What question did this study set out to answer?

To prove the validity of the Collatz conjecture by mapping odd integers to their subsequent values.

May 11, 2026Open Access

A Proof of the Collatz Conjecture

Key Points

To prove the validity of the Collatz conjecture by mapping odd integers to their subsequent values.
Consider the complete map from one odd integer to the next.
Evaluate how this mapping decreases the value for any odd integer x ≥ 3.
All odd integers lead to the cycle {4 → 2 → 1} when following the mapping.

Abstract

We prove the Collatz conjecture by considering the complete map from one odd integer to the next. For any odd x 3, this map strictly decreases the value, forcing all trajectories into the known cycle \4 2 1\.

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Cite This Study

Shengxing He (Sat,) studied this question.

synapsesocial.com/papers/6a0172ac3a9f334c28272d17 https://doi.org/https://doi.org/10.5281/zenodo.20093531

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1A Proof of the Collatz Conjecture2026
2A Proof of the 3x-1 Conjecture2026
3Proof of the Collatz Conjecture using logical and probabilistic approaches2024
4An Unconditional Proof of the Collatz Conjecture By Qin zitai2026
5The Collatz Conjecture: A Complete Proof via Symmetric Numbers and Topological Descent2026

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