Authors: Francesco Cicala , Eyvind Niklasson , Ettore Randazzo , Sami Boukortt , Alessio Basti , Mayalen Etcheverry , Rif A. Saurous , Ben Laurie , James Manyika , Blaise Aguera-Arcas , Blake Richards View PDF HTML (experimental) Abstract: While traditional evolutionary algorithms hard-code reproduction, self-replication can emerge spontaneously within digital ``primordial soups''. This paper investigates the co-evolution of this emergent self-replication alongside problem-solving capabilities. We initialize a population of random 32-byte Z80 assembly programs, requiring self-replication to arise purely through random assembly-level mutations and pairwise program interactions. To link these behaviors, we introduce a task-based validation step: correctly evaluating a polynomial raises a program's interaction probability above a baseline rate. Our experiments yield four primary findings. First, self-replication and mathematical problem-solving successfully co-evolve from initial randomness.…