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Machine-Checkable Weak Covering for the Collatz (3x+1) Problem

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Title: Machine-Checkable Weak Covering for the Collatz (3x+1) Problem
Authors: Kawanishi, Yoshihito
Publisher Information: Zenodo
Publication Year: 2025
Collection: Zenodo
Subject Terms: Collatz Conjecture, Structural Proof, Recursive Compression, Arithmetic Logic, Induction, Number Theory, finite-cover certificate, Lyapunov, automated reasoning, certificate, formal verification
Description: Update 25/Sep/2025 (v94.8-3) Parameters locked: Weak Covering(13,30) as the main target; added a small "Parameter note (27 vs 30)" box in the Artifact section; standardized the example command. Short-window thresholds consolidated: Theta2 = 5, Theta3 = 6 with end-window anchor t_k >= 2; macros aligned across statements and figures. Checker ↔ Theory alignment table placed immediately after Theorem (checker soundness) and before the certified corollary. Typesetting hygiene: T1 + lmodern + microtype, xurl, pdfstring safe commands; all overfull/underfull resolved; first occurrence of 2^m set as 2^{\,m}. Artifacts curated (filenames unchanged): cert.txt, sha256.txt, verify.py (stdlib-only), optional cert_branchsafe.txt; README includes one-command verification. Data/Code Availability updated to point to this version DOI; keywords adjusted for automated reasoning / formal verification. One-command verification:python3 verify.py --cert cert.txt --sha sha256.txt --m 13 --H 30 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 ...
Document Type: report
Language: English
Relation: https://zenodo.org/communities/advancedtheoreticalphysicsandmathematics/; https://zenodo.org/records/17197754; oai:zenodo.org:17197754; https://doi.org/10.5281/zenodo.17197754
DOI: 10.5281/zenodo.17197754
Availability: https://doi.org/10.5281/zenodo.17197754
https://zenodo.org/records/17197754
Rights: Creative Commons Attribution 4.0 International ; cc-by-4.0 ; https://creativecommons.org/licenses/by/4.0/legalcode
Accession Number: edsbas.B4B51E6E
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  Data: Machine-Checkable Weak Covering for the Collatz (3x+1) Problem
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  Data: 2025
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  Data: <searchLink fieldCode="DE" term="%22Collatz+Conjecture%22">Collatz Conjecture</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+Proof%22">Structural Proof</searchLink><br /><searchLink fieldCode="DE" term="%22Recursive+Compression%22">Recursive Compression</searchLink><br /><searchLink fieldCode="DE" term="%22Arithmetic+Logic%22">Arithmetic Logic</searchLink><br /><searchLink fieldCode="DE" term="%22Induction%22">Induction</searchLink><br /><searchLink fieldCode="DE" term="%22Number+Theory%22">Number Theory</searchLink><br /><searchLink fieldCode="DE" term="%22finite-cover+certificate%22">finite-cover certificate</searchLink><br /><searchLink fieldCode="DE" term="%22Lyapunov%22">Lyapunov</searchLink><br /><searchLink fieldCode="DE" term="%22automated+reasoning%22">automated reasoning</searchLink><br /><searchLink fieldCode="DE" term="%22certificate%22">certificate</searchLink><br /><searchLink fieldCode="DE" term="%22formal+verification%22">formal verification</searchLink>
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  Data: Update 25/Sep/2025 (v94.8-3) Parameters locked: Weak Covering(13,30) as the main target; added a small "Parameter note (27 vs 30)" box in the Artifact section; standardized the example command. Short-window thresholds consolidated: Theta2 = 5, Theta3 = 6 with end-window anchor t_k >= 2; macros aligned across statements and figures. Checker ↔ Theory alignment table placed immediately after Theorem (checker soundness) and before the certified corollary. Typesetting hygiene: T1 + lmodern + microtype, xurl, pdfstring safe commands; all overfull/underfull resolved; first occurrence of 2^m set as 2^{\,m}. Artifacts curated (filenames unchanged): cert.txt, sha256.txt, verify.py (stdlib-only), optional cert_branchsafe.txt; README includes one-command verification. Data/Code Availability updated to point to this version DOI; keywords adjusted for automated reasoning / formal verification. One-command verification:python3 verify.py --cert cert.txt --sha sha256.txt --m 13 --H 30 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 ...
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  Data: https://zenodo.org/communities/advancedtheoreticalphysicsandmathematics/; https://zenodo.org/records/17197754; oai:zenodo.org:17197754; https://doi.org/10.5281/zenodo.17197754
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        Value: 10.5281/zenodo.17197754
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      – Text: English
    Subjects:
      – SubjectFull: Collatz Conjecture
        Type: general
      – SubjectFull: Structural Proof
        Type: general
      – SubjectFull: Recursive Compression
        Type: general
      – SubjectFull: Arithmetic Logic
        Type: general
      – SubjectFull: Induction
        Type: general
      – SubjectFull: Number Theory
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      – SubjectFull: finite-cover certificate
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      – SubjectFull: automated reasoning
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      – SubjectFull: certificate
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      – SubjectFull: formal verification
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      – TitleFull: Machine-Checkable Weak Covering for the Collatz (3x+1) Problem
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