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ZENODO
Preprint . 2025
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
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Why the Odd-Only Collatz Map Lacks Persistent Growth Tubes

Authors: Moon, KyungUp;

Why the Odd-Only Collatz Map Lacks Persistent Growth Tubes

Abstract

This repository accompanies the paper “Why the Odd-Only Collatz Map Lacks Persistent Growth Tubes”. The work presents an empirical and structural analysis of the odd-only Collatz map,focusing on the stability of growth-supporting residue structures under 2-adic refinement.Rather than claiming convergence or a proof of the Collatz conjecture,the paper isolates refinement stability as a diagnostic criterion. Empirically, residue classes that exhibit positive expected log-drift at a coarse modulus(e.g. mod 36) fail to remain dominant when refined to mod 72 for the map n ↦ 3n + 1,while the variant n ↦ 3n + 5 exhibits stable lifting of its dominant structure. The repository includes the paper, the analysis code, and the residue-conditioneddrift data used to generate the figures.The results are intended as a structural perspective on the difficulty of sustainingpersistent growth in Collatz-type dynamics.

Keywords

residue dynamics, Collatz conjecture, odd-only Collatz map, 2-adic refinement, empirical number theory, dynamical systems, strongly connected components

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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