We present a two-dimensional numerical reduction of the Concentric Shell Theory (CST) introduced in the companion preprint by De Luca, where elementary particles are modeled as extended shell structures generated by a nonlinear complex scalar field. In the original CST proposal, inertia is interpreted as structural resistance of the shells, while gravity is interpreted as the tendency of overlapping outer shells to restore asymptotic concentricity; in the full three-dimensional theory, the corresponding force is argued to scale as 1/r² from the dilution of shell information over spherical surfaces. Here we do not attempt a full 3D simulation. Instead, we adopt a computationally cheaper 2D reduction designed to preserve the radial shell hierarchy and the competition between short-range inner contributions and long-range outer contributions. Using neutralized damped oscillatory shell profiles and a soft inner-outer partition, we find a robust parameter window in which the outer component is attractive and scales approximately as 1/d, as expected for an effective two-dimensional long-range interaction. We further identify a crossover distance dc beyond which the outer contribution dominates over the inner one. For the best-fit window, dc/T lies in the range 61–72 for cluster sizes from N = 1 to N = 37 and varies only weakly when L/T is changed from 18 to 19. These results support the shell decomposition as a viable mechanism for emergent long-range attraction and motivate a future extension to a fully 3D implementation.
Ernesto De Luca (Thu,) studied this question.