{"schema":"vela.problem-packet.v0.1","problem":272,"statement":"Let $N\\geq 1$. What is the largest $t$ such that there are $A_1,\\ldots,A_t\\subseteq \\{1,\\ldots,N\\}$ with $A_i\\cap A_j$ a non-empty arithmetic progression for all $i\\neq j$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_30e573983a1b6a3a","kind":"dead_end","claim":"attempted via frontier '?' (transfer_strength=n/a) -> already_known","grade":"honest_null","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}