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| Format: | Recurso digital |
| Language: | English |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19651663 |
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| _version_ | 1866902218769170432 |
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| author | BEAU, Jérôme |
| author_facet | BEAU, Jérôme |
| contents | <div> <p><strong>Background:</strong><br>We develop a relational and spectral framework in which metric geometry emerges from correlation structures alone, without assuming a background manifold, coordinates, or fundamental geometric degrees of freedom.<br><br><strong>Methods:</strong><br>Starting from a relational substrate equipped with a symmetric connectivity operator, we define operational distances via minimal path functionals and introduce a non-circular coarse-graining scheme separating combinatorial neighborhoods from geometry-aware weighted distances. Spectral admissibility criteria identify regimes supporting a stable continuum approximation.<br><br><strong>Results:</strong><br>In these projectable regimes, the distance matrix admits a low-dimensional embedding, yielding emergent coordinates and an effective metric structure. Proper time, spatial distance, and curvature arise as coarse-grained summaries of relational organization. In symmetric weak-field limits, the effective metric reproduces Schwarzschild geometry without postulating fundamental gravitational dynamics.<br><br><strong>Conclusions:</strong><br>Breakdown of geometry occurs when spectral gaps close or connectivity becomes non-local, providing intrinsic limits to continuum spacetime. Analytical and numerical benchmarks establish robust spectral invariants, including the $8/3$ eigenvalue ratio on $S^3$. Spacetime thus appears as an operational construct emerging from relational spectral structure rather than a primitive entity.</p> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19651663 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Relational Reconstruction of Spacetime Geometry from Graph Laplacians BEAU, Jérôme Pre-geometric substrate emergent spacetime relational dynamics spectral geometry emergent metric spectral dimension <div> <p><strong>Background:</strong><br>We develop a relational and spectral framework in which metric geometry emerges from correlation structures alone, without assuming a background manifold, coordinates, or fundamental geometric degrees of freedom.<br><br><strong>Methods:</strong><br>Starting from a relational substrate equipped with a symmetric connectivity operator, we define operational distances via minimal path functionals and introduce a non-circular coarse-graining scheme separating combinatorial neighborhoods from geometry-aware weighted distances. Spectral admissibility criteria identify regimes supporting a stable continuum approximation.<br><br><strong>Results:</strong><br>In these projectable regimes, the distance matrix admits a low-dimensional embedding, yielding emergent coordinates and an effective metric structure. Proper time, spatial distance, and curvature arise as coarse-grained summaries of relational organization. In symmetric weak-field limits, the effective metric reproduces Schwarzschild geometry without postulating fundamental gravitational dynamics.<br><br><strong>Conclusions:</strong><br>Breakdown of geometry occurs when spectral gaps close or connectivity becomes non-local, providing intrinsic limits to continuum spacetime. Analytical and numerical benchmarks establish robust spectral invariants, including the $8/3$ eigenvalue ratio on $S^3$. Spacetime thus appears as an operational construct emerging from relational spectral structure rather than a primitive entity.</p> </div> |
| title | Relational Reconstruction of Spacetime Geometry from Graph Laplacians |
| topic | Pre-geometric substrate emergent spacetime relational dynamics spectral geometry emergent metric spectral dimension |
| url | https://doi.org/10.5281/zenodo.19651663 |