Collatz Conjecture: A Reverse Construction Bijective Proof via Layered Directed Acyclic Graphs
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| Sprache: | Englisch |
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2025
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| _version_ | 1866902043298365440 |
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| author | Aaron Brolin Fish |
| author_facet | Aaron Brolin Fish |
| contents | <div>This paper presents a bijective proof of the Collatz Conjecture using a reverse construction framework. By systematically generating all odd predecessors and analyzing their structure through modular decomposition and parity-controlled mappings, we demonstrate that every odd number follows a unique reverse path terminating in the base cycle. A set of closed-form equations defines each sequence, and their disjoint coverage guarantees completeness. The result is a comprehensive bijective mapping of the odd integers within a unified reverse construction, validating the conjecture.</div> <div> </div> <div>aaron.b.fish@gmail.com</div> <div> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15762769 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Collatz Conjecture: A Reverse Construction Bijective Proof via Layered Directed Acyclic Graphs Aaron Brolin Fish Collatz Conjecture, reverse construction, bijective proof, number theory, graph theory, 2-adic analysis <div>This paper presents a bijective proof of the Collatz Conjecture using a reverse construction framework. By systematically generating all odd predecessors and analyzing their structure through modular decomposition and parity-controlled mappings, we demonstrate that every odd number follows a unique reverse path terminating in the base cycle. A set of closed-form equations defines each sequence, and their disjoint coverage guarantees completeness. The result is a comprehensive bijective mapping of the odd integers within a unified reverse construction, validating the conjecture.</div> <div> </div> <div>aaron.b.fish@gmail.com</div> <div> </div> |
| title | Collatz Conjecture: A Reverse Construction Bijective Proof via Layered Directed Acyclic Graphs |
| topic | Collatz Conjecture, reverse construction, bijective proof, number theory, graph theory, 2-adic analysis |
| url | https://doi.org/10.5281/zenodo.15762769 |