Trans-Dimensional Artifacts are residual effects from particularly strong Bridging Events: essentially scars left behind from irreparably altering the fabric of our current reality. These often take the form of shifting, geometric shapes which appear out of space, floating, and do not immediately react or respond to their immediate surroundings. To behold a Trans-Dimensional Artifact for too long often invites insanity, as the average, human, conscious mind is biologically incapable of comprehending exactly what it is seeing.
Several TDA's are identified in the story: Dr. Bryant travels with one before she is able to transfer it out of the country; the Sedona Cult inadvertently created one in the wake of their own Bridging Event; and Fatima created one of her own volition during her exfiltration from Iraq, and continues to safeguard that particular TDA even into the current setting.
The AKASHIC Super Computer requires several components which are likely TDA's in order to function.
Of particular interest is Fatima's TDA, which has been dubbed "The Chalice."