{
  "problem_id": "IMO2026-P3",
  "obligations": [
    {
      "id": "O1",
      "claim": "Fixed-partition game value V=(1+Delta)/2 with pairing strategy",
      "status": "CLAIMED",
      "dependencies": [],
      "load_bearing": true,
      "notes": ""
    },
    {
      "id": "O2",
      "claim": "Candidate optimum c_n = 2^n/(2^{n+1}-1)",
      "status": "CLAIMED",
      "dependencies": [
        "O1"
      ],
      "load_bearing": false,
      "notes": ""
    },
    {
      "id": "O3",
      "claim": "Upper bound: subset-sum proximity + pairing cut budget <= n",
      "status": "CLAIMED",
      "dependencies": [
        "O1"
      ],
      "load_bearing": true,
      "notes": ""
    },
    {
      "id": "O4",
      "claim": "Lower bound: powers of two + tree two-colouring, |R|>=1",
      "status": "CLAIMED",
      "dependencies": [
        "O1"
      ],
      "load_bearing": true,
      "notes": ""
    },
    {
      "id": "O5",
      "claim": "Pairing bound |R| <= Delta'",
      "status": "CLAIMED",
      "dependencies": [
        "O4"
      ],
      "load_bearing": true,
      "notes": ""
    },
    {
      "id": "O6",
      "claim": "Bounds meet at c_n",
      "status": "CLAIMED",
      "dependencies": [
        "O3",
        "O5"
      ],
      "load_bearing": false,
      "notes": ""
    }
  ]
}