Stalker's Resolution of the Collatz Conjecture
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| Format: | Recurso digital |
| Sprache: | Englisch |
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2025
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| _version_ | 1866902046046683136 |
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| author | Stalker, Eric |
| author_facet | Stalker, Eric |
| contents | <p>This paper presents a complete proof of the Collatz Conjecture, establishing that all positive integers under the 3n+1 map converge to the cycle {1, 2, 4}. The proof employs a Lyapunov-style energy function with quantified cumulative decay, exclusion of non-trivial cycles via Diophantine approximation and Baker’s theorem, deterministic total stopping time bounds using the Syracuse function, and an ergodic-theoretic framework for long-term behavior. Computational verification up to $2^{20}$ confirms the absence of alternative cycles. This resolves a longstanding open problem in number theory.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15136563 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Stalker's Resolution of the Collatz Conjecture Stalker, Eric Collatz Conjecture Number Theory Diophantine Approximation Ergodic Theory Mathematical Proof 3x+1 Problem <p>This paper presents a complete proof of the Collatz Conjecture, establishing that all positive integers under the 3n+1 map converge to the cycle {1, 2, 4}. The proof employs a Lyapunov-style energy function with quantified cumulative decay, exclusion of non-trivial cycles via Diophantine approximation and Baker’s theorem, deterministic total stopping time bounds using the Syracuse function, and an ergodic-theoretic framework for long-term behavior. Computational verification up to $2^{20}$ confirms the absence of alternative cycles. This resolves a longstanding open problem in number theory.</p> |
| title | Stalker's Resolution of the Collatz Conjecture |
| topic | Collatz Conjecture Number Theory Diophantine Approximation Ergodic Theory Mathematical Proof 3x+1 Problem |
| url | https://doi.org/10.5281/zenodo.15136563 |