Alexeev and Mixon [arxiv/2510.19804] have disproved this conjecture, showing that $\{1, 2, 4, 8, 13\}$ cannot be
extended to any perfect difference set.
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theorem erdos_707.counterexample_mian_chowla (A : Set ℕ) (hA : A = {1, 2, 4, 8, 13}) :
Finite A ∧ IsSidon A ∧
∀ (B : Set ℕ) (n : ℕ), A ⊆ B → ¬IsPerfectDifferenceSet B n
