{
  "problem_id": "IMO2026-P6",
  "obligations": [
    {
      "id": "O1",
      "claim": "Greedy sequence = increasing enumeration of admissible set A",
      "status": "CLAIMED",
      "dependencies": [],
      "load_bearing": true,
      "notes": ""
    },
    {
      "id": "O2",
      "claim": "A is upward-closed under divisibility and pairwise non-coprime",
      "status": "CLAIMED",
      "dependencies": [
        "O1"
      ],
      "load_bearing": true,
      "notes": ""
    },
    {
      "id": "O3",
      "claim": "Minimal kernels; A = union of b*N over kernels",
      "status": "CLAIMED",
      "dependencies": [
        "O2"
      ],
      "load_bearing": false,
      "notes": ""
    },
    {
      "id": "O4",
      "claim": "Witness-before-power lemma: a_j < d^s",
      "status": "CLAIMED",
      "dependencies": [
        "O1"
      ],
      "load_bearing": true,
      "notes": ""
    },
    {
      "id": "O5",
      "claim": "Prime bound p < a_1^2 -> finitely many kernels",
      "status": "CLAIMED",
      "dependencies": [
        "O3",
        "O4"
      ],
      "load_bearing": true,
      "notes": ""
    },
    {
      "id": "O6",
      "claim": "Translation periodicity a_{n+T} = a_n + L",
      "status": "CLAIMED",
      "dependencies": [
        "O5"
      ],
      "load_bearing": false,
      "notes": ""
    }
  ]
}