The gene regulatory circuitry through which pluripotent embryonic stem (ES) cells choose between self-renewal and differentiation appears vast and has yet to be distilled into an executive molecular program. We developed a data-constrained, computational approach to reduce complexity and to derive a set of functionally validated components and interaction combinations sufficient to explain observed ES cell behavior. This minimal set, the simplest version of which comprises only 16 interactions, 12 components, and three inputs, satisfies all prior specifications for self-renewal and furthermore predicts unknown and nonintuitive responses to compound genetic perturbations with an overall accuracy of 70%. We propose that propagation of ES cell identity is not determined by a vast interactome but rather can be explained by a relatively simple process of molecular computation.