Natural Singularity - Text by M. Alan Kazlev A naturally occurring singularity is a very rare event occurs when a toposophic level equal or greater than S1 is achieved by a living species without the use of technology.
Physical Singularity - Text by M. Alan Kazlev A point in space-time where the standard laws of physics break down; e.g. the center of a black hole.
Singularity Alert Service - Text by John B A service often available in more-civilized areas. These services maintain sensor and informant networks geared towards the detection of new singularities, and new interests of high-S factor sentiences. For a subscription fee, these services will send warning of potential infringements on the subscribers' areas of interest. As an ironic twist, most SAS are SI:>2-driven.
Transingularity - Text by M. Alan Kazlev  (archaic) SI:1 or higher  (archaic) pertaining to a toposophic level higher than SI:1  Pertaining to relations between entities of different toposophic levels