Uniqueness of Conformal Measures and Local Mixing for Anosov Groups

The uploaded paper proves that for any Zariski-dense P–Anosov subgroup Γ of a connected semisimple real algebraic group G of rank ≤ 3 and any ψ in D*_Γ, every (Γ,ψ)-conformal probability measure on F = G/P is supported on the limit set Λ and equals the Patterson–Sullivan measure ν_ψ. This is Theorem 1.4 and is established via local mixing for generalized BMS measures, the Hopf–Tsuji–Sullivan dichotomy (Burger–Landesberg–Lee–Oh), and an appeal to Lee–Oh for uniqueness within the PS class . The candidate solution reaches the same conclusion but relies on two unjustified steps: (i) it asserts a Shadow Lemma for arbitrary (Γ,ψ)-conformal measures (not just PS measures), and (ii) it uses equivalence with ν_ψ to transfer ergodicity, which is not established. The paper avoids these gaps by a different route and is correct; the model’s proof is therefore flawed.