121 MOC Differential Geometry (Multiple Origins with Higher Dimensions)
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2026/04/25
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MOC Differential Geometry (Multiple Origins with Higher Dimensions)
Axiom 1 — Hierarchical Multiple Origins Axiom
Space contains hierarchically nested origins, such as the Galactic origin, the Solar origin, and the Earth origin. Each origin is independent and irreplaceable by another.
Axiom 2 — Intra-layer Curvature Axiom
The differential structure and curvature of each layer are governed by its own origin. The upper layer governs large scales, while the lower layer governs small scales.
Axiom 3 — Dimensional Projection Axiom
Higher-dimensional geometry of an upper layer can be projected downward into lower-dimensional geometry of lower layers. When reduced to a single origin, MOC degenerates into traditional differential geometry.