Monotonicity conjecture for equal-mass central configurations

Consider the planar equal-mass $N$-body problem with homogeneous potential exponent $A$, and let $C_N(A)$ denote the number of equal-mass central configurations. Monotonicity conjecture. The number of equal-mass central configurations never decreases as the exponent $A$ increases. This proposed global monotonicity is based on the authors' numerical experience and is not established in the source.