{
  "(2, 2, 3)": {
    "p": [
      {
        "powers": [
          -2
        ],
        "coefficient": "1"
      },
      {
        "powers": [
          0
        ],
        "coefficient": "-1"
      }
    ]
  },
  "(3, 2, 2)": {
    "d": [
      {
        "powers": [
          -2
        ],
        "coefficient": "1"
      },
      {
        "powers": [
          0
        ],
        "coefficient": "-1"
      }
    ],
    "u": [
      {
        "powers": [
          -1
        ],
        "coefficient": "1"
      },
      {
        "powers": [
          1
        ],
        "coefficient": "-1"
      }
    ],
    "xa": [
      {
        "powers": [
          -2
        ],
        "coefficient": "-1"
      },
      {
        "powers": [
          2
        ],
        "coefficient": "1"
      }
    ],
    "v": [
      {
        "powers": [
          -1
        ],
        "coefficient": "1"
      },
      {
        "powers": [
          1
        ],
        "coefficient": "-1"
      }
    ]
  },
  "(3, 3, 2)": {
    "xb": [
      {
        "powers": [
          -2
        ],
        "coefficient": "1"
      },
      {
        "powers": [
          2
        ],
        "coefficient": "-1"
      }
    ],
    "u": [
      {
        "powers": [
          -1
        ],
        "coefficient": "-1"
      },
      {
        "powers": [
          1
        ],
        "coefficient": "1"
      }
    ],
    "v": [
      {
        "powers": [
          -1
        ],
        "coefficient": "-1"
      },
      {
        "powers": [
          1
        ],
        "coefficient": "1"
      }
    ],
    "d": [
      {
        "powers": [
          -2
        ],
        "coefficient": "-1"
      },
      {
        "powers": [
          0
        ],
        "coefficient": "1"
      }
    ]
  },
  "(4, 2, 3)": {
    "('u', 2, 4)": [
      {
        "powers": [
          -1
        ],
        "coefficient": "1"
      },
      {
        "powers": [
          1
        ],
        "coefficient": "-1"
      }
    ],
    "('v', 2, 4)": [
      {
        "powers": [
          -1
        ],
        "coefficient": "1"
      },
      {
        "powers": [
          1
        ],
        "coefficient": "-1"
      }
    ],
    "('v', 2, 3)": [
      {
        "powers": [
          -1
        ],
        "coefficient": "-1"
      },
      {
        "powers": [
          1
        ],
        "coefficient": "1"
      }
    ],
    "('u', 2, 3)": [
      {
        "powers": [
          -1
        ],
        "coefficient": "-1"
      },
      {
        "powers": [
          1
        ],
        "coefficient": "1"
      }
    ]
  },
  "(3, 4, 2)": {
    "('v', 3, 4)": [
      {
        "powers": [
          -1
        ],
        "coefficient": "1"
      },
      {
        "powers": [
          1
        ],
        "coefficient": "-1"
      }
    ],
    "('u', 3, 4)": [
      {
        "powers": [
          -1
        ],
        "coefficient": "1"
      },
      {
        "powers": [
          1
        ],
        "coefficient": "-1"
      }
    ],
    "('u', 2, 4)": [
      {
        "powers": [
          -1
        ],
        "coefficient": "-1"
      },
      {
        "powers": [
          1
        ],
        "coefficient": "1"
      }
    ],
    "('v', 2, 4)": [
      {
        "powers": [
          -1
        ],
        "coefficient": "-1"
      },
      {
        "powers": [
          1
        ],
        "coefficient": "1"
      }
    ]
  },
  "status": "PASS: correct two-letter formulas and common exchange sum suffice on all three-letter permutations"
}