Suslin cardinals and cutpoints in mouse limits

We obtain a partial result on the following conjecture. Conjecture. Let (P, Σ) be a projectum stable mouse pair, and let κbe a cardinal of V such that κ< o(M_\infty(P, Σ)); then the following are equivalent: (1) κis a Suslin cardinal, (2) κis a cutpoint of M_\infty(P, Σ).