NONEXISTENCE OF A MINIMAL COUNTEREXAMPLE TO THE COLLATZ CONJECTURE

Abstract. We show through a well-founded “seeded interval” framework that there is no minimal counterexample to the Collatz Conjecture. By partitioning Z+ into dyadic intervals anchored at a finite list of verified odd seeds, we prove that each Collatz step strictly descends in lexicographic order on these intervals, forcing eventual arrival in the known 1 ↔ 2 loop.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-09-12
DOI
https://doi.org/10.5281/zenodo.17103961
Primary Topic
Geochemistry and Geologic Mapping
Type
article
Field-Weighted Citation Impact
0.00
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article

NONEXISTENCE OF A MINIMAL COUNTEREXAMPLE TO THE COLLATZ CONJECTURE

Zenodo (CERN European Organization for Nuclear Research)
Geochemistry and Geologic Mapping
article

NONEXISTENCE OF A MINIMAL COUNTEREXAMPLE TO THE COLLATZ CONJECTURE

article en

Abstract

Abstract. We show through a well-founded “seeded interval” framework that there is no minimal counterexample to the Collatz Conjecture. By partitioning Z+ into dyadic intervals anchored at a finite list of verified odd seeds, we prove that each Collatz step strictly descends in lexicographic order on these intervals, forcing eventual arrival in the known 1 ↔ 2 loop.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 44%
Geochemistry and Geologic Mapping
DOIOpen Access PDFOpenAlex
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NONEXISTENCE OF A MINIMAL COUNTEREXAMPLE TO THE COLLATZ CONJECTURE · Zenodo (CERN European Organization for Nuclear Research) (2025) | TGRS Research Map | TGRS