{"schema":"vela.problem-packet.v0.1","problem":510,"statement":"If $A\\subset \\mathbb{Z}$ is a finite set of size $N$ then is there some absolute constant $c>0$ and $\\theta$ such that\\[\\sum_{n\\in A}\\cos(n\\theta) < -cN^{1/2}?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_8956f5b8efe5de2d","kind":"dead_end","claim":"attempted via frontier '?' (transfer_strength=n/a) -> no_progress","grade":"honest_null","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}