The Galactic Plateau as a Result of Observational Relativity. Double-Chain Structure and Integral Residual

Here a reconstruction-based description of galactic rotation curves is developed in which the flat plateau is not a special equilibrium point, but a finite “bounded branch” of the dynamics between two transition layers. Within this framework, the observable galaxy is described by a multichannel operator that is reduced to a nondegenerate two-operator sector; its projective class defines a single reduced degree of freedom whose natural symmetry is given by Möbius transformations. The infinitesimal action of this symmetry leads to a Riccati-type dynamics and a double-kink (double-chain) structure, which in a central field produces an additional effective 1/r-contribution and hence a constant term in the squared rotation velocity. Using SPARC rotation curves in invariant coordinates, the study shows that disk galaxies exhibit a hyperbolic “saddle” structure, a finite-width plateau in normalized radius, and a strong asymmetry of the integrated geometric residual between inner and outer branches. The same bounded-branch reconstruction is consistent with the observed radial acceleration relation and the baryonic Tully–Fisher relation, suggesting that these phenomena share a common geometric origin rather than representing independent empirical constraints.