What question did this study set out to answer?

The aim is to establish how motion is derived from admissibility and constraint within the Paton System.

April 3, 2026Open Access

From Admissibility to Motion: Constraint as the Origin of Dynamics Within the Paton System

Key Points

The aim is to establish how motion is derived from admissibility and constraint within the Paton System.
Analyzed the structural relationship between admissibility and motion.
Defined motion as traversal within admissible regions.
Examined the concepts of viability and constraint compatibility for trajectories.
Demonstrated that motion is not a fundamental primitive but arises from defined constraints.
Clarified that all trajectories are bounded by viability.
Showed that dynamics can be understood across various domains without changing existing laws.

Abstract

This paper establishes the structural relationship between admissibility and motion within the Paton System. It shows that motion arises only within admissible regions defined by constraint and is not a fundamental primitive. Motion is reframed as traversal within admissible space, with all trajectories bounded by viability and constraint compatibility. This clarifies the origin of dynamics across domains without modifying existing physical or mathematical laws.

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Authors

Andrew John Paton

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From Admissibility to Motion: Constraint as the Origin of Dynamics Within the Paton System

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Abstract

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