International Association
for Cryptologic Research

Abstract The Singularity Random Number Generator (SRNG) represents a groundbreaking advancement in the generation of random numbers by integrating two key properties - computational irreducibility and seed independence - into a deterministic algorithm. Unlike conventional pseudorandom number generators (PRNGs) whose randomness is intrinsically linked to seed quality or chaotic sensitivity, SRNG transforms even low-entropy seeds into complex, unpredictable outputs. SRNG demonstrates high-quality randomness can emerge independently of seed entropy or size. This paper explores how SRNG not only challenges classical paradigms of predictability in deterministic systems but also offers transformative applications in cryptography, artificial intelligence (AI), and interdisciplinary research. Furthermore, by drawing parallels with cognitive variability research - such as insights from the Forbes article “Why A ‘Productively Distracted’ Brain Is A Superpower” - we discuss how the emergent unpredictability of SRNG may contribute to enhanced adaptive learning and decision-making processes in AI systems. Ultimately, SRNG is presented as a model that bridges the realms of science and mystery, inviting a new understanding of randomness and the limits of scientific inquiry, thereby expanding the frontiers of interdisciplinary research.