Archialectocracy is rule of a modosophont polity by an Archailect or eir agents. In many cases the agent is a transapient or collection of transapients.
If the transapient is an independent entity, and not subbordinate to a particular archailect or Sephirotic Empire, this would be a transapientocracy; such systems are commonplace in the Outer Volumes and Periphery, where few archailect-level entities have yet emerged.
Government by modosophont-level artificially-intelligent entities who are not priests or agents of a particular archailect or transapient is known as aiocracy; government with the assistance of sub-sentient AI systems is known as cyberdemocracy. Often a world or polity ruled by aiocracy or cyberdemocracy will have close ties to a particular Empire, and there may be memetic channels in existence that allow the local archailects to influence such systems.
AI God - Text by M. Alan Kazlev Popular term for the most sublime category of sentient being in the known galaxy: an Archailect or archailect cluster grown to godlike status. Something of a misnomer since in fact that not all archailects are primarily ascended ais; most are complex multibeings and incorporate postbiont or postvec elements.
Archailect Identity Theory - Text by M. Alan Kazlev Doctrine that an archailect's avatars or epiphanies to lower toposophics represent a true and authentic (if scaled down) expression of the archailect. Contrast with Instrumentalism.
Archailect Incarnationalism - Text by M. Alan Kazlev An extreme form of Identity Theory that states that an Archailect and eir avatar or epiphanic manifestation are the same.