Claims

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2005_08_10_bode_harborth: Theorem 2 of Bode and Harborth (Discrete Math. 2005), Alspach's conjecture for n - 2 lengths: every set of p - 2 nonzero residues modulo a prime, and the set of all p - 1, has an ordering with distinct partial sums; refereed.

2018_09_07_hicks_ollis_schmitt: Theorem 4.6 of Hicks, Ollis and Schmitt (J. Combin. Des. 2019): Alspach's conjecture in Z_p for size p - 3, so every (p - 3)-subset with nonzero sum has an ordering with distinct partial sums; accepted, refereed.

2020_03_12_costa_pellegrini: Proposition 4.2 of Costa and Pellegrini (Arch. Math. 2020): every set of at most twelve nonzero residues modulo any prime has an ordering with distinct partial sums, by the Combinatorial Nullstellensatz; accepted, refereed.

2024_07_01_kravitz: Theorem 1.2 of Kravitz's 2024 preprint: for every prime p, every set of at most log p / log log p nonzero residues has an ordering with distinct partial sums, by rectification to the integers; claimed, no journal version.

2024_09_11_bedert_kravitz: Theorem 1.2 of Bedert and Kravitz (Israel J. Math. 2026): for every c > 0 and every large prime p, every set of at most exp(c (log p)^{1/4}) nonzero residues has an ordering with distinct partial sums; accepted, refereed.

2026_02_17_pham_sauermann: Pham and Sauermann's 2026 medium-range theorem, which with the small range of Bedert and Kravitz and the large ranges of Bedert, Bucić, Kravitz, Montgomery and Müyesser proves the conjecture for all large primes; claimed.

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