A Space-Time-Topology-Prime, stTS Metric for a Self-operating Mathematical Universe Uses Dodecanion Geometric Algebra of 2-20 D Complex Vectors

Advancing from eight imaginary worlds of octonion algebra, for the first time we introduce dodecanion algebra, a mathematical universe made of twelve imaginary worlds one inside another. The difference between eight and twelve imaginary worlds is that the Fano plane that sets the products of imaginary vectors is replaced by a triplet of manifolds that could coexist in three forms. In the proposed algebra product tensors-like quaternion, octonion, dodecanion, and icosanion are deconstructed as a composition of prime dimensional tensors. We propose a generic conformal cylinder of imaginary worlds, similar to modulo or clock arithmetic, using that one could build the group multiplication tables of multinions, which would enable developing the associated algebra. Space-time (st) metric is known, we added two concepts, 15 geometric shapes as topology (T) and 15 primes as symmetry (S) to build a new metric, space-time-topology-prime(stTS) for a self-operating mathematical universe with n nested imaginary worlds. The stTS metric delivers a decision as shape-changing geometry with time, following fractal information theory (FIT) proposed earlier for hypercomputing in the brain. FIT includes two key aspects, the geometric musical language (GML) and the phase prime metric (PPM) that operates using clock architectures spread over 12 dimensions.