An Axiomatic Framework for Hierarchical, Field-Based Computation in Living Systems

This work presents an axiomatic framework for understanding biological systems as field-based computational entities. Departing from classical symbol-manipulating models of computation, the framework formalizes life as a spatial, constraint-driven process in which logic and physical substrate are inseparable. The model introduces the Hierarchical Turing System, in which computation emerges through interacting continuous fields (chemical, electrical, mechanical) organized across local and global scales. Within this architecture, DNA is treated as an initialization mechanism that defines permissible reaction spaces rather than an executable program, while real-time computation occurs through spatial dynamics and environmental coupling. Consciousness is reinterpreted as a global governance layer that coordinates distributed local computations to maintain organism-level coherence and persistence. This formulation removes the need for homuncular, symbolic, or dualistic explanations, grounding cognition, adaptation, and self-repair in thermodynamically irreversible field processes. The framework is intended as a foundational, cross-disciplinary contribution spanning biology, neuroscience, physics, and artificial intelligence, offering a unified language for persistence, self-organization, and embodied computation in living