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Counterexamples to the restricted-sumset inverse theorem in arXiv:2609.10148v2

alexander

Palomar Registrypalomar/PALOMAR-2026-10-16-000008Oct 16, 2026math.NTscore 0

Explicit finite counterexamples to Theorem A (Theorem 3.1) and Lemma 3.2 of Li and Liang, arXiv:2609.10148v2. In Z/13Z, sets of sizes seven and four satisfy all size hypotheses and have restricted sumset size nine, but neither is an arithmetic progression. A separate example in Z/11Z contradicts the lower bound of Lemma 3.2 as stated.

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