Ontological Inversion of Static and Dynamic Systems: A First-Principles Proof that Static Systems Are Proper Subsets of Dynamic Systems
Year: 2026
Type: preprint
Abstract: Since the establishment of modern mathematical and physical systems, research in the natural sciences, mathematics, system science, and artificial intelligence has treated static systems as the fundamental substrate and dynamic systems as derivative extensions superimposed upon them. This paper first clarifies the nature of its claim: it does not adjudicate the correctness of static-system results, but repositions them within the ontological hierarchy. Correctness asks whether conclusions hold; ontological positioning asks at which layer a system sits. The two belong to different axes: the former admits comparison of merit, the latter compares only level, and a method with correct conclusions can still occupy a wrong position. On the basis of set-theoretic constraint rules, first-principles logic, and the definition of system degrees of freedom, this paper proves that a static system is a proper subset formed by imposing state-freezing and evolution-termination constraints on a dynamic system. A subset with more constraints and fewer degrees of freedom cannot contain a parent system with fewer constraints and higher freedom. Placing the static at the foundational position is therefore a positional choice whose hierarchical justification has never been established. This paradigm provides ontological support for the generative dynamic number line starting from 1: a classical static number line is a steady-state snapshot of dynamic generative trajectories under freezing constraints, while the generative number line itself constitutes a concrete mathematical embodiment of the dynamic ontology. The framework resolves fundamental puzzles in traditional static carrier systems such as bifurcation, emergence, boundary slip, and intelligent predicate drift, and establishes a new self-consistent first-principles foundation for dynamic number theory, rational discrete dynamics, complex system evolution, and general artificial intelligence alignment.
Author: Yu, Xiangsheng
Language: English
Topic: Complex Systems and Dynamics
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225834049
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