An Attempted Symbolic Entropy Proof of the Collatz Conjecture via Canonical Rewrite Grammars
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| Natura: | Recurso digital |
| Lingua: | inglese |
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Zenodo
2025
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| _version_ | 1866902069350236160 |
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| author | Fathi, Kevin |
| author_facet | Fathi, Kevin |
| contents | <p>We prove the Collatz Conjecture using symbolic entropy and canonical rewrite<br>grammars. Instead of tracking numeric descent, we analyze the compressibility of<br>derivation trees under a canonical grammar for the Collatz map. By showing that<br>all infinite non-terminating sequences violate bounds on symbolic entropy, we derive a<br>contradiction from Kolmogorov incompressibility. Our approach avoids residue-based<br>assumptions, potential descent inequalities, and affine-cycle exclusions, replacing them<br>with formal entropy-based arguments in a fully symbolic, stratified logical system.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15632432 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | An Attempted Symbolic Entropy Proof of the Collatz Conjecture via Canonical Rewrite Grammars Fathi, Kevin Collatz Conjecture Kolmogorov Complexity Symbolic Dynamics Compression Theory Incompressibility Algorithmic Information Theory Binary Encoding of Orbits Termination Proof Recursive Systems Universal Turing Machine Information-Theoretic Contradiction Computability Trajectory Encoding Dynamical Systems Complexity Bounds Uncomputable Sequences Mathematical Logic Proof Theory Symbolic Logic Entropy of Orbits <p>We prove the Collatz Conjecture using symbolic entropy and canonical rewrite<br>grammars. Instead of tracking numeric descent, we analyze the compressibility of<br>derivation trees under a canonical grammar for the Collatz map. By showing that<br>all infinite non-terminating sequences violate bounds on symbolic entropy, we derive a<br>contradiction from Kolmogorov incompressibility. Our approach avoids residue-based<br>assumptions, potential descent inequalities, and affine-cycle exclusions, replacing them<br>with formal entropy-based arguments in a fully symbolic, stratified logical system.</p> |
| title | An Attempted Symbolic Entropy Proof of the Collatz Conjecture via Canonical Rewrite Grammars |
| topic | Collatz Conjecture Kolmogorov Complexity Symbolic Dynamics Compression Theory Incompressibility Algorithmic Information Theory Binary Encoding of Orbits Termination Proof Recursive Systems Universal Turing Machine Information-Theoretic Contradiction Computability Trajectory Encoding Dynamical Systems Complexity Bounds Uncomputable Sequences Mathematical Logic Proof Theory Symbolic Logic Entropy of Orbits |
| url | https://doi.org/10.5281/zenodo.15632432 |