PROVED (LEAN), the site's label; its suffix is a catalog label explained under Formalization. The status-defining source is Chang (Ann. of Math. (2) 157 (2003), 939--957, refereed). Section 2 proves the lower bound of her Theorem 2 in the form (2.2): $g(A)>k^{(\frac18-\varepsilon)\log k/\log\log k}$ for every $\varepsilon>0$ and every set $A$ of $k$ positive integers with $k$ large, where $g(A)$ is the number of simple sums plus the number of simple products of $A$. Theorem 2 as printed, display (0.21), asserts its two bounds for some $\varepsilon>0$. This bound exceeds every fixed power of $k$; the case of a set of integers of either sign follows by the sign reduction on the claim page, so the answer is yes. The claim page is Chang, accepted on the site curator's credit and the refereed publication; the 2026 Lean development that declares itself a formalization of her result is linked there and gives no formalized evidence, since this corpus has not built or audited it.