{
  "problem_id": "IMO2026-P5",
  "obligations": [
    {
      "id": "O1",
      "claim": "Substitution x=f(y) gives f(f(y)) = 2 f(y) - y",
      "status": "CLAIMED",
      "dependencies": [],
      "load_bearing": true,
      "notes": ""
    },
    {
      "id": "O2",
      "claim": "g=f-x: g(f(y))=g(y); orbit f^n(y)=y+n g(y); hence g>=0",
      "status": "CLAIMED",
      "dependencies": [
        "O1"
      ],
      "load_bearing": true,
      "notes": ""
    },
    {
      "id": "O3",
      "claim": "Quantitative squeeze bounding g(x)-g(y)",
      "status": "CLAIMED",
      "dependencies": [],
      "load_bearing": true,
      "notes": ""
    },
    {
      "id": "O4",
      "claim": "Positive values of g equal a single constant c (positive-step equality)",
      "status": "CLAIMED",
      "dependencies": [
        "O2",
        "O3"
      ],
      "load_bearing": true,
      "notes": ""
    },
    {
      "id": "O5",
      "claim": "Exclusion of mixed values {0,c}",
      "status": "CLAIMED",
      "dependencies": [
        "O3",
        "O4"
      ],
      "load_bearing": true,
      "notes": ""
    },
    {
      "id": "O6",
      "claim": "f(x)=x+c, c>=0",
      "status": "CLAIMED",
      "dependencies": [
        "O4",
        "O5"
      ],
      "load_bearing": false,
      "notes": ""
    }
  ]
}