{"schema":"vela.problem-packet.v0.1","problem":54,"statement":"A set of integers $A$ is Ramsey $2$-complete if, whenever $A$ is $2$-coloured, all sufficiently large integers can be written as a monochromatic sum of elements of $A$. Burr and Erdős [BuEr85] showed that there exists a constant $c>0$ such that it cannot be true that\\[\\lvert A\\cap \\{1,\\ldots,N\\}\\rvert \\leq c(\\log N)^2\\]for all large $N$ and that there exists a Ramsey $2$-complete $A$ such that for all large $N$\\[\\lvert A\\cap \\{1,\\ldots,N\\}\\rvert < (2\\log_2N)^3.\\]Improve either of these bounds.","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)"}