Description of the business and summary of significant accounting policies: - Property and equipment (Details)	Dec. 31, 2024
IRU Finance Lease Agreement
Property and equipment
Property, Plant, and Equipment, Useful Life, Term, Description [Extensible Enumeration]	us-gaap:UsefulLifeShorterOfTermOfLeaseOrAssetUtilityMember
IRU Finance Lease Agreement \| Minimum
Property and equipment
Depreciation or amortization period (in years)	15 years
IRU Finance Lease Agreement \| Maximum
Property and equipment
Depreciation or amortization period (in years)	20 years
Network equipment \| Minimum
Property and equipment
Depreciation or amortization period (in years)	2 years
Network equipment \| Maximum
Property and equipment
Depreciation or amortization period (in years)	8 years
Owned buildings and leasehold improvements
Property and equipment
Property, Plant, and Equipment, Useful Life, Term, Description [Extensible Enumeration]	us-gaap:UsefulLifeShorterOfTermOfLeaseOrAssetUtilityMember
Software
Property and equipment
Depreciation or amortization period (in years)	5 years
Owned buildings \| Minimum
Property and equipment
Depreciation or amortization period (in years)	16 years
Owned buildings \| Maximum
Property and equipment
Depreciation or amortization period (in years)	40 years
Office and other equipment \| Minimum
Property and equipment
Depreciation or amortization period (in years)	2 years
Office and other equipment \| Maximum
Property and equipment
Depreciation or amortization period (in years)	7 years
Asset retirement obligations
Property and equipment
Depreciation or amortization period (in years)	4 years
System infrastructure (including owned fiber) \| Minimum
Property and equipment
Depreciation or amortization period (in years)	5 years
System infrastructure (including owned fiber) \| Maximum
Property and equipment
Depreciation or amortization period (in years)	40 years

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 7A
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-7A

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- Definition

Useful life of long lived, physical assets used in the normal conduct of business and not intended for resale, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days. Examples include, but not limited to, land, buildings, machinery and equipment, office equipment, furniture and fixtures, and computer equipment.

+ References

No definition available.

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- Definition

Indicates description of term of useful life for property, plant, and equipment when not stated as numeric value.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 360
-SubTopic 10
-Name Accounting Standards Codification
-Section 35
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482190/360-10-35-3

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