Toward a Unified Theory of Complexity and Information: Phase, Form, and Coherence Beyond Shannon

We propose a New Theory of Complexity and Information (NSI) that unifies Shannon entropy, Kolmogorov complexity, and nonlinear phase-structured models of meaning and form. Classical information theories quantify uncertainty or compressibility but fail to account for morphology, coherence, and semantic resonance. NSI introduces a hybrid metric combining entropy with morphological structure, governed by a coherence parameter κ\kappaκ. We formulate a 17-axiom foundation, prove key inclusion theorems (Shannon, Kolmogorov), define a category-theoretic structure, and demonstrate the theory through simulations on images, text, and signals. NSI offers a fundamentally new framework for perception, computation, cognition, and information health. We invite further exploration of its physical, cognitive, and technological implications.