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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.17964124 |
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Table of Contents:
- <p>This paper explores the relational foundations of zero-dimensional objects in geometry, challenging the classical view of points as absolute primitives without extension or scale. We demonstrate that zero-dimensionality is inherently dependent on the ambient space's dimensional structure, introducing concepts such as dimensional closure (the ability to recover all geometric degrees of freedom intrinsically) and informational leakage (unaccounted freedoms in lower-dimensional embeddings). Through rigorous propositions and proofs grounded in topology, differential geometry, and information theory, we show that scale is relative and observer-dependent in lower dimensions, while higher-dimensional embeddings reveal hidden indeterminacies. This framework reframes dimensionality as a measure of informational capacity, resolving paradoxes like ultraviolet divergences, non-local correlations, and singularities in physics. Implications extend to alternative geometric foundations (e.g., categorical or information-theoretic) and emergent properties in quantum gravity. </p>