In the framework of multi-origin geometry, the novel curvature of space exhibits a positive correlation with the rotation and revolution of celestial bodies: the greater the curvature, the higher both the intrinsic rotational angular velocity and the orbital revolutionary angular velocity, and the three are unified in a consistent geometric-dynamic relationship.

Under multi-origin geometry, rotation and revolution are no longer externally imposed motions,
but the dual breathing of curvature itself.
Curvature is no longer an indifferent background geometry,
but the common geometric origin of both rotation and revolution.

The multi-origin geometric framework established in this paper is not merely a formal mathematical construction. Its profound motivation stems from a fundamental physical intuition concerning rotational phenomena in nature: all real rotations are not ideal single-center motions, but composite dynamical processes coupled by intrinsic rotation and orbital revolution. From the intrinsic spin and orbital angular momentum of elementary particles at the microscopic scale, to the rotation and orbital revolution of celestial bodies and galaxies at the macroscopic scale, this dual structure is universally present. Yet in traditional single-origin geometry and classical mechanics, they are treated separately — rotation is attributed to the object itself, revolution to an external center, and curvature regarded as an independent property of the background spacetime. The three lack a unified foundational description.

Within the multi-origin geometric system, this physical intuition acquires a rigorous geometric correspondence. The two independent origins attached to the surface correspond to the dual centers of rotation: one is the intrinsic origin, representing the object’s own center of mass or rotation, directly associated with intrinsic rotation; the other is the orbital origin, representing the external reference center around which the object moves, directly associated with orbital revolution. The difference vector between the two origins forms a geometric bridge connecting rotation and revolution, so that the two types of rotation are no longer independent physical quantities, but different manifestations of the same multi-origin spatial structure.

The novel non-Riemannian curvature constructed in this paper physically represents the geometric distortion generated by the coupling of rotation and revolution. Unlike Riemannian curvature, which only describes the bending of a single background space, this new curvature directly reflects the relative rotational intensity between the intrinsic origin and the orbital origin. The local rotation from intrinsic rotation and the spatial deflection from orbital revolution superimpose to form a composite curvature that cannot be fully described by traditional geometry. In other words, curvature is no longer a background property external to motion, but a geometric representation of the coupled effect of rotation and revolution.

On this basis, multi-origin angular momentum naturally decomposes into intrinsic rotational angular momentum and orbital revolutionary angular momentum, which together constitute the complete dynamical measure of rotation. Through rigorous derivation, a direct equivalence relation is established between the novel curvature and the composite angular momentum: the magnitude and distribution of curvature are determined by the relative intensity of rotation and revolution, while the evolution of rotational dynamics in turn shapes the geometric curvature characteristics of space. This unified relation fundamentally breaks down the barrier between geometric curvature and rotational physics, proving that curvature is the geometrized coupling of rotation and revolution, and angular momentum is the dynamized form of multi-origin curvature.

This interpretation not only conforms to the universal physical picture from the microscopic to the macroscopic scale, but also reveals the limitations of the fragmented description in traditional theories. The single-origin assumption is essentially a simplification of the dual structure of real rotations; multi-origin geometry and novel curvature return to the fundamental nature of rotational phenomena, unify geometric structure and dynamical behavior, and provide a brand-new theoretical perspective for understanding the deep connection between spin, orbital motion, and spatial bending.

In the framework of multi-origin geometry, when the spatial scale under consideration is fixed, the novel curvature is positively correlated with the rotational and revolutionary angular velocities of celestial bodies; the greater the curvature, the faster the intrinsic rotation and orbital revolution, and the three are unified in the same geometric-dynamic relation

\mathcal{K} = \frac{\Delta \mathbf{r} \times \dot{\Delta \mathbf{r}}}{|\Delta \mathbf{r}|^3}

It is directly defined by the relative rotation of the two origins, and is inherently a unified field of “rotation + revolution”.
When the endpoint of \Delta \mathbf{r} revolves around the other origin, one obtains the revolutionary curvature; when \Delta \mathbf{r} itself rotates about its center, one obtains the rotational curvature — both are contained within the same expression

\mathcal{K} = \frac{\Delta \mathbf{r} \times \dot{\Delta \mathbf{r}}}{|\Delta \mathbf{r}|^3}