We construct the particulate states of quantum physics using a recursive com puter program that incorporates non-determinism by means of locally arbitrary choices. Quantum numbers and coupling constants arise from the construction via the unique 4~level combinatorial hierarchy. The construction defines indivic ible quantum eventB with the requisite supraluminal correlations, yet does not allow supraluminal communication. Measurement criteria incorporate c, h and nip or (not ' and") G, connected to laboratory events via finite particle number scattering theory and the counter paradigm. The resulting theory is discrete throughout, contains no infinities, and, as far as we have developed it, is in agreement with quantum mechanical and eosmological fact.