| _version_ | 1866902287914369024 |
|---|---|
| author | Raein Shiravani |
| author_facet | Raein Shiravani |
| contents | <p>This paper introduces a structural observation in the Collatz sequence for odd numbers — the Raein Ratio — and builds a formal inductive framework toward the resolution of the Collatz Conjecture. By showing that every sequence initiated at any natural number eventually reaches a smaller value through a finite set of rules, the work proposes a proof outline that demystifies the chaotic appearance of the sequence and supports convergence to 1.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15875824 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Raein Collatz Ratio & A Structured Inductive Proof of the Collatz Conjecture Raein Shiravani Number Theory <p>This paper introduces a structural observation in the Collatz sequence for odd numbers — the Raein Ratio — and builds a formal inductive framework toward the resolution of the Collatz Conjecture. By showing that every sequence initiated at any natural number eventually reaches a smaller value through a finite set of rules, the work proposes a proof outline that demystifies the chaotic appearance of the sequence and supports convergence to 1.</p> |
| title | The Raein Collatz Ratio & A Structured Inductive Proof of the Collatz Conjecture |
| topic | Number Theory |
| url | https://doi.org/10.5281/zenodo.15875824 |