{"schema":"vela.problem-packet.v0.1","problem":930,"statement":"Is it true that, for every $r$, there is a $k$ such that if $I_1,\\ldots,I_r$ are disjoint intervals of consecutive integers, all of length at least $k$, then\\[\\prod_{1\\leq i\\leq r}\\prod_{m\\in I_i}m\\]is not a perfect power?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_da45e965ee28ebe3","kind":"partial_proof","claim":"#930 (multi-block Erdős–Selfridge) is OPEN and NOT settled by the known Erdős–Graham counterexamples, which fix block length and grow the number of blocks r — the DUAL quantifier order of #930 (which ","grade":"partial_proof","gateStatus":"needs_verification","superseded":false},{"id":"att_523b9dc76c85b7d2","kind":"partial_proof","claim":"Erdos #930 OPEN (r>=2). Reframed r-block square as squarefree-part/parity identity (perfect-power analog of #931 radical equality); RIGOROUS NEGATIVE TRANSFER: Stormer/S-unit/bounded-cofactor from #93","grade":"partial_proof","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}