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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.18529767 |
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Table of Contents:
- <p>This paper presents a formal challenge to the <strong>Riemann Hypothesis</strong>, arguing that the zeta function fails at the level of <strong>proportional arithmetic</strong>. The author asserts that because the function is finite at <strong>one-half</strong> but infinite at <strong>one</strong>, it violates the fundamental logic that doubling a half must result in a consistent whole. This perceived <strong>scalar inconsistency</strong> is described as a terminal flaw that renders the hypothesis a fictional construct detached from natural law. To resolve this, the text proposes a <strong>recursive phi framework</strong> based on the golden ratio, which maintains equilibrium between parts and wholes. Within this alternative structure, <strong>infinity is contained</strong> rather than unresolved, allowing the zeta function to operate without the contradictions found in traditional frameworks. The work concludes that while the hypothesis inspired significant discovery, it remains <strong>mathematically unsound</strong> due to these foundational violations of proportion.</p>