The site's wording sets no range for $|A|$, and as printed the answer is no for every $k>2$: for $|A|<k$ the multiset $A_k$ is empty and for $|A|=k$ it is the single sum of $A$, so distinct sets of those sizes share it (Kruyt's observation, recorded in the site's commentary); for $|A|=2k$ a set with sum $0$ and its negative share $A_k$, since each $k$-sum of the negative is minus a $k$-sum of $A$, which is the complementary $k$-sum (Tao's observation, in the commentary and in Tao's forum comment of 30 August 2025, which says the case "needs to be ruled out"; Theorem 3 of [SeSt58], p. 850, shows $n=2s$ is the only size above $s$ at which a nontrivial transformation preserves the $s$-fold sums); for $k=3$ the sizes $27$ and $486$ are reported as further exceptions (see Formulation). Bloom reads the problem with a size condition. The commentary records the two failures as remarks on the wording, says "Presumably some condition like '$|A|$ sufficiently large' is intended", and labels the problem PROVED on the theorem of Gordon, Fraenkel and Straus [GFS62] that "for all $k$, the multiset $A_k$ uniquely determines $A$ provided $|A|$ is sufficiently large", added on 14 October 2025 after msellke's forum comment of 13 October 2025 supplied the reference. The corrected Statement adopts that reading in Bloom's words, adding "provided $|A|$ is sufficiently large in terms of $k$" and changing nothing else. It is the conjecture Gordon, Fraenkel and Straus attribute to Selfridge and Straus [GFS62, §1, p. 187], that for $s>2$ one has $F_s(n)=1$ "for all but a finite number of $n$", which for fixed $k$ says the same thing. Under the site's wording the answer is no, by the small sizes above; under Bloom's reading it is yes, by the theorem of Section 4 of [GFS62], with the explicit ranges $k=3$, $|A|>6$ other than $27$ and $486$, and $k=4$, $|A|>12$, from [SeSt58]. The missing range is older than the site: Erdős's report of the problem ([Er61], item I.33, p. 238) states the Selfridge--Straus conjecture for $k>2$ with no size condition (and with products in place of sums; see Formulation), while Selfridge and Straus ask "To what extent is $\{x\}$ determined by $\{\sigma\}$" ([SeSt58], §1, p. 847) and call the exceptional pairs $(s,n)$ "in a certain sense quite rare" (p. 854). Results on the site's wording are credited here and do not bear on the standing: Kruyt's failure at $|A|=k$, Tao's at $|A|=2k$, Theorem 3 of [SeSt58], and the Lean development Erdos494.lean in Boris Alexeev's repository (added 2026-08-16; Codex and GPT-5.6 Sol as formal authors; file at a pinned commit), whose only theorem, card_eq_2k, proves the failure at $|A|=2k$ for every $k>2$ and whose own section heading reads "The literal problem has a negative answer". The theorem answers the site's wording, not the corrected Statement, which asks only about sufficiently large $|A|$; it presents itself as a solution of Problem 494 and so has a claim page (Alexeev, 2026), which is rejected and does not count toward the standing. The page's standing judges the corrected Statement.