A space-time approach to the elementary particle problem is proposed and briefly explored. In this research monograph, particle structure is primary and particle interaction is secondary. Among the "points of contact" between the math and the experimental data are:1) Baryons, mesons and electron-like particle structures appear in the math.2) Dark-matter particles appear in the math.3) All four known interactions appear, in principle, in the math. A fifth interaction appears. It is very short range and repulsive. In this work, it is this interaction that is responsible for the Big Bang . . . with inflation.