Equality of the images of the fans associated to L_1 and L_{d-1}

Establish whether the fans associated with the loci L_1 and L_{d-1} of tropical curves with d-split Jacobians have the same image in the moduli space M^{tr}_2 for every d.

Background

The paper decomposes the locus of curves with d-split Jacobians as a union of subsets L_k indexed by the units k modulo d. Each L_k is organized by a fan obtained from Selling reduction and is mapped into the tropical moduli space M^{tr}_2 by linear maps associated with its maximal cones. The authors verify equality of the images for L_1 and L_{d-1} when d=3 and report sporadic higher-degree examples pointing in the same direction, but do not establish the assertion in general.