{"schema":"vela.problem-packet.v0.1","problem":336,"statement":"For $r\\geq 2$ let $h(r)$ be the maximal finite $k$ such that there exists a basis $A\\subseteq \\mathbb{N}$ of order $r$ (so every large integer is the sum of at most $r$ integers from $A$) and exact order $k$ (so every large integer is the sum of exactly $k$ integers from $A$). Find the value of\\[\\lim_r \\frac{h(r)}{r^2}.\\]","status":"open","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)"}