Resolving this question would provide a template for understanding mixing at first-order phase transitions more broadly, a regime that is far less understood than continuous transitions. It would clarify whether the deterministic sweep order in systematic scan genuinely alters the universality class of the mixing transition compared to random-update Glauber dynamics, which has implications for the efficiency of systematic scan as a computational sampling algorithm in statistical inference and machine learning. It would also likely require new probabilistic tools connecting spectral theory of non-reversible chains to metastability, tools that could transfer to understanding regime-switching models and Markov-modulated processes in the first paper on affine recurrences.