A characterization of entropy dimensions of minimal tridimensional subshifts of finite type

TL;DR

This paper characterizes the possible entropy dimensions of minimal three-dimensional subshifts of finite type under a computability condition, utilizing Goldbach's theorem on Fermat numbers.

Contribution

It provides a novel characterization linking entropy dimensions of minimal 3D subshifts of finite type to number theory, specifically Goldbach's theorem.

Findings

Entropy dimensions are characterized for minimal 3D subshifts of finite type.

The characterization relies on a computability condition and number theory.

Goldbach's theorem is used to establish the results.

Abstract

We prove in this text a characterization of the possible entropy dimensions of minimal tridimensional subshifts of finite type with a computability condition, using Goldbach's theorem on Fermat numbers.