Foundational Geometric Frameworks for Curvature Dynamics and Orbital Geometry
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| Format: | Recurso digital |
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Zenodo
2025
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| _version_ | 1866901541359714304 |
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| author | Lâu, Thiat-uî |
| author_facet | Lâu, Thiat-uî |
| contents | <p>This document presents a unified conceptual summary of five foundational geometric frameworks for curvature-based gravitational dynamics and orbital geometry. It introduces:<br>(1) a curvature-based formulation of the N-body problem,<br>(2) a universal Hamiltonian curvature criterion for secular instability,<br>(3) a geometric condition for secular chaos boundaries,<br>(4) the Focal–Curvature Duality linking orbital focal geometry to Hamiltonian curvature, and<br>(5) the Focal–Curvature Dynamical Atlas for classifying orbital regimes.</p> <p>The document formalizes the core definitions, invariants, theorem statements, and geometric structures underlying curvature-driven gravitational dynamics. It also provides system-class coverage, symbolic skeleton equations, and a three-layer mapping between Hamiltonian curvature, focal geometry, and dynamical regimes.</p> <p>This summary establishes conceptual authorship priority for the theoretical framework.<br>Full derivations, proofs, and applications will appear in forthcoming peer-reviewed publications.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17815010 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Foundational Geometric Frameworks for Curvature Dynamics and Orbital Geometry Lâu, Thiat-uî <p>This document presents a unified conceptual summary of five foundational geometric frameworks for curvature-based gravitational dynamics and orbital geometry. It introduces:<br>(1) a curvature-based formulation of the N-body problem,<br>(2) a universal Hamiltonian curvature criterion for secular instability,<br>(3) a geometric condition for secular chaos boundaries,<br>(4) the Focal–Curvature Duality linking orbital focal geometry to Hamiltonian curvature, and<br>(5) the Focal–Curvature Dynamical Atlas for classifying orbital regimes.</p> <p>The document formalizes the core definitions, invariants, theorem statements, and geometric structures underlying curvature-driven gravitational dynamics. It also provides system-class coverage, symbolic skeleton equations, and a three-layer mapping between Hamiltonian curvature, focal geometry, and dynamical regimes.</p> <p>This summary establishes conceptual authorship priority for the theoretical framework.<br>Full derivations, proofs, and applications will appear in forthcoming peer-reviewed publications.</p> |
| title | Foundational Geometric Frameworks for Curvature Dynamics and Orbital Geometry |
| url | https://doi.org/10.5281/zenodo.17815010 |