The destiny of constant structure discrete time closed semantic systems

TL;DR

This paper analyzes constant structure closed semantic systems, showing that their iterative redefinition process rapidly stabilizes into pairwise isomorphic states, with implications for understanding their long-term behavior.

Contribution

It provides a formal proof that such systems tend to stabilize into isomorphic states and explores potential directions for future research.

Findings

Iterative redefinition leads to pairwise isomorphic states

Systems quickly stabilize into fixed structures

Provides a foundation for further exploration of semantic system dynamics

Abstract

Constant structure closed semantic systems are the systems each element of which receives its definition through the correspondent unchangeable set of other elements of the system. Discrete time means here that the definitions of the elements change iteratively and simultaneously based on the "neighbor portraits" from the previous iteration. I prove that the iterative redefinition process in such class of systems will quickly degenerate into a series of pairwise isomorphic states and discuss some directions of further research.