On the Dual Formulation in a Withdrawn Proposed Proof of Talagrand's Creating Large Sets Conjecture

This technical note examines the dual formulation introduced in the withdrawn preprint of Xuan Fang and Tianyu Wang, “A Proof of Talagrand's Creating Large Sets Conjecture” (arXiv:2511.17336v1). We give an explicit counterexample to Lemma 1 of that manuscript. For every integer k≥1k\geq 1, let X=[2k+1]X=[2k+1] and let F\mathcal F consist of all subsets of XX having cardinality at most 22. Then XX cannot be covered by kk members of F\mathcal F, whereas the binary dual quantity introduced in the manuscript has value only 11, rather than at least k+1k+1. This disproves the claimed covering–packing equivalence. We also identify the precise invalid step in the minimal-cover argument and show that the subsequent selector-process identity, stated as Lemma 2, already fails for the three-point example X={1,2,3}X=\{1,2,3\}. For Bernoulli parameter 0<p<10<p<1, the two sides of the claimed identity become respectively 1−(1−p)31-(1-p)^3 and 1+p31+p^3. These observations invalidate the particular duality-based proof route used in version 1 of the Fang–Wang manuscript. They do not disprove Talagrand's Creating Large Sets Conjecture itself. The Fang–Wang preprint was withdrawn before the preparation of this note, and no claim is made here concerning the reason for its withdrawal.