Lawrence Berkeley National Laboratory

A divergence-free, parameter-free, path-based discrete-time quantum dynamics is designed to not only enlarge the achievements of general relativity and the standard particle model, by approximations at spacetime scales far above Planck scale while far below Hubble scale, but to allow tackling of hitherto inaccessible questions. "Path space" is larger than and precursor to Hilbert-space basis. The wave-function-propagating paths are action-carrying structured graphs-cubic and quartic structured vertices connected by structured "fermionic" or "bosonic" "particle" and "nonparticle" arcs. A Planck-scale path step determines the gravitational constant while controlling all graph structure. The basis of the theory's (zero-rest-mass) elementary-particle Hilbert space (which includes neither gravitons nor scalar bosons) resides in particle arcs. Nonparticle arcs within a path are responsible for energy and rest mass.