Formal Proof of the Collatz Conjecture Using the Three-Part Transition System

This paper presents a structured proof of the Collatz Conjecture using a novel Three-Part Transition System. We categorize the behavior of Collatz sequences into Fast Decreasing (FD), Fluctuating (FL), and Increasing Before Decrease (IBD) groups. Through this system, we show that all numbers eventually reach 1, proving the conjecture for all positive integers.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-04-12
DOI
https://doi.org/10.5281/zenodo.15203146
Primary Topic
Benford’s Law and Fraud Detection
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Formal Proof of the Collatz Conjecture Using the Three-Part Transition System

Zenodo (CERN European Organization for Nuclear Research)
Benford’s Law and Fraud Detection
article

Formal Proof of the Collatz Conjecture Using the Three-Part Transition System

article en

Abstract

This paper presents a structured proof of the Collatz Conjecture using a novel Three-Part Transition System. We categorize the behavior of Collatz sequences into Fast Decreasing (FD), Fluctuating (FL), and Increasing Before Decrease (IBD) groups. Through this system, we show that all numbers eventually reach 1, proving the conjecture for all positive integers.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 49%
Benford’s Law and Fraud Detection
DOIOpen Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Formal Proof of the Collatz Conjecture Using the Three-Part Transition System · Zenodo (CERN European Organization for Nuclear Research) (2025) | TGRS Research Map | TGRS