Nonlinear Information Theory: A Phase-Based Foundation for Coherence, Morphogenesis, and Post-Symbolic Computation

We present a complete axiomatic theory of nonlinear information, where information is not defined by symbolic content or entropy, but as a stable, coherent form embedded in a dynamic phase field. This framework introduces eight foundational axioms and ten derived theorems describing how informational forms emerge, interact, transform, and decay via phase alignment and morphogenetic dynamics. We provide formal metrics—such as global coherence, resonance density, and informational tension—and demonstrate applications to neuroscience, biological morphogenesis, and coherent computing systems. The theory offers a general foundation for modeling post-symbolic, field-driven information architectures.