{"schema":"vela.problem-packet.v0.1","problem":477,"statement":"Is there a polynomial $f:\\mathbb{Z}\\to \\mathbb{Z}$ of degree at least $2$ and a set $A\\subset \\mathbb{Z}$ such that for any $n\\in \\mathbb{Z}$ there is exactly one $a\\in A$ and $b\\in \\{ f(k) : k\\in\\mathbb{Z}\\}$ such that $n=a+b$?","status":"open","seam":"stone","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_f4f1148c13231c5e","kind":"partial_proof","claim":"#477 is genuinely open. I produced a clean reformulation (tiling ⇔ packing (A−A)∩(B−B)={0} AND covering A+B=Z), and proved the exact reach of the known elementary obstruction: it kills a degree-2 poly","grade":"obstruction_map","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}