OBSTRUCTIONS TO ASYMPTOTIC STABILIZATION

The paper’s main theorem (Theorem 1) requires D to be an involutive C1 regular distribution and leverages Lyapunov functions, straightening the Y-flow, foliations from involutivity, and a spray/exponential-map construction to build a nonvanishing homotopy between X|U\A and Y|U\A (see the statement and proof outline, including Remark 2 and the Exp-based homotopy construction) . By contrast, the model’s solution omits involutivity entirely and proposes a purely local “dominant offset” homotopy argument that (if valid) would also apply when D is not involutive—contradicting the paper’s explicit counterexample showing the involutive hypothesis is essential (Section 5) . Moreover, the model’s key technical step (the star-refinement/partition-of-unity assembly that forces the constructed section T to coincide locally with a single constant choice) is incorrect: ‘constant in different trivializations’ need not agree on overlaps, so the sum need not inherit the intended uniform separation; this gap is nontrivial to fix and, even if repaired, cannot bypass the paper’s counterexample.