{"schema":"vela.problem-packet.v0.1","problem":153,"statement":"Let $A$ be a finite Sidon set and $A+A=\\{s_1<\\cdots<s_t\\}$. Is it true that\\[\\frac{1}{t}\\sum_{1\\leq i<t}(s_{i+1}-s_i)^2 \\to \\infty\\]as $\\lvert A\\rvert\\to \\infty$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_6d6ff27f57708d32","kind":"dead_end","claim":"attempted via frontier 'sidon/B2' (transfer_strength=partial) -> no_progress","grade":"honest_null","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}