{"schema":"vela.problem-packet.v0.1","problem":819,"statement":"Let $f(N)$ be maximal such that there exists $A\\subseteq \\{1,\\ldots,N\\}$ with $\\lvert A\\rvert=\\lfloor N^{1/2}\\rfloor$ such that $\\lvert (A+A)\\cap [1,N]\\rvert=f(N)$. Estimate $f(N)$.","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)"}