Version 1
: Received: 1 June 2024 / Approved: 4 June 2024 / Online: 5 June 2024 (10:19:24 CEST)
Version 2
: Received: 21 June 2024 / Approved: 21 June 2024 / Online: 24 June 2024 (08:08:06 CEST)
Version 3
: Received: 12 July 2024 / Approved: 15 July 2024 / Online: 15 July 2024 (09:50:14 CEST)
How to cite:
Diedrich, E. Resolving the Collatz Conjecture: A Rigorous Proof through Inverse Discrete Dynamical Systems and Inverse Algebraic Trees. Preprints2024, 2024060256. https://doi.org/10.20944/preprints202406.0256.v3
Diedrich, E. Resolving the Collatz Conjecture: A Rigorous Proof through Inverse Discrete Dynamical Systems and Inverse Algebraic Trees. Preprints 2024, 2024060256. https://doi.org/10.20944/preprints202406.0256.v3
Diedrich, E. Resolving the Collatz Conjecture: A Rigorous Proof through Inverse Discrete Dynamical Systems and Inverse Algebraic Trees. Preprints2024, 2024060256. https://doi.org/10.20944/preprints202406.0256.v3
APA Style
Diedrich, E. (2024). Resolving the Collatz Conjecture: A Rigorous Proof through Inverse Discrete Dynamical Systems and Inverse Algebraic Trees. Preprints. https://doi.org/10.20944/preprints202406.0256.v3
Chicago/Turabian Style
Diedrich, E. 2024 "Resolving the Collatz Conjecture: A Rigorous Proof through Inverse Discrete Dynamical Systems and Inverse Algebraic Trees" Preprints. https://doi.org/10.20944/preprints202406.0256.v3
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.
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.
