Systems and methods of modeling the structure and behavior of the quantum continuum based on geometrical principles are provided. In some embodiments, systems and methods of modeling quantum structure and behavior may include modeling a region of space as a three-dimensional projection of a field of N-dimensional hard-spheres, modeling a stable particle within the region of space as a locally stably packed set of hard-spheres, defining an energy subspace comprising one or more additional dimensions, and modeling an energy of the stable particle as an amount of hard-sphere geometry shifted out of the three spatial dimensions into the energy subspace sufficient for the set of hard-spheres to pack stably.