What question did this study set out to answer?

The aim is to investigate the stability of zero-scale closure in T-structured systems and its implications for dynamical behavior.

February 19, 2026Open Access

Dynamic Inaccessibility of Zero-Scale Closure in T-Structured Systems

Key Points

The aim is to investigate the stability of zero-scale closure in T-structured systems and its implications for dynamical behavior.
Establishment of the relation T = ( I · C ) / S
Analysis of bounded I and C with perturbable S > 0
Examination of the mapping S → T as S approaches zero
Mapping S → T becomes non-Lipschitz as S approaches zero
S → 0⁺ cannot serve as a robust Lyapunov-stable endpoint
Effective zero-scale closure is dynamically inaccessible within the Schuijf Law framework

Abstract

This technical note establishes the dynamical instability of pure zero-scale closure within T-structured systems governed by the relationT = ( I · C ) / S. Under minimal assumptions of bounded I and C and perturbable S > 0, the mapping S → T becomes non-Lipschitz as S approaches zero. It is shown that S → 0⁺ cannot represent a robust Lyapunov-stable endpoint under generic T-sensitive dynamics. This result implies that singular endpoints requiring effective zero-scale closure are dynamically inaccessible within the Schuijf Law framework. The work extends:Schuijf, J. (2026). The Schuijf Law: A Domain-Agnostic Formalism for Structured Systems. Zenodo. DOI: 10.5281/zenodo.17945385

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