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2025
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| Online Access: | https://doi.org/10.5281/zenodo.18096844 |
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| _version_ | 1866901193925591040 |
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| author | Claudio Menéndez |
| author_facet | Claudio Menéndez |
| contents | <p>This document serves as <em>Paper 0</em> of the Finite Closure Geometry (FGC) research program. It provides a conceptual overview and a structured entry point to the technical papers that develop the framework.</p> <p>Rather than introducing new mathematical results, this work clarifies the scope, motivation, and internal architecture of the FGC program. Its role is to organize the existing papers into a coherent research agenda and to guide readers through their conceptual connections.</p> <p>The central idea explored in the FGC program is that certain classical geometric constants—most notably <span><span>π\pi</span><span><span><span>π</span></span></span></span>—can be interpreted as effective descriptors emerging from finite generative systems in appropriate asymptotic regimes. From this perspective, continuum quantities appear as limits associated with growth and refinement processes rather than as primitive ingredients of the underlying structures.</p> <p>This paper therefore:</p> <p>• clarifies the conceptual scope of Finite Closure Geometry and what the program does and does not claim<br>• explains the mathematical motivation for studying generative systems with finite closure properties<br>• provides a guided overview of the foundational papers of the program</p> <p>The document is intended as an entry point for readers interested in discrete geometry, geometric growth, asymptotic limits, and structural approaches to the emergence of continuum behavior.</p> <h2>Keywords</h2> <p>finite closure geometry<br>discrete geometry<br>generative systems<br>asymptotic limits<br>geometric constants<br>Gromov–Hausdorff convergence</p> <h2>Upload type</h2> <p>Publication → <strong>Preprint</strong></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18096844 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Finite Closure Geometry (FGC): A Structural Program for Global Non-Closure Claudio Menéndez <p>This document serves as <em>Paper 0</em> of the Finite Closure Geometry (FGC) research program. It provides a conceptual overview and a structured entry point to the technical papers that develop the framework.</p> <p>Rather than introducing new mathematical results, this work clarifies the scope, motivation, and internal architecture of the FGC program. Its role is to organize the existing papers into a coherent research agenda and to guide readers through their conceptual connections.</p> <p>The central idea explored in the FGC program is that certain classical geometric constants—most notably <span><span>π\pi</span><span><span><span>π</span></span></span></span>—can be interpreted as effective descriptors emerging from finite generative systems in appropriate asymptotic regimes. From this perspective, continuum quantities appear as limits associated with growth and refinement processes rather than as primitive ingredients of the underlying structures.</p> <p>This paper therefore:</p> <p>• clarifies the conceptual scope of Finite Closure Geometry and what the program does and does not claim<br>• explains the mathematical motivation for studying generative systems with finite closure properties<br>• provides a guided overview of the foundational papers of the program</p> <p>The document is intended as an entry point for readers interested in discrete geometry, geometric growth, asymptotic limits, and structural approaches to the emergence of continuum behavior.</p> <h2>Keywords</h2> <p>finite closure geometry<br>discrete geometry<br>generative systems<br>asymptotic limits<br>geometric constants<br>Gromov–Hausdorff convergence</p> <h2>Upload type</h2> <p>Publication → <strong>Preprint</strong></p> |
| title | Finite Closure Geometry (FGC): A Structural Program for Global Non-Closure |
| url | https://doi.org/10.5281/zenodo.18096844 |