A Proof of the Collatz Conjecture Using an Attractor Set and a Lexicographic Measure for 7-Class Numbers

We prove the Collatz conjecture using:• Classification of odd numbers by residue modulo 8.• An attractor set A = {Aj = (4j − 1)/3} ∪ {4m}.• The observation that every odd number lies at an even distance from both boundaryattractors.• A lexicographic measure Φ(n) = (−j, min(x, y)) for 7 (mod 8) numbers, whichstrictly decreases after every finite sequence of steps.All lemmas are rigorously proved. The proof is complete.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-29
DOI
https://doi.org/10.5281/zenodo.21042955
Primary Topic
Benford’s Law and Fraud Detection
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

A Proof of the Collatz Conjecture Using an Attractor Set and a Lexicographic Measure for 7-Class Numbers

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

A Proof of the Collatz Conjecture Using an Attractor Set and a Lexicographic Measure for 7-Class Numbers

mahir elhisadi
preprint en

Abstract

We prove the Collatz conjecture using:• Classification of odd numbers by residue modulo 8.• An attractor set A = {Aj = (4j − 1)/3} ∪ {4m}.• The observation that every odd number lies at an even distance from both boundaryattractors.• A lexicographic measure Φ(n) = (−j, min(x, y)) for 7 (mod 8) numbers, whichstrictly decreases after every finite sequence of steps.All lemmas are rigorously proved. The proof is complete.

Zenodo (CERN European Organization for Nuclear Research)
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.

A Proof of the Collatz Conjecture Using an Attractor Set and a Lexicographic Measure for 7-Class Numbers — mahir elhisadi · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS