{"schema":"vela.problem-packet.v0.1","problem":949,"statement":"Let $S\\subset \\mathbb{R}$ be a set containing no solutions to $a+b=c$. Must there be a set $A\\subseteq \\mathbb{R}\\backslash S$ of cardinality continuum such that $A+A\\subseteq \\mathbb{R}\\backslash S$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_a04c6632e09e2f4f","kind":"partial_proof","claim":"erdos_949 (general sum-free version) is OPEN; the Sidon variant in the Lean file is already proven. State of the art covers #S<𝔠 (unconditional), S Sidon, and S with the Baire property (Chojecki). My ","grade":"partial_proof","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}