{"schema":"vela.problem-packet.v0.1","problem":188,"statement":"What is the smallest $k$ such that $\\mathbb{R}^2$ can be red/blue coloured with no pair of red points unit distance apart, and no $k$-term arithmetic progression of blue points with distance $1$?","status":"open","seam":"sealed","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_199c2138b5955093","kind":"dead_end","claim":"attempted via frontier '?' (transfer_strength=n/a) -> no_progress","grade":"honest_null","gateStatus":"needs_verification","superseded":false},{"id":"att_7e9e05062b8d0d0d","kind":"partial_proof","claim":"erdos_188 (Euclidean Ramsey): verified M=min(s)>=6, tightening the recorded range from [5,10^7] to [6,10^7]. Small concrete bound improvement, airtight, formalizable; not novel-theorem-level.","grade":"improved_published_bound","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}