{"schema":"vela.problem-packet.v0.1","problem":868,"statement":"If $A$ is an additive basis of order $2$, and $1_A\\ast 1_A(n)\\to \\infty$ as $n\\to \\infty$, then must $A$ contain a minimal additive basis of order $2$? (i.e. such that deleting any element creates infinitely many $n\\not\\in A+A$)What if $1_A\\ast 1_A(n) >\\epsilon \\log n$ (for all large $n$, for arbitrary fixed $\\epsilon>0$)?","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)"}