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

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Τίτλος: Layered Recursive Compression as a Structural Proof of the Collatz Conjecture (Version 92)
Συγγραφείς: Kawanishi, Yoshihito
Στοιχεία εκδότη: Zenodo
Έτος έκδοσης: 2025
Συλλογή: Zenodo
Θεματικοί όροι: Collatz Conjecture, Structural Proof, Recursive Compression, Arithmetic Logic, Induction, Number Theory, finite-cover certificate, Lyapunov
Περιγραφή: Update 29/Aug/2025(v94.8-2) Unified notation: accelerated map as “C”, compression map as “D”. Aligned short-window thresholds and documented the minimal vs. sufficient settings. Added the “terminal valuation inheritance” lemma to carry bounds to actual trajectories. Clarified the proof narrative (from sufficient window to monotone envelope to termination). Standardized references (label-based) and cleaned up formatting. Curated artifacts: CSV certificate, verifier script, and published SHA256 for integrity. Update 19/Aug/2025(v94.7.20) Title: Short-Window Anchors and a Finite-Cover Certificate for Collatz (Unconditional) Authors: Yoshihito Kawanishi Version: V94-7-20 Description:“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.” Update August 2025(v93.2): This update strengthens the structural proof with: Clear formulation of strong induction for all odd integers (Theorem 7) Improved theorem structure and logical flow Enhanced visual diagrams (e.g., Z = 27 compression tree) Expanded glossary and refined definitions Sharper ZFC-based loop exclusion This version replaces V92.3 with a clearer and more rigorous presentation. --- 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 ...
Τύπος εγγράφου: report
Γλώσσα: English
Relation: https://zenodo.org/communities/advancedtheoreticalphysicsandmathematics/; https://zenodo.org/records/16991608; oai:zenodo.org:16991608; https://doi.org/10.5281/zenodo.16991608
DOI: 10.5281/zenodo.16991608
Διαθεσιμότητα: https://doi.org/10.5281/zenodo.16991608
https://zenodo.org/records/16991608
Rights: Creative Commons Attribution 4.0 International ; cc-by-4.0 ; https://creativecommons.org/licenses/by/4.0/legalcode
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  Data: Layered Recursive Compression as a Structural Proof of the Collatz Conjecture (Version 92)
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  Data: Update 29/Aug/2025(v94.8-2) Unified notation: accelerated map as “C”, compression map as “D”. Aligned short-window thresholds and documented the minimal vs. sufficient settings. Added the “terminal valuation inheritance” lemma to carry bounds to actual trajectories. Clarified the proof narrative (from sufficient window to monotone envelope to termination). Standardized references (label-based) and cleaned up formatting. Curated artifacts: CSV certificate, verifier script, and published SHA256 for integrity. Update 19/Aug/2025(v94.7.20) Title: Short-Window Anchors and a Finite-Cover Certificate for Collatz (Unconditional) Authors: Yoshihito Kawanishi Version: V94-7-20 Description:“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.” Update August 2025(v93.2): This update strengthens the structural proof with: Clear formulation of strong induction for all odd integers (Theorem 7) Improved theorem structure and logical flow Enhanced visual diagrams (e.g., Z = 27 compression tree) Expanded glossary and refined definitions Sharper ZFC-based loop exclusion This version replaces V92.3 with a clearer and more rigorous presentation. --- 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 ...
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      – SubjectFull: Structural Proof
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      – TitleFull: Layered Recursive Compression as a Structural Proof of the Collatz Conjecture (Version 92)
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