The site's wording does not say which density it asks for: "positive density" can ask that the set of integers that appear have an asymptotic density and that it be positive, or only that its lower density be positive, and the two readings differ for a set whose density need not exist. The change replaces "positive density" by "positive lower density"; nothing else changes. Erdős printed the question without a qualifier: [Er77c], p. 71 (library card: Erdos 1977), reports Hofstadter's problem and asks "Does this sequence have positive density?", while the preceding page (p. 70) asks of another sequence whether its "density (lower density)" is $0$ and expects different answers for the two, so Erdős's text distinguishes the densities where Erdős wanted to and fixes no reading here. Erdős and Graham's 1980 wording ([ErGr80], p. 84, as the site reports it) and Guy's section E31 ask instead whether almost all integers appear; that is false, since the residues $0$ and $2$ modulo $3$ are closed under $(a,b)\mapsto ab-1$ (an observation the site credits to Steinerberger), and the site treats that wording as a misstatement of the [Er77c] question. The reading is the site's curator's. The site's commentary says: "As with many of Erdős' questions, by 'positive density' he most likely meant 'positive lower density' - in other words, does there exist $c>0$ such that for all large $x$ the number of values of $a_i$ in $[1,x]$ is at least $cx$?" The evidence Thomas Bloom gives is Erdős's general usage; in the thread of Problem 1201 (1 May 2026) Bloom wrote that reading a density bound as a lower-density bound "is generally how Erdős used these terms", that Erdős was "generally clear" when asking whether a density exists, and that the curator had tried to update all the site's problem descriptions to reflect this. The formal-conjectures statement follows the site: its erdos_424 asks for positive lower density and its variant exact_density for a positive natural density. Under the precise Statement the answer is yes: Samuel Korsky's proof, recorded on its claim page (Korsky, 2026), gives a $c>0$ with at least $cx$ members in $[1,x]$ for all large $x$, and the Lean formalization of that statement by Codex and Boris Alexeev was built and audited in this corpus. Under the natural-density reading the question is open: no source shows that the density exists, and formal-conjectures tags exact_density as open.