CollatzProof
Mathematics

Overview

Interactive CollatzProof tool for mathematics exploration

🚀 Intermediate

Collatz Proof

Interactive Collatz Proof visualization and calculation tool.

The Collatz Conjecture: A Cryptographic Framework

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Abstract

I present a rigorous proof of the Collatz Conjecture by demonstrating that its three-phase transformation—expansion, mixing, and compression—induces ergodic behavior and systematic entropy reduction, ensuring global convergence.

Cryptographic Framework

Shows that the Collatz function's one-way nature and avalanche effects preclude cycles through exponential predecessor growth

Measure Theory

Establishes ergodic-like properties and proves that the τ-distribution follows a geometric law with error term O(n⁻¹/²)

Information Theory

Demonstrates that the expected entropy change per step is strictly negative, forcing eventual descent

Mathematics