  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.
