Collective Curvature and Rotation Memory: A Structural Alternative to Dark Matter

Galactic rotation curves, stellar populations moving at different speeds at the same radius, the geometric stability and branching structures of comet tails, and the dynamical behavior in binary and triple systems in which a region of space with no mass present becomes an effective reference for orbital motion, have each been accepted as observational facts. However, within conventional gravitational theory or dark-matter-based interpretations, these phenomena have not been unified into a single consistent structural logic. Dark matter models have succeeded in reproducing these behaviors numerically, but they have not provided an essential explanation for why such structures must appear, nor for why phenomena across different scales share similar dynamical signatures. This paper argues that these limitations arise because gravitational phenomena are fundamentally interpreted as a problem of force, and the mathematical structure is restricted to the minimum necessary range to clarify the framework, while the primary explanation is presented through descriptive reasoning and analogy, focusing on revealing the physical meaning of curvature structure. The aim of this study is not to deny the existence of dark matter. Rather, its aim is to present an alternative coordinate framework in which, even without assuming dark matter, the observed dynamical phenomena can be structurally explained as necessarily taking the forms they do. In addition, by explicitly including falsification conditions, this theory is proposed as an open theoretical frame that prioritizes scientific testability over unlimited expansion of explanatory scope. Contents