The site's wording fails at every negative irrational $\alpha$: for positive integers $x,y,z$ the quantity is $x^2+y^2+|\alpha|z^2\ge2+|\alpha|$, so $\alpha=-\sqrt2$ and $\epsilon=1$ admit no triple. The failure covers half the parameter's domain, so it is a failure of setting, not of range. The change replaces "$\alpha\in\mathbb{R}$" by "$\alpha>0$"; nothing else changes. The evidence is the setting the site names: its commentary calls the problem originally a conjecture of Oppenheim and credits the proof to Margulis [Ma89], and Margulis states the conjecture he proves for real nondegenerate indefinite quadratic forms in at least three variables (Banach Center Publ. 23 (1989), p. 399, §1 and Theorem 1; §1 calls it Davenport's conjecture, and its footnote 1 credits the case of at least five variables to Oppenheim, Ann. of Math. 32 (1931), 271--288). The form $x^2+y^2-\alpha z^2$ is indefinite exactly when $\alpha>0$ and positive definite when $\alpha<0$, so the corrected Statement is the ternary case of that conjecture with the coordinates made positive; the form follows from the setting, not from the result that settles it. The site's credit to Oppenheim and Margulis corroborates Margulis's statement of the conjecture. The correction does not rest on Oppenheim's 1931 paper or on the Oslo chapter the site cites as [Ma89]. The sign is already unstated in Erdős's question of 1961 (p. 239), which asks about every irrational $\alpha$ in integers with no positivity or nonzero condition; there the zero triple answers the negative case trivially, and the site's requirement of positive integers turns that case into a failure. One result answers the site's wording (every irrational $\alpha$), not the corrected Statement ($\alpha>0$), so it does not count toward the problem's standing. A Lean development Erdos496.lean in Boris Alexeev's repository, added on 2026-08-21 with Codex and GPT-5.6 Sol as formal authors (file at a pinned commit), proves the negation of the site's wording at $\alpha=-\sqrt2$, $\epsilon=1$ (not_erdos_496); it is recorded as a rejected claim page (Alexeev, 2026). The page's standing judges the corrected Statement.