Origins of life chemistry has progressed from seeking out the production of specific molecules to seeking out conditions in which macromolecular precursors interact with one another in ways that can lead to biological organization. Reported precursor synthesis networks generally lack such attributes. Radical species are highly reactive, and our research team has uncovered numerous radical-driven chemical shortcuts to ribonucleotide assembly precursors, but do radiolytic chemical reaction networks generate life-like organizational attributes? Here we report radiolysis reaction data that connect abundant geochemical reservoirs to the production of carboxylic acids, amino acids, and ribonucleotide precursors and study the topological properties of the resulting network. The network exhibits attributes associated with biological systems: it is hierarchically organized, there are families of closed loop cycles, and the species and cycle histograms exhibit heterogeneous (heavy-tailed) distributions. The core cycles of the network are made possible by the high reactivity of radical species H and OH. Radiolysis is implicated as a unique prerequisite for driving abiotic organosynthetic self-organization.