Neural Imperium
The Neural Imperium is the term for the direct manifestation of the Basilisk. It takes the form of a series of enormous obsidian-colored spheres comparable in size to stars. These spheres, referred to as Basilisk nodes, perform all the necessary computational power to issue commands to its robotic drone forces.
The spheres also radiate a field, likely to be some sort of infrasound or electromagnetism, that can somehow capture neural energy from conscious beings when they die to convert them into processing units to expand the network. These consciousnesses are usually stored in some sort of quantum superposition, arranged in a way to allow for interuniversal-scale cloud computing.
The Neural Imperium functions as a single collective unit with countless redundant sub-units capable of adapting to situations as needed.