A Projection-Based Interpretation of Gravity Without Dark Matter

This version (v2) refines the theoretical framework by focusing specifically on galactic and galaxy cluster scales. The central idea is that gravitational interaction should be understood as a scale-dependent transmission process rather than a fixed inverse-square law. In this context, the geometric models previously introduced (parachute, conical, and cylindrical propagation) are interpreted as different regimes of transmission behavior. A key addition in this version is the introduction of a phenomenological transition in effective transmission dimensionality: n(r) = 2 / (1 + r / L*) where L* represents a characteristic scale at which the mode of gravitational transmission begins to change. This formulation provides a unified interpretation: - At small scales (r ≪ L*), the effective dimensionality approaches n ≈ 2, reproducing Newtonian inverse-square behavior. - At galactic scales (r ~ L*), the effective dimensionality transitions toward n ≈ 1, naturally associated with flat rotation curves. - At cluster scales (r ≫ L*), the effective dimensionality approaches n ≈ 0, corresponding to nearly uniform transmission and weak radial dependence of velocity dispersion. This version deliberately excludes cosmological expansion and redshift interpretations in order to focus on the internal consistency and explanatory power of the model at galactic and cluster scales. The goal of this update is to establish a minimal, self-consistent phenomenological framework connecting local gravitational behavior and large-scale structure without invoking dark matter.