{
  "problem_id": "IMO2026-P1",
  "obligations": [
    {
      "id": "O1",
      "claim": "Each move yields positive integers; moves are well-defined",
      "status": "CLAIMED",
      "dependencies": [],
      "load_bearing": false,
      "notes": ""
    },
    {
      "id": "O2",
      "claim": "Process terminates via lexicographic descent of (S,k)",
      "status": "CLAIMED",
      "dependencies": [
        "O1"
      ],
      "load_bearing": true,
      "notes": ""
    },
    {
      "id": "O3",
      "claim": "Terminal state has exactly one integer M>1",
      "status": "CLAIMED",
      "dependencies": [
        "O2"
      ],
      "load_bearing": false,
      "notes": ""
    },
    {
      "id": "O4",
      "claim": "Per-prime valuation-column gcd g_p is invariant",
      "status": "CLAIMED",
      "dependencies": [
        "O1"
      ],
      "load_bearing": true,
      "notes": ""
    },
    {
      "id": "O5",
      "claim": "Final-state uniqueness: M = prod p^{gcd(v_p(x_i))}",
      "status": "CLAIMED",
      "dependencies": [
        "O3",
        "O4"
      ],
      "load_bearing": true,
      "notes": ""
    }
  ]
}