Unique equilibrium states for some partially hyperbolic diffeomorphisms with dominated splittings

The paper proves robust uniqueness via a Climenhaga–Thompson (CT) decomposition, establishing specification and Bowen property on a good core, and obtaining strict pressure gaps for both the non-expansive part and the prefix/suffix parts using LVY13 and a quantitative lemma that excludes measures with small central exponents. The model follows a similar high-level plan, but its pressure-gap step is flawed: it lower-bounds P(g,ϕ) by h_top(g|_Λ)+inf ϕ and upper-bounds P_exp^⊥ by max{hu,hs}+osc(ϕ), then subtracts to claim a uniform positive gap independent of inf ϕ, which is false when inf ϕ is negative. It also asserts, without justification, that the pressure of the prefix/suffix sets is controlled by the non-expansive pressure. The paper explicitly proves these pressure bounds; the model does not.