Structure of My Geometry

Author: Suhang Zhang
（Luoyang School of Mathematics）

1. The overall barycenter of the Milky Way → First Origin, First Hierarchy
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2. The Sun (local barycenter within the Milky Way) → Second Origin, Second Hierarchy
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3. The Earth (local barycenter within the Solar System) → Third Origin, Third Hierarchy

Each hierarchy possesses an independent origin.
Each hierarchy warps the surrounding spacetime.
All hierarchies are nested, superimposed, and non-canceling.

The formula is given by

1. Galactic center O_G completes one revolution → large spiral

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2. Sun O_S orbits the Galaxy while rotating itself → medium spiral

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3. Earth O_E nested within the Sun’s motion → small spiral

Combined:

Layer upon layer intertwined, the entire structure forms a gigantic spacetime twist.

Under the MOC multi-origin curvature framework, this layered precessional and coupled motion structure can be naturally extended to higher-dimensional manifolds. Higher spatial hierarchies, local origins, and intrinsic curvature motions can be hierarchically defined within high-dimensional intrinsic space, with geodesic evolutions and periodic motions of all scales superposed and coupled in the high-dimensional system.

This paper constructs a nested geometric model of three local origins—the Galactic center, the Sun, and the Earth—within the MOC (Multi-Origin Curvature) geometric framework. The hierarchical worldline position expression is given as:

\boldsymbol{P}(t) = O_G + R_G(t)\big(O_S + R_S(t)\,O_E(t)\big)

It describes the helical-knot configuration formed when a high-dimensional primordial manifold projects onto four-dimensional spacetime via direct-oblique mapping. As a kinematic construction of the MOC system, this model can serve as the geometric foundation for the Unified Curvature Equation (UCE).

The Unified Curvature Equation (UCE) is a geometric extremal equation for total curvature: taking the variation of the action built from the norm of total curvature \delta\int \|\mathbb R\|^2 d^4x=0, the core equation \nabla^*\mathbb{R}=0 is obtained after variation. UCE unifies spacetime curvature and gauge field curvature into a single total curvature object. Through geometric projection, it can derive the Einstein field equations and the fiber bundle gauge curvature equations respectively.

In follow-up research, the curvature vectors corresponding to each local origin can be extracted from the hierarchical worldlines presented in this paper and substituted into the UCE dynamic framework, to further investigate the evolution law of multi-layer nested curvature fields.