Toposophic classification, limits of computation, and the vast array of technologies, physical principles, memetic differentiation, and information theory make theology a bizarrely difficult subject to exchange information about, even when the two beings conversing have relevant conceptual equipment based upon roughly similar protocols. In such discourse, short-hand is necessary to even agree upon common reference memes. Throughout the history of memetics and theology, several tropes have descended towards common baseline understanding, particularly when describing the physical basis of theology. Several examples are given below, with disambiguation references. Each trope can be likewise fractally expanded to suitable complexity for a given information protocol.
M-Brain, Moon Brain: An archailect based upon a computational substrate comparable in mass and size to a small moon or rocky core of a planet. More here.
J-Brain: An archailect based upon a computational substrate comparable in mass and size to a gas giant planet. More here.
N-Brain: Also called a neuron star, an archailect based upon a computational substrate comparable in mass, size, and density to a neutron star. More here.
S-Brain: Also known as a Godstar. An archailect based upon a computational substrate comparable in mass and size to the most massive stars, at minimum 10 solar masses. More here.
Many S-Brains are surrounded by Matrioshka layers of computation (which may also be confusingly called M-Brains). Such systems are sometimes called SM-Brains to distinguish them from pure S-Brains (which look and mostly act like large bright stars), and to distinguish M-Brains from Matrioshka-Brains, though technically a Matrioshka-Brain can be deployed around any star.
One iconic type of S-Brain or Godstar is the Betelgeuse Brain; however, this particular star is currently too unstable to be converted to an S-Brain, so the idea remains no more than a concept.
W-Brain: An archailect based upon a computational substrate consisting of large numbers of entangled wormholes (>1E9 comm-gauge wormholes), with a metric mass equivalence of about 1 solar mass or greater. More here.
B-Brain, Black hole Brain: An archailect based upon a computational substrate composed of the Cauchy horizon of a black hole. More here.
A-Brain, Omega-Brain: Also called a Tipler Oracle. An archailect based upon forcible expansion of a wormhole into a pocket universe, with the inter-universal wormhole throat maintaining communication between disparate universes. As with B-Brains, such constructions remain in the realm of folklore. The computational parameters, set of compactification parameters and physical principles, and the like remain almost completely unknown (and arguably) unknowable. Nevertheless, they remain fertile grounds for speculation. More on Tipler oracles here.
Galaxy Brain A hypothetical entity able to draw upon the processing power of an entire galaxy's mass. None are known for certain. More here.