ON N-TUPLEWISE IP-SENSITIVITY AND THICK SENSITIVITY

The paper proves that in a non-trivial weakly mixing system, n-tuplewise thick sensitivity holds iff there are at least n minimal points (Theorem 4.4), using an equivalent proximal–minimal characterization (Proposition 4.3) to pass between thick sensitivity and separated minimal n-tuples. The candidate solution establishes the same equivalence: (⇒) it extracts a δ-separated minimal n-tuple from an ω-limit set; (⇐) it constructs, via a Baire argument in the product system, thick blocks witnessing separation. Apart from a minor technical slip (taking limits in an open separation set; easily fixed by using a closed separation set or shrinking δ), the model’s arguments align with the paper’s result. The two approaches differ in technique: the paper leverages proximality to a minimal point in X^n, while the model uses a Baire-category construction.