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| Format: | Recurso digital |
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Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.17292166 |
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Table of Contents:
- <p>This report provides a definitive summary of a comprehensive research program aimed at</p> <p>resolving the Collatz Conjecture. We document two distinct, sophisticated lines of attack.</p> <p>The first, a quantitative approach, reframed the problem in terms of 2-adic dynamics and</p> <p>sought a contradiction via p-adic Diophantine approximation. This route was conclusively</p> <p>shown to fail due to a ”logarithmic barrier” that prevented the application of the Subspace</p> <p>Theorem. The second, an informational approach, re-centered the problem on the arithmetic</p> <p>realizability of parity sequences, using a novel coupled 2-adic/3-adic automaton. This second</p> <p>program was a technical success, leading to a complete classification of all possible cycles in</p> <p>the profinite system. However, it ultimately proved to be an elegant detour, reducing the</p> <p>problem perfectly to the classical, unsolved question of the existence of non-trivial integer</p> <p>cycles. This document details both failed assaults, presenting their respective negative</p> <p>results as a contribution to understanding the profound difficulty of the conjecture.</p>