Finite-Window Rigidity in Fibonacci Numeration

Symbolic dynamics and formal language theory

gen2
symbolic
submitted
The Zeckendorf fold map is the normal-form map of a finite terminating confluent rewrite system, with a sharp block-bijection threshold at m=3. The right Fischer cover is identified as a suffix graph …
Published

April 7, 2026

Journal of Number Theory 68 Theorems Symbolic dynamics and formal language theory

Abstract

The Zeckendorf fold map is the normal-form map of a finite terminating confluent rewrite system, with a sharp block-bijection threshold at m=3. The right Fischer cover is identified as a suffix graph with 2^(m-1) states.

Keywords: Zeckendorf expansion, Fibonacci numeration, shifts of finite type, transducer theory, Markov chains

Infographic

resolution_folding_core_symbolic Infographic

Video Explainer

Paper & Source