Resolving the Collatz Conjecture: A Rigorous Proof through Inverse Discrete Dynamical Systems and Algebraic Inverse Trees

Eduardo Diedrich

doi:10.20944/preprints202310.0773.v15

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preprints.org > computer science and mathematics > mathematics > doi: 10.20944/preprints202310.0773.v15

Preprint Article Version 15 Preserved in Portico This version is not peer-reviewed

Resolving the Collatz Conjecture: A Rigorous Proof through Inverse Discrete Dynamical Systems and Algebraic Inverse Trees

Eduardo Diedrich

Version 1 : Received: 11 October 2023 / Approved: 12 October 2023 / Online: 12 October 2023 (04:43:40 CEST)
Version 2 : Received: 13 October 2023 / Approved: 13 October 2023 / Online: 13 October 2023 (04:48:03 CEST)
Version 3 : Received: 13 October 2023 / Approved: 17 October 2023 / Online: 17 October 2023 (10:26:40 CEST)
Version 4 : Received: 17 October 2023 / Approved: 18 October 2023 / Online: 18 October 2023 (10:09:49 CEST)
Version 5 : Received: 19 October 2023 / Approved: 20 October 2023 / Online: 20 October 2023 (10:28:38 CEST)
Version 6 : Received: 21 October 2023 / Approved: 23 October 2023 / Online: 23 October 2023 (10:35:42 CEST)
Version 7 : Received: 26 October 2023 / Approved: 26 October 2023 / Online: 27 October 2023 (09:14:36 CEST)
Version 8 : Received: 28 October 2023 / Approved: 30 October 2023 / Online: 30 October 2023 (09:38:23 CET)
Version 9 : Received: 30 October 2023 / Approved: 31 October 2023 / Online: 31 October 2023 (11:01:44 CET)
Version 10 : Received: 1 November 2023 / Approved: 2 November 2023 / Online: 2 November 2023 (08:16:04 CET)
Version 11 : Received: 8 November 2023 / Approved: 8 November 2023 / Online: 8 November 2023 (07:53:02 CET)
Version 12 : Received: 21 November 2023 / Approved: 22 November 2023 / Online: 24 November 2023 (04:11:49 CET)
Version 13 : Received: 27 December 2023 / Approved: 28 December 2023 / Online: 29 December 2023 (01:14:06 CET)
Version 14 : Received: 16 March 2024 / Approved: 17 March 2024 / Online: 18 March 2024 (10:42:38 CET)
Version 15 : Received: 24 March 2024 / Approved: 25 March 2024 / Online: 26 March 2024 (11:50:16 CET)
Version 16 : Received: 28 March 2024 / Approved: 28 March 2024 / Online: 29 March 2024 (11:23:27 CET)
Version 17 : Received: 30 March 2024 / Approved: 1 April 2024 / Online: 2 April 2024 (11:53:22 CEST)

How to cite: Diedrich, E. Resolving the Collatz Conjecture: A Rigorous Proof through Inverse Discrete Dynamical Systems and Algebraic Inverse Trees. Preprints 2023, 2023100773. https://doi.org/10.20944/preprints202310.0773.v15 Diedrich, E. Resolving the Collatz Conjecture: A Rigorous Proof through Inverse Discrete Dynamical Systems and Algebraic Inverse Trees. Preprints 2023, 2023100773. https://doi.org/10.20944/preprints202310.0773.v15

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MDPI and ACS Style

Diedrich, E. Resolving the Collatz Conjecture: A Rigorous Proof through Inverse Discrete Dynamical Systems and Algebraic Inverse Trees. Preprints 2023, 2023100773. https://doi.org/10.20944/preprints202310.0773.v15

APA Style

Diedrich, E. (2024). Resolving the Collatz Conjecture: A Rigorous Proof through Inverse Discrete Dynamical Systems and Algebraic Inverse Trees. Preprints. https://doi.org/10.20944/preprints202310.0773.v15

Chicago/Turabian Style

Diedrich, E. 2024 "Resolving the Collatz Conjecture: A Rigorous Proof through Inverse Discrete Dynamical Systems and Algebraic Inverse Trees" Preprints. https://doi.org/10.20944/preprints202310.0773.v15

Abstract

This article introduces the Theory of Inverse Discrete Dynamical Systems (TIDDS), a novel methodology for modeling and analyzing discrete dynamical systems via inverse algebraic models. Key concepts such as inverse modeling, structural analysis of inverse algebraic trees, and the establishment of topological equivalences for property transfer between a system and its inverse are elucidated. Central theorems on homeomorphic invariance and topological transport validate the transfer of cardinal attributes between dynamic representations, offering a fresh perspective on complex system analysis. A significant application presented is an alternative proof of the Collatz Conjecture, achieved by constructing an associated inverse model and leveraging analytical property transfers within the inverted tree structure. This work not only demonstrates the theory's capability to address and solve open problems in discrete dynamics but also suggests vast implications for expanding our understanding of such systems

Keywords

discrete dynamical systems; inverse modeling; topological equivalence; topological transport; algebraic trees; collatz conjecture; homeomorphic invariance

Subject

Computer Science and Mathematics, Mathematics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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