Sparad:
| Huvudupphovsman: | |
|---|---|
| Materialtyp: | Recurso digital |
| Språk: | engelska |
| Publicerad: |
Zenodo
2025
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| Ämnen: | |
| Länkar: | https://doi.org/10.5281/zenodo.16991608 |
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Innehållsförteckning:
- <p><strong>Update 29/Aug/2025(v94.8-2)</strong></p> <ul> <li> <p>Unified notation: accelerated map as “C”, compression map as “D”.</p> </li> <li> <p>Aligned short-window thresholds and documented the minimal vs. sufficient settings.</p> </li> <li> <p>Added the “terminal valuation inheritance” lemma to carry bounds to actual trajectories.</p> </li> <li> <p>Clarified the proof narrative (from sufficient window to monotone envelope to termination).</p> </li> <li> <p>Standardized references (label-based) and cleaned up formatting.</p> </li> <li> <p>Curated artifacts: CSV certificate, verifier script, and published SHA256 for integrity.</p> </li> </ul> <p><strong>Update 19/Aug/2025(v94.7.20)</strong></p> <ul> <li> <p><strong>Title</strong>: <em>Short-Window Anchors and a Finite-Cover Certificate for Collatz (Unconditional)</em></p> </li> <li> <p><strong>Authors</strong>: Yoshihito Kawanishi</p> </li> <li> <p><strong>Version</strong>: V94-7-20</p> </li> <li> <p><strong>Description</strong>:<br>“Using short-window thresholds (Θ₂=5, Θ₃=6), a finite-cover certificate at M=8192 (H=27), and a distance potential φ(r)=0.60·d(r), this package provides the paper and machine-checkable artifacts certifying unconditional anchor hitting and subsequent termination. Includes CSV/LP/PNG, verification scripts, and SHA256 checksums.”</p> </li> </ul> <p><strong>Update August 2025(v93.2):</strong></p> <p>This update strengthens the structural proof with:</p> <ul> <li> <p>Clear formulation of <strong>strong induction</strong> for all odd integers (Theorem 7)</p> </li> <li> <p>Improved <strong>theorem structure</strong> and logical flow</p> </li> <li> <p>Enhanced <strong>visual diagrams</strong> (e.g., <em>Z = 27 compression tree</em>)</p> </li> <li> <p>Expanded <strong>glossary</strong> and refined definitions</p> </li> <li> <p>Sharper <strong>ZFC-based loop exclusion</strong></p> </li> </ul> <p>This version replaces V92.3 with a clearer and more rigorous presentation.</p> <p><strong>---</strong></p> <p><strong>Update July 2025 (v92.3):</strong><br> This version presents the proof in a clearer and more reader-friendly structure, aligned with the expectations of top mathematical journals.</p> <p>---</p> <p>[Update July 2025] The updated version (v92.1.2) is titled: <br>**"A Structural Proof of the Collatz Conjecture via Recursive Compression"** <br>This reflects the refined formulation and educational emphasis in the final version.- Added full section numbering for journal submission<br>- Improved Glossary (Appendix E) with alphabetized terms<br>- Enhanced structural clarity and notation consistency</p> <p>---</p> <p>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.</p>