Toward a Domain-Specific Language for Reasoning: A Practical Introduction to Reasoning DNA Units

This paper introduces the framework of Reasoning DNA Units (RDUs): composable proof objects that formalize reasoning as a traversable, analyzable, and generative process. Over more than a decade of independent research, the author has developed a model of reasoning based on three core mechanisms: Combinatorial Layering, POT Generator Functions (Pruning–Ordering–Type), and Path Transversal. Together, these mechanisms describe how intelligence constructs structure from uncertainty, generating, constraining, and realizing potential through dynamic traversal. Through examples ranging from maze navigation and chess to tool-assisted speedrunning and real-world tasks, the framework illustrates reasoning across unstructured, semi-structured, and structured modes. The resulting model reframes reasoning as an operational substrate—a universal architecture in which both human and artificial intelligence can be analyzed, shared, and built. This work serves as a practical introduction and conceptual bridge toward the development of a Domain-Specific Language for Reasoning, providing a formal grammar for constructing, manipulating, and evolving reasoning proof objects within a shared substrate of intelligence.