FINITE MEAN DIMESNION AND MARKER PROPERTY

The paper proves that for any η>0 there exists an aperiodic system with mean dimension <η that does not have the marker property (Theorem 1.2 / 6.2), via an inverse limit construction and a 1/n-time scaling argument, and records that extensions of aperiodic minimal systems do have the marker property [Lin99, Lemma 3.3] ; ; ; . The candidate’s proposed counterexample X=K×Y with T(x,y)=(g(x),R(y)) is an extension of the aperiodic minimal odometer (K,g), hence, by that lemma, must have the marker property—contradicting the model’s Step 4 claim that it fails markers. Moreover, the model’s key sub-claim ("shrink A so that g^{-1}(A)⊂A") is generally false for the odometer, so the intersection argument near the spine S breaks down.