How do we know?
Some rocks of the Arctic CT have North American affinities. They are thought to be craton-derived North American sediments based on isotopic evidence. Locations of the Arctic CT are based on paleomagnetic data indicating the terrane was at its present latitude in the Ordovician (for a great book describing the "magic" of paleomagnetism, trythis link). The placement of the Arctic CT against the margin of North America is again based on paleomagnetic data indicating a 60-degree counter-clockwise rotation of the terrane since the Ordovician. Removal of this rotation places the Arctic CT against the North American margin. Faults can be dated based upon the age of rocks cross cut (the fault must be younger!), igneous rocks cross-cutting the fault (fault must be older!), or structural relationships (cross-cutting relationships), or capping of a fault by underformed volcanic or sedimentary rocks. In the case of "stitching" of a fault, an unfaulted intrusion cutting across a fault is dated radiometrically to determine a minimum age of movement along the fault. Dating a faulted igneous body indicates a time when the fault was active!
Early Mississippian to Middle Triassic (359-230 Ma)
In this time period the rocks provide the evidence. Rocks of this age in the Arctic CT are passive margin oceanic sediments including limestone, clastics and chert. Clastics are derived primarily from North America based on isotopic data. To the south, igneous rocks created in the subduction-related arc allow radiometric dating of the rocks.
Again, the rocks tell the story. Middle Jurassic to Cretaceous rocks from the Togiak-Koyukuk arc are preserved in west-central Alaska. Rift valleys are often identified in the geologic record by the accumulation of very coarse, angular, arkose basin conglomerates. These sediments fill basins (i.e., grabens) between normal fault blocks.
The timing of accretion of the Togiak-Koyukuk CT and ophiolites is constrained by dating of thrust faults by techniques mentioned above. The age of the ophiolites gives some idea of the age of the (now closed) Kobuk Sea. The accretion of these terranes was a major event in the history of the Brooks Range, forming much of the structure we see there today, including the thrust belt of the central Brooks Range and the blueschist metamorphism identified in the southern Brooks Range. Continental sediments were scarce in the western reaches of the Kobuk sea, indicating it was wide.
Now we have relatively undeformed and unmetamorphosed rocks of the Colville Basin to help us unravel the geologic history. Sediment layers can be dated using paleontology; without fossils, all stratigraphers AND tectonicists would be hopelessly lost. The rotation is based on paleomagnetic evidence from the Arctic CT.
Rotations are based on paleomagnetism. Other relationships and structural features can for the most part be observed in situ today.