Множества перемешивания жестких пуассоновских надстроек

The paper proves that for any zero-density set M there exists a rigid, invertible, probability-preserving transformation that mixes along M by constructing a rigid infinite-measure rank-one system R and passing to Poisson/Gaussian suspensions; the model’s solution packages the same idea spectrally via a Gaussian system whose spectral measure has Fourier–Stieltjes coefficients vanishing on M and approaching 1 along a rigidity subsequence, and it explicitly cites (and relies on) Ryzhikov’s result to guarantee existence. Hence both are correct and essentially the same argument pathway.