Parity Pattern Audit for the Collatz Map: A Classification Framework with Empirical Descent Evidence (Alpha Specification v1.0)

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Authors: Ryan Fields
Cited by: 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