Exhibit 4.1

FIRST SUPPLEMENTAL INDENTURE

Dated as of June 15, 2026

among

COGENT COMMUNICATIONS GROUP, LLC and

COGENT FINANCE, INC., as the Issuers,

the Guarantors party hereto

and

WILMINGTON TRUST, NATIONAL ASSOCIATION,

as Trustee

6.500% SENIOR SECURED NOTES DUE 2032

FIRST SUPPLEMENTAL INDENTURE (this “Supplemental Indenture”), dated as of June 15, 2026, among Cogent Communications Group, LLC (the “Company”), Cogent Finance, Inc. (the “Co-Issuer” and, together with the Company, the “Issuers”), the Guarantors party hereto (the “Guarantors”) and Wilmington Trust, National Association, a national banking association organized and existing under the laws of the United States of America, as trustee (the “Trustee”) and collateral agent (the “Collateral Agent”).

W I T N E S S E T H:

WHEREAS, each of the Issuers and the Guarantors have heretofore executed and delivered to the Trustee and the Collateral Agent an indenture, dated as of June 17, 2025 (the “Original Indenture” and, together with this Supplemental Indenture and any other supplements thereto, the “Indenture”), providing for the issuance of $600,000,000 aggregate principal amount of the Issuers’ 6.500% Senior Secured Notes due 2032 (the “Notes”);

WHEREAS, pursuant to Section 9.02 of the Original Indenture, the Issuers, the Guarantors, the Trustee and the Collateral Agent may amend or supplement the Original Indenture with the consent of the Holders of at least a majority in aggregate principal amount of the Notes then outstanding (the “Requisite Consents”);

WHEREAS, as of June 15, 2026, the Issuers have received and caused to be delivered to the Trustee evidence of receipt of the Requisite Consents from or on behalf of Holders to amend the Original Indenture as set forth herein and such evidence is attached to the Officer’s Certificate delivered as of the date hereof to the Trustee and the Collateral Agent in connection with the execution of this Supplemental Indenture;

WHEREAS, the Issuers and the Guarantors have each duly authorized the execution and delivery of this Supplemental Indenture; and

NOW, THEREFORE, in consideration of the foregoing and for other good and valuable consideration, the receipt of which is hereby acknowledged, the parties mutually covenant and agree for the equal and ratable benefit of the Holders as follows:

1.            Capitalized Terms. Capitalized terms used herein without definition shall have the meanings assigned to them in the Indenture.

2.            Amendments to the Original Indenture.

(a)            Section 1.01 (“Definitions”) of the Original Indenture is hereby amended by adding the following definition:

“Data Center Proceeds” means the net cash proceeds from the sale by Cogent Holdco (or any Subsidiary of Cogent Holdco that is not a Subsidiary of the Company) of certain data centers, which net cash proceeds are contributed or otherwise provided to the Company and/or one or more of its Restricted Subsidiaries; provided that only the greater of (i) the first $175.0 million of such net cash proceeds and (ii) the net cash proceeds from the first 10 such data center sales occurring after June 15, 2026 shall constitute Data Center Proceeds.

(b)            Clause (5) of the definition of “Permitted Liens” in Section 1.01 (“Definitions”) of the Original Indenture is hereby amended by replacing the reference therein to “4.00” with “4.75”.

(c)            Section 4.04(a)(3)(b) (“Limitation on Restricted Payments”) of the Original Indenture is hereby amended as follows:

“100.0% of the aggregate amount received by the Company in cash and the Fair Market Value of property other than cash since April 1, 2025 as a contribution to its common equity capital or from the issue or sale of Equity Interests (other than Disqualified Stock) of the Company or any Restricted Subsidiary (other than Data Center Proceeds) and the amount of reduction of Indebtedness of the Company or its Restricted Subsidiaries that has been converted into or exchanged for such Equity Interests (other than Equity Interests sold to, or Indebtedness held by, a Subsidiary of the Company); plus”

(d)            Section 4.04(b)(3) (“Limitation on Restricted Payments”) of the Original Indenture is hereby amended as follows:

“any Restricted Payment in exchange for, or out of the net proceeds of a contribution to the common equity of the Company or a substantially concurrent sale (other than to a Subsidiary of the Company) of, Equity Interests (other than Disqualified Stock) of the Company or, to the extent the proceeds from such contribution or sale of Equity Interests are contributed to the common equity capital of the Company or used to purchase Capital Stock (other than Disqualified Stock) of the Company, a direct or indirect parent of the Company (other than Data Center Proceeds); provided that the amount of any such net proceeds that are utilized for such Restricted Payment will be excluded from Section 4.04(a)(3)(b);”

