PROVED (LEAN). Beker's Theorem 1.2 ([Be23b], Bull. London Math. Soc. 56 (2024), refereed) gives an absolute $c>0$ and, for every $n$, integers $1\le a_1<\cdots<a_k\le n$ with at least $cn^2$ distinct sums of consecutive terms, so the answer is yes; the site records the solution as Beker's, and the claim page (Beker, 2023) carries the acceptance. Konieczny's theorem ([Ko15]) concerns the permutation variant (Problem 34) and is not a claim on this question. The Lean suffix is the site's label for a 2026 formalization of Beker's result in Boris Alexeev's public repository, registered by the community database; it declares Beker as its informal author, so it is a formalization link on his claim page, not built or audited by this corpus, and gives no formalized evidence.