| _version_ | 1866902322653691904 |
|---|---|
| author | yun, younghwan |
| author_facet | yun, younghwan |
| contents | <p>We develop a structural framework for the 3x+1 map linking the odd subsequence, derive<br>the Diophantine cycle constraint (2Mt − 3t)x = Σ(a), and exclude all odd cycles up to a<br>finite length T0 via reproducible computations. We further prove partial descent on positive-<br>density residue classes and conditional contraction results. While the global conjecture<br>remains open, our results sharpen cycle obstructions and provide verifiable progress toward<br>global convergence.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_16935124 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Partial Structural Results Toward the Collatz Conjecture via Non-Repeating Odd Trajectories and Recursive Decay yun, younghwan <p>We develop a structural framework for the 3x+1 map linking the odd subsequence, derive<br>the Diophantine cycle constraint (2Mt − 3t)x = Σ(a), and exclude all odd cycles up to a<br>finite length T0 via reproducible computations. We further prove partial descent on positive-<br>density residue classes and conditional contraction results. While the global conjecture<br>remains open, our results sharpen cycle obstructions and provide verifiable progress toward<br>global convergence.</p> |
| title | Partial Structural Results Toward the Collatz Conjecture via Non-Repeating Odd Trajectories and Recursive Decay |
| url | https://doi.org/10.5281/zenodo.16935124 |