, to form a statutory trust under the Delaware Statutory Trust Act (12 Del. C. Section 3801 et seq.) (the "Act").

1.            Name. The name of the trust formed hereby is Third Point Private Capital Income Fund.

2.            Registered Office; Registered Agent. The business address of the Trust’s registered office in the State of Delaware is The Corporation Trust Company, Corporation Trust Center, 1209 Orange Street, Wilmington, Delaware 19801. The name of the Trust’s registered agent at such address is The Corporation Trust Company.

3.            Investment Company. Pursuant to 12 Del. C. Section 3807(b) of the Act, the Trust intends to become a regulated business development company under the Investment Company Act of 1940, as amended, within 180 days following the first issuance of beneficial interests.

4.            Effective Date. This Certificate of Trust shall be effective upon filing.

[SIGNATURE PAGE FOLLOWS]

IN WITNESS WHEREOF, the undersigned, being the sole trustee of the Trust, has duly executed this Certificate of Trust in accordance with the Act, as of this 5th day of December, 2025.