Planar Constraint Geometry in the Local Group: Structural Implications of Non-Spherical Dark Matter Inference

Recent trajectory-based reconstructions of the Local Group environment increasingly favor a markedly non-spherical distribution of the dominant gravitating component, with solutions converging on a flattened, sheet-like geometry extending across tens of megaparsecs. Such reconstructions reconcile several long-standing observational discrepancies—including coherent satellite galaxy planes, suppressed relative velocities, and alignment with the supergalactic plane—but are often interpreted dynamically, as requiring compensatory gravitational effects or finely tuned mass distributions. This paper advances an alternative structural interpretation. We argue that the inferred planar distribution functions as an upstream constraint manifold that restricts admissible trajectories prior to any consideration of force balance. Within such a geometry, reduced dispersion, coherent alignment, and long-lived planar motion arise naturally as kinematic consequences of restricted degrees of freedom rather than as signatures of modified dynamics. By separating geometric preconditions from dynamical evolution, this perspective unifies multiple Local Group anomalies within a single organizing principle while preserving standard gravitational theory and dark matter phenomenology. The results motivate a modeling strategy in which environmental geometry is treated as a primary input to galactic dynamics rather than as a secondary outcome inferred from it.