Layered Recursive Compression as a Structural Proof of the Collatz Conjecture (Version 92)

Update July 2025 (v92.3):
 This version presents the proof in a clearer and more reader-friendly structure, aligned with the expectations of top mathematical journals.

---

[Update July 2025] The updated version (v92.1.2) is titled:  
**"A Structural Proof of the Collatz Conjecture via Recursive Compression"**  
This reflects the refined formulation and educational emphasis in the final version.- Added full section numbering for journal submission
- Improved Glossary (Appendix E) with alphabetized terms
- Enhanced structural clarity and notation consistency

---

This document presents a complete structural proof of the Collatz Conjecture based on a recursive compression framework. By applying a unified arithmetic transformation compress(Z) = (Z + 1) / 2 and a hierarchical convergence structure, the paper shows that all positive integers, both even and odd, must converge to 1 in a finite number of steps. Visual appendices include flowcharts and hierarchical induction diagrams to support the logical structure of the proof.