Core-label-order transmutation for Hochschild lattices

Prove that the core-label-order of the Hochschild lattice of dimension n is a transmuted partner of the poset P_{t_n} associated with the corresponding arbor.

Background

Hochschild lattices are congruence-uniform lattices on the vertices of Hochschild polytopes. The notion of transmuted partners requires equality of Zeta polynomials and the prescribed transmutation relation between M-triangles. These properties have been checked computationally through dimension 9, but the paper presents the general relationship only tentatively.