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Geographic and segment information: (Tables)
12 Months Ended
Dec. 31, 2025
Geographic and segment information:  
Schedule of service revenues and long-lived assets by geographic region

Year Ended December 31, 2025

  ​ ​ ​

On-net

  ​ ​ ​

Off-net

  ​ ​ ​

Wavelengths

  ​ ​ ​

Non-core

  ​ ​ ​

Total

North America

$

400,765

$

373,289

$

37,443

$

8,026

$

819,523

Europe

101,395

19,455

944

217

122,011

Oceania

 

20,791

3,916

66

63

24,836

South America

8,072

708

28

8,808

Africa

486

102

588

Total

$

531,509

$

397,470

$

38,453

$

8,334

$

975,766

Year Ended December 31, 2024

  ​ ​ ​

On-net

  ​ ​ ​

Off-net

Wavelengths

  ​ ​ ​

Non-core

  ​ ​ ​

Total

North America

$

424,437

$

426,857

$

19,015

$

17,692

$

888,001

Europe

 

94,363

21,242

172

347

116,124

Oceania

 

18,205

5,013

9

91

23,318

South America

7,080

896

43

8,019

Africa

543

99

642

Total

$

544,628

$

454,107

$

19,196

$

18,173

$

1,036,104

Year Ended December 31, 2023

  ​ ​ ​

On-net

  ​ ​ ​

Off-net

Wavelengths

  ​ ​ ​

Non-core

  ​ ​ ​

Total

North America

$

401,213

$

367,210

$

5,653

$

28,614

$

802,690

Europe

 

88,310

19,913

147

108,370

Oceania

 

15,769

5,587

71

21,427

South America

6,957

684

8

7,649

Africa

687

99

786

Total

$

512,936

$

393,493

$

5,653

$

28,840

$

940,922

December 31, 

December 31, 

  ​ ​ ​

2025

  ​ ​ ​

2024

Long lived assets, net

North America

$

1,523,789

$

1,579,495

Europe and other

 

197,285

158,854

Total

$

1,721,074

$

1,738,349