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April 21, 20260 citationsOpen Access

2-Adic State Automaton Framework for the Collatz Conjecture Reduction

A 2-Adic State Automaton Reduction Framework for the Collatz Conjecture

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Authors

KMKyung-Up Moon

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Overview

This work introduces a framework that simplifies the Collatz conjecture, suggesting new avenues for exploration.

Key Points

  • The aim is to provide a structural reduction framework for the Collatz conjecture using a 2-adic state automaton.
  • Developed a reduction framework based on 2-adic state automaton concepts.
  • Established results independent of orbit convergence.
  • Eliminated sources of periodic behavior within the framework.
  • Reduced periodic orbits to state cycles.
  • Identified a remaining challenge related to the boundedness of sibling-rank spread.
  • Provided a structural decomposition of the Collatz conjecture.
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Cite This Study

Kyung-Up Moon (2026) studied this question.

synapsesocial.com/papers/69e71423cb99343efc98d8aehttps://doi.org/10.5281/zenodo.19650191
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