О спектральных задачах Колмогорова и Рохлина в классе перемешивающих автоморфизмов

The paper proves Theorem 1 by an explicit Q_r–P_r averaging/Gram-matrix argument that places Tr f ⊗ f + f ⊗ Tr f in the cyclic subspace of f ⊗ f and yields simplicity of T ⊙ T, failure of the group property, and multiplicity 2 for T ⊗ T when r_j ∼ j^d with d < 1/5. The candidate solution’s core Step 1 is incorrect: polynomials in U ⊙ U acting on f ⊙ f produce only diagonal terms U^n f ⊙ U^n f and cannot approximate off-diagonal vectors f ⊙ U^ℓ f as claimed; moreover, the posited O(r_j^5/h_j) error and its attribution to the paper are unsupported. The model thus reaches the right conclusions for the wrong reasons.