Work

Collatz Conjecture Proof

Year: 2025

Type: article

Abstract: This paper presents a deterministic proof of the Collatz Conjecture, demonstrating that every positive integer converges to 1 under the standard Collatz iteration. By leveraging the 2-adic valuation v2(3n+1)v_2(3n+1)v2(3n+1) and analyzing the dynamics of the Syracuse function, we establish a universal logarithmic contraction. Key results include bounding the average valuation per odd step and rigorously excluding non-trivial cycles and divergence. Supported by simulations up to 10 to power 10, this work offers a resolution to a long-standing problem and highlights the power of valuation-based methods in dynamic number theory.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.15075793

Author: parry, dean alan

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6911722732

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