Parity Pattern Audit for the Collatz Map: A Classification Framework with Empirical Descent Evidence (Alpha Specification v1.0)
Abstract
This document presents a systematic audit of parity patterns under the Collatz map, providing a classification framework for behavior classes rather than individual trajectories.Key Contributions:Implementation of a Lyapunov-like descent property across k-step windows.Empirical demonstration of strictly negative drift for all realized patterns across k∈{6,7,8}.Public verification script for pattern classification and first-hit seed identification.Commercial Notice: This preprint includes the classification framework and verification script. The proprietary descent functional, mathematical derivations for drift non-positivity, and extension techniques for pattern coverage are REDACTED and available only under commercial license.Contact for Full Methodology and Licensing: UncleBroFields@proton.me
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Analytic Number Theory Research
Advanced Mathematical Theories
Publication details
- Journal / source
- Figshare
- Publication date
- 1 January 2026
- Document type
- Preprint