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Claim. For every prime $p$, every $A\subseteq\mathbb F_p\setminus\{0\}$ with $|A|\le\log p/\log\log p$ has an ordering whose partial sums are distinct, the question of Problem 475 for sets of that size. This is Theorem 1.2 of N. Kravitz, Rearranging small sets for distinct partial sums (arXiv:2407.01835, 1 July 2024, revised 18 August 2024), a range of sizes that grows with $p$, the paper's stated novelty. The proof has two steps (p. 2): Theorem 1.3, every finite set of nonzero integers has an ordering with distinct partial sums, indeed one listing the positive elements before the negative ones, by induction on the size; and Lev's rectification theorem, which carries $A\cup\{0\}$ Freiman-isomorphically to a set of integers when $|A|\le\log p/\log\log p$, so that an ordering of the image with distinct partial sums, a condition on sums of at most $|A|-1$ elements, pulls back to $A$. The paper records (p. 1) that Will Sawin had given a very similar argument in a 2015 MathOverflow post, which the site's commentary repeats; that post is not a dated manuscript and has no page. Read depth: claims checked for the statements in the arXiv version, and the two half-page proofs read in full; neither proof is independently reviewed.

Covers. Every prime $p$ and every size $t\le\log p/\log\log p$; the bound exceeds the twelve sizes of Costa and Pellegrini only once $\log p/\log\log p>12$, roughly for $p>10^{20}$. For large primes the range was later widened to $t\le e^{c(\log p)^{1/4}}$ by Bedert and Kravitz (their claim page) and to $t\le e^{c(\log p)^{1/3}}$ by Costa and Della Fiore, recorded on the chain's page.

Depends on. Nothing in this wiki: the result is the paper's own, filed on its library result page.

Standing. Claimed. Not refereed: no journal version was located (Crossref bibliographic query; the arXiv record carries no journal reference). Not reviewed: the site's commentary credits the range to this paper, but the site's label DECIDABLE leaves the problem open and settles no part of it, so that credit is not acceptance. Not formalized: no Lean statement or proof of the problem existed in the catalog on 2026-09-18.