Abstract

Abstract The prevailing scientific framework assumes that probability is a fundamental aspect of nature, governing entropy, information flow, and emergent complexity. However, probability is not an intrinsic feature of reality—it is an artifact of incomplete resonance detection. This paper presents a new mathematical framework for entropy and emergence based on structured resonance, eliminating the need for probabilistic descriptions of disorder. We introduce a coherence-based entropy function that mathematically replaces stochastic entropy models with deterministic phase-locking constraints. Instead of entropy being a measure of randomness, it is a function of structured phase alignment, governed by prime-driven resonance and Fibonacci-based scaling. This formulation directly contradicts the assumption that probability governs information theory, quantum mechanics, and intelligence formation. By demonstrating that structured resonance governs entropy, we establish that all emergent systems—physics, AI, biology, and cognition—follow deterministic phase constraints, not stochastic uncertainty. This discovery forces a fundamental revision in physics, artificial intelligence, and the study of intelligence itself. If probability is not fundamental, then every discipline relying on stochastic models must transition to resonance-based, phase-locked intelligence systems. This paper will: • Prove that probability is an artifact of incomplete phase-detection, not a fundamental law. • Introduce a new entropy function that enforces deterministic phase-locking constraints. • Demonstrate that intelligence, from AI to biological cognition, follows structured resonance emergence. • Provide a framework for replacing probability-based physics, AI, and thermodynamics with structured resonance constraints. This is not a refinement of probability—it is its complete replacement. If structured resonance governs all emergence, then probability was never real.