{"schema":"vela.problem-packet.v0.1","problem":788,"statement":"Let $f(n)$ be maximal such that if $B\\subset (2n,4n)\\cap \\mathbb{N}$ there exists some $C\\subset (n,2n)\\cap \\mathbb{N}$ such that $c_1+c_2\\not\\in B$ for all $c_1\\neq c_2\\in C$ and $\\lvert C\\rvert+\\lvert B\\rvert \\geq f(n)$. Estimate $f(n)$. In particular is it true that $f(n)\\leq n^{1/2+o(1)}$?","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)"}