{"schema":"vela.problem-packet.v0.1","problem":880,"statement":"Let $A\\subset\\mathbb{N}$ be an additive basis of order $k$. Let $B=\\{b_1<b_2<\\cdots\\}$ be the set of integers which are the sum of $k$ or fewer distinct $a\\in A$. Is it true that $b_{n+1}-b_n=O(1)$? (Where the implied constant may depend on both $A$ and $k$.)","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}