What question did this study set out to answer?

The aim is to clarify how mathematics functions as a structural element in the Paton System.

April 3, 2026Open Access

Mathematics as the Bridge Between Admissibility and Usability: A Structural Clarification Within the Paton System

Key Points

The aim is to clarify how mathematics functions as a structural element in the Paton System.
Analytical framework established for examining the relationship between mathematics and system admissibility.
Discussion on the transformation of admissible structures into usable systems.
Identified that mathematics does not determine system validity but operates on admissibility.
Established that admissibility is crucial for defining system existence and application.

Abstract

This paper clarifies the structural role of mathematics within the Paton System. It establishes that mathematics operates on admissible systems rather than determining system validity. Admissibility defines whether a system may exist, while mathematics transforms admissible structure into usable, measurable, and operational forms. This positions mathematics as a bridge between structural validity and application across domains.

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Cite This Study

Andrew John Paton (Tue,) studied this question.

synapsesocial.com/papers/69cf5ea85a333a821460d2b8 https://doi.org/https://doi.org/10.5281/zenodo.19346044