{"schema":"vela.problem-packet.v0.1","problem":25,"statement":"Let $1\\leq n_1<n_2<\\cdots$ be an arbitrary sequence of integers, each with an associated residue class $a_i\\pmod{n_i}$. Let $A$ be the set of integers $n$ such that for every $i$ either $n<n_i$ or $n\\not\\equiv a_i\\pmod{n_i}$. Must the logarithmic density of $A$ exist?","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)"}