Title: Collatz-6 Python Implementation Author: Hiroshi Harada Year: 2026 License: CC BY 4.0

Description: This archive provides a minimal and clean Python implementation of the Collatz-6 dynamical system. The Collatz-6 map is defined by modular rules based on n mod 6, including divisions by 6, 3, and 2, and jump operations of the form 7n±1 with 6-adic valuation reduction.

The system is strongly convergent, but some numbers exhibit temporary "glider-like" behavior, remaining in the Chaos Rim (numbers congruent to 1 or 5 mod 6) for many steps before eventually falling to the fixed point 1. This code supports numerical exploration of such behavior.

Included Functions:

• v6(n): 6-adic valuation
• collatz6_step(n): one iteration of the map
• collatz6_orbit(n): orbit generation until 1
• analyze_orbit_rim(n): steps, maximum value, growth ratio, Chaos Rim count
• scan_rim(start, end): search for glider-like numbers in a range

Files in this archive:

• collatz6.py (main implementation)
• README.md (GitHub-style documentation)
• LICENSE (CC BY 4.0)

Purpose: This archive is intended for reproducible research, numerical experiments, and exploration of escape-like behavior in the Collatz-6 system.

Citation: If you use this code, please cite the Zenodo DOI associated with this archive.

Contact: Hiroshi Harada