Formal Proof of the Collatz Conjecture Using the Three-Part Transition System
Year: 2025
Type: article
Abstract: This paper presents a structured proof of the Collatz Conjecture using a novel Three-Part Transition System. We categorize the behavior of Collatz sequences into Fast Decreasing (FD), Fluctuating (FL), and Increasing Before Decrease (IBD) groups. Through this system, we show that all numbers eventually reach 1, proving the conjecture for all positive integers.
Author: Owies, Samer
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6949701540
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