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      {
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      },
      {
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        ],
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      },
      {
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          "p:a",
          "p:b",
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        ],
        "closure_growth_rounds": 2
      }
    ],
    "system": {
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        "food"
      ],
      "reactions": {
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          "reactants": [
            "food",
            "marker:a:0",
            "marker:a:1"
          ],
          "products": [
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          ],
          "catalysts": [
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          ]
        },
        "g:b": {
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            "marker:b:1"
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          ],
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        "g:c": {
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            "marker:c:1"
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            "marker:dead:2",
            "marker:dead:3",
            "marker:dead:4",
            "marker:dead:5",
            "marker:dead:6",
            "marker:dead:7"
          ],
          "products": [
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          ],
          "catalysts": [
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          ]
        },
        "p:a": {
          "reactants": [
            "food"
          ],
          "products": [
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            "marker:b:0",
            "marker:b:1",
            "marker:c:0",
            "marker:c:1",
            "marker:dead:1",
            "marker:dead:4",
            "marker:dead:5",
            "marker:dead:7"
          ],
          "catalysts": [
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          ]
        },
        "p:b": {
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          ],
          "products": [
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            "marker:a:0",
            "marker:a:1",
            "marker:c:0",
            "marker:c:1",
            "marker:dead:2",
            "marker:dead:4",
            "marker:dead:6",
            "marker:dead:7"
          ],
          "catalysts": [
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          ]
        },
        "p:c": {
          "reactants": [
            "food"
          ],
          "products": [
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            "marker:a:0",
            "marker:a:1",
            "marker:b:0",
            "marker:b:1",
            "marker:dead:3",
            "marker:dead:5",
            "marker:dead:6",
            "marker:dead:7"
          ],
          "catalysts": [
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          ]
        },
        "p:dead": {
          "reactants": [
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          ],
          "products": [
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            "marker:a:1",
            "marker:b:1",
            "marker:c:1"
          ],
          "catalysts": [
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          ]
        }
      }
    }
  },
  "worked_examples": {
    "feedback": {
      "analysis": {
        "family": [
          [],
          [
            "a",
            "b"
          ],
          [
            "a",
            "b",
            "g"
          ]
        ],
        "N_including_empty": 3,
        "counts": {
          "a": 2,
          "b": 2,
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        "abundant": [
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        ],
        "fibres": [
          {
            "exterior": [],
            "bodies": {
              "a": [
                "b"
              ],
              "b": [
                "a"
              ]
            },
            "family": [
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                "a",
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            ],
            "slack": 0,
            "bad_zero_cells": 2,
            "bad_one_cells": 2,
            "injection": [
              {
                "source_deleted": [
                  "a"
                ],
                "source_column": "b",
                "move": "vertical",
                "target_deleted": [
                  "a"
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                "target_column": "a"
              },
              {
                "source_deleted": [
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                ],
                "source_column": "a",
                "move": "vertical",
                "target_deleted": [
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                "target_column": "b"
              }
            ],
            "counts": {
              "a": 1,
              "b": 1
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          },
          {
            "exterior": [
              "g"
            ],
            "bodies": {
              "a": [
                "a"
              ],
              "b": [
                "a"
              ]
            },
            "family": [
              [
                "a",
                "b"
              ]
            ],
            "slack": 2,
            "bad_zero_cells": 2,
            "bad_one_cells": 4,
            "injection": [
              {
                "source_deleted": [
                  "a"
                ],
                "source_column": "b",
                "move": "vertical",
                "target_deleted": [
                  "a"
                ],
                "target_column": "a"
              },
              {
                "source_deleted": [
                  "b"
                ],
                "source_column": "a",
                "move": "horizontal",
                "target_deleted": [
                  "a",
                  "b"
                ],
                "target_column": "a"
              }
            ],
            "counts": {
              "a": 1,
              "b": 1
            }
          }
        ],
        "weighted_partition": "3",
        "weighted_core_counts": {
          "a": "2",
          "b": "2"
        },
        "weighted_core_frequencies": {
          "a": "2/3",
          "b": "2/3"
        },
        "weighted_abundant": [
          "a",
          "b"
        ]
      },
      "projection": {
        "preserves_projection": true,
        "failures": []
      },
      "defect": {
        "core": [
          "a",
          "b"
        ],
        "bad_rows": [],
        "lhs": 8,
        "rhs": 6
      }
    },
