Corollary 1. There is an integer N_0≥2 such that, for every N≥N_0 and Q=3(N-1) , H_ N,Q ≥1 25 (I-P_ L,N ) ^N U_Q, where P_ L,N projects onto the line spanned by Ψ_ L,N =∏_ i<j (u_iv_j-u_jv_i)^3.