The authors thank Bernardo Subercaseaux for calling to their attention the problem addressed in this manuscript and for several insightful conversations. The authors also thank Will Ma and Elchanan Mossel for useful discussions and pointers to the literature. The authors acknowledge the use of Claude (Anthropic, July 2026) in identifying an error in an earlier proof of Lemma 6 and in developing the argument given here. Part of this work was done while the third author was a postdoc and the fourth author was a visitor at the Centro de Modelamiento Matemático at Universidad de Chile.