Physics has yet to complete a catalog of properties of objects, complete a list of elementary particles, describe dark matter, and explain dark energy phenomena. This paper shows modeling that catalogs properties (such as charge and mass) and elementary particles (such as quarks and gluons). The catalog of properties includes known properties and suggests new properties. The catalog of elementary particles includes all known elementary particles and suggests new elementary particles. The modeling has bases in integer arithmetic and complements popular modeling that has bases in space-time coordinates. This paper shows applications that combine popular modeling, the expanded set of properties, and the expanded set of elementary particles. Applications describe dark matter, explain known ratios of dark matter effects to ordinary matter effects, point to possible resolutions for so-called tensions (between data and popular modeling) regarding dark energy phenomena, and suggest insight about galaxy evolution.