On the multigraded Hilbert and Poincaré-Betti series and the Golod property of monomial rings

The conjecture implies that A is Golod if and only if the product (i.e. the first Massey operation) on the Koszul homology is trivial. Under the assumption of the conjecture we finally prove that a very simple purely combinatorial condition on the minimal monomial generating system of a implies Golodness for A.