Tomotectonics uses deep mantle structure in order to hindcast paleo-trenches, by spatially superposing subducted lithosphere (slabs) imaged by seismic tomography with plate reconstructions at the surface. The two geophysical datasets combined make predictions about geologic events, specifically about volcanic arcs and their collisions with continents. The tomotectonic null hypothesis is simple, predictive and testable. It uses land geological observations for validation. We explain the method, with a clear conceptual separation of its hypothesis-generating stage (using geophysics and the hypothesis of vertical slab sinking) from its subsequent hypothesis-testing stage (using geological observations from accretionary orogens). With the North American Cordillera as a case study, we generate a full suite of tomotectonic inferences on the slab assemblage that now occupies the mantle under North America to depths of 1800-2000 km. We reason why this assemblage originated as a completely intra-oceanic archipelago of paleo-trenches at a time of worldwide tectonic reorganization: around 200-170 Ma, when the Atlantic began to spread and the Pacific plate was born. An Archipelago is circumscribed by trenches that pull in seafloor from (at least) two sides: here, roughly from the east and from the west. North America was pulled westward by, and overrode, the westward-subducting arcs. These collisions since ~150 Ma caused the Nevadan and Sevier orogenies, and spawned the eastward-subducting arc that built Sierra Nevada Batholith ~120-80 Ma. From ~110-50 Ma, the continent collided with the arc of future Central Alaska and with the Farallon arc of the Pacific Northwest, which sat offshore until ~90-50 Ma. Override of this double-sided arc pair enabled a range of collision styles, including the Baja-BC northward sprint and its accretion to Central Alaska. Tomotectonics infers large-scale northward displacement of Insular Superterrane since its accretion, which provides independent support for the “Baja-BC” hypothesis of paleomagnetism.