Optimal compressed sensing for mixing stochastic processes

The uploaded paper’s Main Theorem states exactly the claimed converse: for finite-variance, stationary, ψ*-mixing processes with local-dimension-regular finite-dimensional marginals, if lim inf m_n/n < mid(X), then for every family of Borel decompressors the normalized L2 error 1/√n ||X^n − F_n(A_n X^n, A_n)||_2 does not converge to 0 in (µ×ν)-probability . The proof proceeds via a general converse using the correlation-dimension rate (Theorem 4.1), then a ψ*-mixing bridge to mean average local dimension (Theorem 5.1), and finally an identification mdim_AL = mid under local-dimension-regular marginals (Lemma 2.9) . The candidate solution applies this exact theorem chain. The only minor issue is wording: the paper does not claim an outright equality mdim_cor(X) = mid(X); rather it proves a general lower bound via mdim_cor and then, under ψ*-mixing and local-dimension-regular marginals, connects to mdim_AL and hence to mid(X) .