{"schema":"vela.problem-packet.v0.1","problem":52,"statement":"Let $A$ be a finite set of integers. Is it true that for every $\\epsilon>0$\\[\\max( \\lvert A+A\\rvert,\\lvert AA\\rvert)\\gg_\\epsilon \\lvert A\\rvert^{2-\\epsilon}?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A263996","name":"Smallest possible cardinality of the union of the set of pairwise sums and the set of pairwise products from a set of n positive integers.","terms":"1,4,7,11,15,20,26,30,36,44,49,57,64,71,80,86,96,104,112,121,131,141,150,160,169,179,190,200,212,222,235,248,260,272,283,","url":"https://oeis.org/A263996"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}