Understanding Beth, the Particulate Mass Functional

A geometric relationship between loop quantum gravity and partitioned (triangulated) string theory is discussed. Combinatorial analysis reveals that three spatial and three curvature dimensions, intrinsic to the partitioned string, are necessary to replicate Standard Model particles and interactions. This analysis has established that particulate mass is determined by a functional relationship involving these six extra dimensions. The combinatorial analysis involves non-commutative 3D-matrix algebra which forms the mathematical underpinnings of Dirac notation. The functional relationship (symbolized by Beth) requires exponential, Randall-Sundrum, scaling to compute mass. Through the proper interpretation of complex gravity a cyclic cosmological model is developed. This formulation of cyclic cosmology inherently involves observed dark energy. Thus, a comprehensive theory is constructed from geometric fundamentals which models both massive, oscillating neutrinos and the current epoch of mini-inflation.