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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.17815010 |
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Table of 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>