    "false_average": {
      "analysis": {
        "family": [
          [],
          [
            "a"
          ],
          [
            "a",
            "g",
            "l"
          ]
        ],
        "N_including_empty": 3,
        "counts": {
          "a": 2,
          "g": 1,
          "l": 1
        },
        "abundant": [
          "a"
        ],
        "fibres": [
          {
            "exterior": [],
            "bodies": {
              "a": [
                "a"
              ]
            },
            "family": [
              [],
              [
                "a"
              ]
            ],
            "slack": 0,
            "bad_zero_cells": 0,
            "bad_one_cells": 0,
            "injection": [],
            "counts": {
              "a": 1
            }
          },
          {
            "exterior": [
              "g"
            ],
            "bodies": {
              "a": [
                "a"
              ]
            },
            "family": [],
            "slack": 0,
            "bad_zero_cells": 1,
            "bad_one_cells": 1,
            "injection": [
              {
                "source_deleted": [],
                "source_column": "a",
                "move": "horizontal",
                "target_deleted": [
                  "a"
                ],
                "target_column": "a"
              }
            ],
            "counts": {
              "a": 0
            }
          },
          {
            "exterior": [
              "l"
            ],
            "bodies": {
              "a": [
                "a"
              ]
            },
            "family": [],
            "slack": 0,
            "bad_zero_cells": 1,
            "bad_one_cells": 1,
            "injection": [
              {
                "source_deleted": [],
                "source_column": "a",
                "move": "horizontal",
                "target_deleted": [
                  "a"
                ],
                "target_column": "a"
              }
            ],
            "counts": {
              "a": 0
            }
          },
          {
            "exterior": [
              "g",
              "l"
            ],
            "bodies": {
              "a": [
                "a"
              ]
            },
            "family": [
              [
                "a"
              ]
            ],
            "slack": 1,
            "bad_zero_cells": 0,
            "bad_one_cells": 1,
            "injection": [],
            "counts": {
              "a": 1
            }
          }
        ],
        "weighted_partition": "3",
        "weighted_core_counts": {
          "a": "2"
        },
        "weighted_core_frequencies": {
          "a": "2/3"
        },
        "weighted_abundant": [
          "a"
        ]
      },
      "projection": {
        "preserves_projection": false,
        "failures": [
          {
            "head": "l",
            "witness": [
              "a",
              "g",
              "l"
            ],
            "projection": [
              "a",
              "l"
            ]
          }
        ]
      },
      "defect": {
        "core": [
          "a"
        ],
        "bad_rows": [
          [
            "a",
            "g",
            "l"
          ]
        ],
        "lhs": 4,
        "rhs": 4
      }
    },
    "failed_projection": {
      "analysis": {
        "family": [
          [],
          [
            "a"
          ],
          [
            "b",
            "g"
          ],
          [
            "a",
            "b",
            "g"
          ]
        ],
        "N_including_empty": 4,
        "counts": {
          "a": 2,
          "b": 2,
          "g": 2
        },
        "abundant": [
          "a",
          "b",
          "g"
        ],
        "fibres": [
          {
            "exterior": [],
            "bodies": {
              "a": [
                "a"
              ]
            },
            "family": [
              [],
              [
                "a"
              ]
            ],
            "slack": 0,
            "bad_zero_cells": 0,
            "bad_one_cells": 0,
            "injection": [],
            "counts": {
              "a": 1
            }
          },
          {
            "exterior": [
              "b"
            ],
            "bodies": {
              "a": [
                "a"
              ]
            },
            "family": [],
            "slack": 0,
            "bad_zero_cells": 1,
            "bad_one_cells": 1,
            "injection": [
              {
                "source_deleted": [],
                "source_column": "a",
                "move": "horizontal",
                "target_deleted": [
                  "a"
                ],
                "target_column": "a"
              }
            ],
            "counts": {
              "a": 0
            }
          },
          {
            "exterior": [
              "g"
            ],
            "bodies": {
              "a": [
                "a"
              ]
            },
            "family": [],
            "slack": 0,
            "bad_zero_cells": 1,
            "bad_one_cells": 1,
            "injection": [
              {
                "source_deleted": [],
                "source_column": "a",
                "move": "horizontal",
                "target_deleted": [
                  "a"
                ],
                "target_column": "a"
              }
            ],
            "counts": {
              "a": 0
            }
          },
          {
            "exterior": [
              "b",
              "g"
            ],
            "bodies": {
              "a": [
                "a"
              ]
            },
            "family": [
              [],
              [
                "a"
              ]
            ],
            "slack": 0,
            "bad_zero_cells": 0,
            "bad_one_cells": 0,
            "injection": [],
            "counts": {
              "a": 1
            }
          }
        ],
        "weighted_partition": "4",
        "weighted_core_counts": {
          "a": "2"
        },
        "weighted_core_frequencies": {
          "a": "1/2"
        },
        "weighted_abundant": [
          "a"
        ]
      },
      "projection": {
        "preserves_projection": false,
        "failures": [
          {
            "head": "b",
            "witness": [
              "a",
              "b",
              "g"
            ],
            "projection": [
              "a",
              "b"
            ]
          }
        ]
      },
      "defect": {
        "core": [
          "a"
        ],
        "bad_rows": [
          [
            "b",
            "g"
          ],
          [
            "a",
            "b",
            "g"
          ]
        ],
        "lhs": 4,
        "rhs": 4
      }
    }
  },
  "scope": "finite exact audits; no kinetics, no Lean rerun, no unrestricted half-frequency proof"
}
