Maximal separation: all four characteristics pairwise different for S_{I,ε} (and for E_{I,ε})

Determine whether there exists a model of ZFC in which, for some or for all pairs (I, ε) with I a partition of ω into finite nonempty intervals and ε ∈ ℓ^1_+, the four cardinal characteristics add(S_{I,ε}), cov(S_{I,ε}), non(S_{I,ε}), and cof(S_{I,ε}) are pairwise different; and analogously for E_{I,ε}.

Background

For several classical ideals (e.g., N, E, and SN) there are models in which the four associated cardinal characteristics are all different. The paper asks whether similar maximal separations can be achieved for the new layered ideals S_{I,ε} and E_{I,ε}.

Such results would demonstrate the full independence strength of these ideals' characteristics and situate them among known separation phenomena in set theory of the reals.