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Revenue (Schedule of Revenue by Geographic Destination) (Details) - USD ($)
$ in Millions
 12 Months Ended
Jan. 02, 2026
Jan. 03, 2025
Dec. 29, 2023
Disaggregation of Revenue [Line Items]      
Revenues $ 7,786 $ 7,710 $ 6,956
United States      
Disaggregation of Revenue [Line Items]      
Revenues 4,244 4,045 3,617
Europe      
Disaggregation of Revenue [Line Items]      
Revenues 1,584 1,894 1,816
Middle East      
Disaggregation of Revenue [Line Items]      
Revenues 790 731 528
Australia      
Disaggregation of Revenue [Line Items]      
Revenues 548 526 496
Africa      
Disaggregation of Revenue [Line Items]      
Revenues 253 201 176
Asia      
Disaggregation of Revenue [Line Items]      
Revenues 142 152 169
Other countries      
Disaggregation of Revenue [Line Items]      
Revenues 225 161 154
U.S. Government Defense and Intelligence Clients      
Disaggregation of Revenue [Line Items]      
Revenues 3,370 3,292 3,039
U.S. Government Federal Civilian Clients      
Disaggregation of Revenue [Line Items]      
Revenues 1,057 1,112 1,052
International Government Clients      
Disaggregation of Revenue [Line Items]      
Revenues 905 891 791
Commercial and Infrastructure Clients      
Disaggregation of Revenue [Line Items]      
Revenues 2,454 2,415 2,074
MTS      
Disaggregation of Revenue [Line Items]      
Revenues 5,581 5,555 5,119
MTS | United States      
Disaggregation of Revenue [Line Items]      
Revenues 3,772 3,503 3,096
MTS | Europe      
Disaggregation of Revenue [Line Items]      
Revenues 1,313 1,595 1,569
MTS | Middle East      
Disaggregation of Revenue [Line Items]      
Revenues 123 110 105
MTS | Australia      
Disaggregation of Revenue [Line Items]      
Revenues 219 202 204
MTS | Africa      
Disaggregation of Revenue [Line Items]      
Revenues 77 70 70
MTS | Asia      
Disaggregation of Revenue [Line Items]      
Revenues 20 18 17
MTS | Other countries      
Disaggregation of Revenue [Line Items]      
Revenues 57 57 58
MTS | U.S. Government Defense and Intelligence Clients      
Disaggregation of Revenue [Line Items]      
Revenues 3,370 3,292 3,039
MTS | U.S. Government Federal Civilian Clients      
Disaggregation of Revenue [Line Items]      
Revenues 1,057 1,112 1,052
MTS | International Government Clients      
Disaggregation of Revenue [Line Items]      
Revenues 905 891 791
MTS | Commercial and Infrastructure Clients      
Disaggregation of Revenue [Line Items]      
Revenues 249 260 237
MTS | Science & Space      
Disaggregation of Revenue [Line Items]      
Revenues 1,126 1,188 1,127
MTS | Defense & Intel      
Disaggregation of Revenue [Line Items]      
Revenues 3,178 2,887 2,497
MTS | Readiness & Sustainment      
Disaggregation of Revenue [Line Items]      
Revenues 1,277 1,480 1,495
STS      
Disaggregation of Revenue [Line Items]      
Revenues 2,205 2,155 1,837
STS | United States      
Disaggregation of Revenue [Line Items]      
Revenues 472 542 521
STS | Europe      
Disaggregation of Revenue [Line Items]      
Revenues 271 299 247
STS | Middle East      
Disaggregation of Revenue [Line Items]      
Revenues 667 621 423
STS | Australia      
Disaggregation of Revenue [Line Items]      
Revenues 329 324 292
STS | Africa      
Disaggregation of Revenue [Line Items]      
Revenues 176 131 106
STS | Asia      
Disaggregation of Revenue [Line Items]      
Revenues 122 134 152
STS | Other countries      
Disaggregation of Revenue [Line Items]      
Revenues 168 104 96
STS | U.S. Government Defense and Intelligence Clients      
Disaggregation of Revenue [Line Items]      
Revenues 0 0 0
STS | U.S. Government Federal Civilian Clients      
Disaggregation of Revenue [Line Items]      
Revenues 0 0 0
STS | International Government Clients      
Disaggregation of Revenue [Line Items]      
Revenues 0 0 0
STS | Commercial and Infrastructure Clients      
Disaggregation of Revenue [Line Items]      
Revenues $ 2,205 $ 2,155 $ 1,837