(e)            Section 4.04 (“Limitation on Restricted Payments”) of the Original Indenture is hereby amended by adding paragraphs (e) and (f) as follows:

“(e)         Notwithstanding the foregoing, the Company may not make a Restricted Payment constituting the dividend, distribution, sale, transfer or contribution of IRUs, whether directly or through a dividend or distribution of the Equity Interests of an entity or entities that is or are the owner(s) of such IRUs. In addition, no IRU that is owned or held by the Company or any Guarantor as of June 15, 2026, may be transferred to, assumed by or refinanced by any Unrestricted Subsidiary or any Restricted Subsidiary that is not a Guarantor, except (1) in connection with bona fide tax planning or reorganization activities or (2) any transfers, assumptions or refinancings of IRUs having an aggregate Fair Market Value (measured on the date of each applicable transfer, assumption or refinancing and without giving effect to subsequent changes in value) not exceeding $50.0 million.

(f)            The Company shall utilize Data Center Proceeds only to repurchase, defease or otherwise retire Indebtedness at a discount to the par value thereof or at maturity of such Indebtedness, and at least 50.0% of the aggregate Data Center Proceeds shall be used to redeem, repurchase, defease or otherwise retire the Notes at a discount to the par value thereof or at maturity of the Notes.”

(f)            A new Section 4.18 (“Data Center Proceeds”) is hereby added following Section 4.17 (“Post-Closing Undertakings”) in the Original Indenture:

“Section 4.18         Data Center Proceeds. Cogent Holdco shall contribute or otherwise provide to the Company and/or one or more of its Restricted Subsidiaries all Data Center Proceeds within 30 days of receipt thereof by Cogent Holdco or any of its Subsidiaries.”

3.            Effectiveness. This Supplemental Indenture will become effective immediately upon its execution and delivery by the parties hereto.

4.            Governing Law. THIS SUPPLEMENTAL INDENTURE WILL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK.

5.            Ratification and Reaffirmation of Indenture; Supplemental Indenture Part of Indenture. Except as expressly amended hereby, the Indenture (including the Guarantees contained therein) is in all respects ratified and reaffirmed and all the terms, conditions and provisions thereof shall remain in full force and effect. This Supplemental Indenture shall form a part of the Indenture for all purposes, and every Holder heretofore or hereafter authenticated and delivered shall be bound hereby.

6.            No Recourse Against Others. No director, officer, employee, incorporator, stockholder, member, manager or partner of either Issuer, any Subsidiary or any direct or indirect parent of either Issuer, as such, will have any liability for any obligations of either Issuer or the Guarantors under the Notes, any Note Guarantees, the Indenture or any Supplemental Indenture or for any claim based on, in respect of, or by reason of, such obligations or their creation. Each Holder by accepting Notes waives and releases all such liability. The waiver and release are part of the consideration for issuance of the Notes and the Note Guarantees. The waiver may not be effective to waive liabilities under the federal securities laws and it is the view of the SEC that such a waiver is against public policy.

7.            Counterparts. The parties may sign any number of copies of this Supplemental Indenture. Each signed copy shall be an original, but all of them together represent the same agreement. Delivery of an executed counterpart of a signature page to this Supplemental Indenture by facsimile, email or other electronic means shall be effective as delivery of a manually executed counterpart of this Supplemental Indenture.

8.            Effect of Headings. The section headings herein are for convenience only and shall not affect the construction hereof.

9.            The Trustee and the Collateral Agent. Neither the Trustee nor the Collateral Agent shall be responsible in any manner whatsoever for or in respect of the validity or sufficiency of this Supplemental Indenture or for or in respect of the recitals contained herein, all of which recitals are made solely by the Issuers. Neither the Trustee nor the Collateral Agent makes any representation or warranty as to the validity or sufficiency of this Supplemental Indenture or as to the accuracy of the recitals to this Supplemental Indenture.

[Signature Pages Follow]

IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed as of the date first above written.

[Signature Page to First Supplemental Indenture (6.500% Senior Secured Notes due 2032)]

[Signature Page to First Supplemental Indenture (6.500% Senior Secured Notes due 2032)]