Finding Attracting Sets using Combinatorial Multivector Fields

The paper explicitly states that for a down set I the Morse interval MI is an attractor but provides no proof. The candidate solution reaches the same conclusion but contains gaps: it incorrectly asserts that every invariant set is V-compatible and assumes an essential solution through an arbitrary x in cl(MI) without justification. Thus, while the conclusion aligns with the paper’s claim, the provided argument is not fully rigorous, and the paper’s treatment is only a stated claim without proof (see the definitions of ΠV, attractor, connection sets, Morse intervals, and the stated attractor fact in the PDF).