✅CollatzProof
MathematicsOverview
Interactive CollatzProof tool for mathematics exploration
🚀 Intermediate
Collatz Proof
Interactive Collatz Proof visualization and calculation tool.
The Collatz Conjecture: A Cryptographic Framework
Enter a starting number and click "Compute" to begin
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