Data and Code for "A Sharp Transition in Force Law Recoverability at Three Spatial Dimensions"

Source code, simulation data, and experiment results for the paper "A Sharp Transition in Force Law Recoverability at Three Spatial Dimensions." This study investigates whether the recoverability of gravitational force laws from N-body trajectory data depends on the spatial dimension D. Using Interaction Networks (graph neural networks) trained on D-dimensional gravitational N-body simulations (D ∈ {2, 3, 4, 5}), we extract effective force exponents via log-log regression and measure law recovery accuracy across a systematic N × D grid scan (160 independent training runs, ε = 0.1, uniform parameters). The central finding is a sharp transition at D = 3: the R² of force-exponent regression reaches 0.22 at D = 3 but drops below 0.015 for all other dimensions. A two-way ANOVA confirms that spatial dimension accounts for 98.5% of the total variance (η² = 0.98, p < 10⁻¹⁶), while network depth contributes less than 4%. The pattern disappears under Hookean spring forces, establishing that the α = D − 1 coupling between force exponent and spatial dimension is the essential ingredient.