Estimating basins of attraction for arbitrary dynamical systems

The paper describes a finite-state-machine (FSM) algorithm with states att_search, att_found, att_hit, bas_hit, and lost, and asserts informally that its operation is “guaranteed by the Poincaré recurrence theorem,” but it provides no formal termination/correctness proof and even acknowledges scenarios where the method may never halt without parameter tuning (e.g., grid limits/∆t) . The model’s solution gives a more formal sketch that attempts to prove termination and correctness, but it silently adds strong assumptions (e.g., eventual confinement to cells intersecting the attractor and full recurrent coverage of those cells) and uses a key lemma that is not generally valid for coarse grids. Hence, the paper lacks a rigorous proof, and the model’s proof depends on unarticulated or false premises. Both are incomplete.