This paper introduces Emergence Dynamics, a novel mathematical paradigm designed to reformulate the foundational boundaries of computation, computational complexity, and artificial generative intelligence (AGI). Traditional computational models, inherently constrained by discrete, static Turing machines, struggle to capture the non-linear, continuous, and most importantly, Evolutionary Non-deterministic State Transitions that characterize complex, systemic "Intelligence Emergence". To bridge this gap, I propose a framework centered on Continuous Measurement and Non-deterministic State Flows, treating computational evolution not as a sequence of isolated symbolic steps, but as a dynamic trajectory within a continuous measure space. By mapping algorithmic states to flow topologies, this work provides a fresh geometric and measure-theoretic lens to Geometrize the P versus NP Problem. I further conjecture that the traditional Turing machine manifests as a degenerate case under this paradigm and propose a Geometric Definition of Computation and Computational Complexity. Finally, I widely discuss the profound implications and applications of this novel paradigm on the ultimate boundaries of computation, suggesting that computational "hardness" is fundamentally an emergent property of measurement constraints. This work establishes a conceptual and mathematical bridge connecting theoretical computer science, measure theory, topology, and the dynamical systems governing complex evolutionary intelligence emergence structures.
Emergence Dynamics, Continuous Measurement, Non-deterministic State Flows, Geometrization of P versus NP, Computation as the Topography of Emergence, Computational Complexity
I realized that the chronological genesis of an idea carries deeper scientific value than the paper itself. Therefore, I have open-sourced all intermediary materials, including the conversations (human prompts and AI responses), draft papers, images, corpora, etc.—to serve as a rigorous empirical case study for future investigations into cognitive science, psychology, and the heuristics of scientific discovery. Visit https://github.com/Waygo-financial/OpenEvent to download these materials.