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    "name": "mixed_star",
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    "name": "theta_odd",
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        3
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    "ODE_multiplicity": 3,
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    "name": "theta_even",
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    "name": "theta_wrong_parity",
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        "2"
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        3,
        1
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    "ODE_multiplicity": 1,
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    "name": "figure_eight",
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        3
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    "ODE_multiplicity": 3,
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    "name": "figure_eight_bad",
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        1
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    "ODE_multiplicity": 1,
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    "name": "Dirichlet_lasso",
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        2
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    "ODE_multiplicity": 2,
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    "name": "Neumann_lasso",
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        2,
        2
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    "ODE_multiplicity": 2,
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    "name": "barbell",
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        3,
        3
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    "ODE_multiplicity": 3,
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    "name": "branch_lasso_tree",
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        2,
        "2"
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    "ODE_multiplicity": 3,
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    "name": "loop_at_degree_four",
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        4,
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    "ODE_multiplicity": 1,
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    "name": "bouquet_3",
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      "reason": "The proposed index is not integral."
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        3,
        4
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    "name": "bouquet_4",
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      "reason": "A nonexceptional loop must be pendant at a degree-three vertex."
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        4,
        5
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    "ODE_multiplicity": 5,
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    "name": "bouquet_5",
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        0,
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        0,
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        0,
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      "family": "none",
      "reason": "The proposed index is not integral."
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        5,
        6
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    "ODE_multiplicity": 6,
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    "name": "bouquet_6",
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        0,
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        0,
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        0,
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        0,
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        6,
        7
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    "ODE_multiplicity": 7,
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    "name": "pumpkin_2",
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        1,
        "1"
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      "reason": "The circle has a different bound."
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        1,
        2
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    "ODE_multiplicity": 2,
    "passed": true
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    "name": "pumpkin_3",
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      "family": "theta",
      "reason": "Three positive integer cell counts of common parity."
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        1,
        3
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    "ODE_multiplicity": 3,
    "passed": true
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        1,
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      "reason": "The proposed index is not integral."
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        1,
        4
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        1,
        5
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      "family": "none",
      "reason": "The proposed index is not integral."
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        1,
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    "passed": true
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        1,
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      "family": "excluded-topology",
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        1,
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    "ODE_multiplicity": 7,
    "passed": true
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    "name": "atlas_0_0",
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      "family": "none",
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    "ODE_multiplicity": 0,
    "passed": true
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      "reason": "All exact topology and metric conditions hold."
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        1
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    "ODE_multiplicity": 1,
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    "name": "atlas_1_0",
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    "classification": {
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    "classification": {
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      "reason": "A skeleton edge violates the integer/half-integer phase rule."
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    "exact": {
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        7,
        0
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    },
    "ODE_multiplicity": 0,
    "passed": true
  },
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    "name": "atlas_10_1",
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        "2"
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        "2"
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    "ODE_multiplicity": 0,
    "passed": true
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    "name": "atlas_10_2",
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        "1"
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        3,
        "2"
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        3,
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        "1"
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    "classification": {
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      "reason": "A skeleton edge violates the integer/half-integer phase rule."
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        0
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    },
    "ODE_multiplicity": 0,
    "passed": true
  },
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    "name": "atlas_11_0",
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        0,
        1,
        "1/2"
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        0,
        4,
        "1/2"
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        1,
        2,
        "1"
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        2,
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        "3/2"
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    "classification": {
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      "reason": "All exact topology and metric conditions hold."
    },
    "exact": {
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      "top_index": 4,
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        3,
        1
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    },
    "ODE_multiplicity": 1,
    "passed": true
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    "name": "atlas_11_1",
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        0,
        1,
        "2"
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        0,
        4,
        "3/2"
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        1,
        2,
        "3/2"
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        2,
        3,
        "2"
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    ],
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      4
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    "classification": {
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      "reason": "All exact topology and metric conditions hold."
    },
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        6,
        1
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    },
    "ODE_multiplicity": 1,
    "passed": true
  },
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    "name": "atlas_11_2",
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        0,
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        "1"
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        1,
        2,
        "1"
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        2,
        3,
        "3/2"
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      "reason": "All exact topology and metric conditions hold."
    },
    "exact": {
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      "adjacency_dimension": 11,
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        5,
        5,
        1
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    },
    "ODE_multiplicity": 1,
    "passed": true
  },
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    "name": "atlas_12_0",
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        0,
        4,
        "2"
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        1,
        4,
        "3/2"
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        2,
        3,
        "2"
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      [
        2,
        4,
        "1"
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        3,
        4,
        "1"
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    ],
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      "reason": "A nonexceptional loop must be pendant at a degree-three vertex."
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    "exact": {
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      "top_index": 8,
      "adjacency_dimension": 15,
      "adjacency_inertia": [
        7,
        7,
        1
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    },
    "ODE_multiplicity": 1,
    "passed": true
  },
  {
    "name": "atlas_12_1",
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        0,
        4,
        "1"
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      [
        1,
        4,
        "3/2"
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      [
        2,
        3,
        "3/2"
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      [
        2,
        4,
        "3/2"
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      [
        3,
        4,
        "2"
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    ],
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      1
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      "reason": "A nonexceptional loop must be pendant at a degree-three vertex."
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    "exact": {
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      "adjacency_dimension": 13,
      "adjacency_inertia": [
        6,
        6,
        1
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    },
    "ODE_multiplicity": 1,
    "passed": true
  },
  {
    "name": "atlas_12_2",
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        0,
        4,
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      [
        1,
        4,
        "1/2"
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      [
        2,
        3,
        "1"
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      [
        2,
        4,
        "1"
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      [
        3,
        4,
        "3/2"
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    "classification": {
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    },
    "exact": {
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      "top_index": 4,
      "adjacency_dimension": 9,
      "adjacency_inertia": [
        4,
        5,
        0
      ]
    },
    "ODE_multiplicity": 0,
    "passed": true
  },
  {
    "name": "atlas_13_0",
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        0,
        1,
        "2"
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      [
        0,
        2,
        "3/2"
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      [
        0,
        4,
        "1"
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      [
        1,
        2,
        "1"
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      [
        2,
        3,
        "1/2"
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    ],
    "Dirichlet": [
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      4
    ],
    "classification": {
      "saturated": false,
      "family": "none",
      "reason": "The proposed index is not integral."
    },
    "exact": {
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      "top_index": 5,
      "adjacency_dimension": 10,
      "adjacency_inertia": [
        5,
        5,
        0
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    },
    "ODE_multiplicity": 0,
    "passed": true
  },
  {
    "name": "atlas_13_1",
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        0,
        1,
        "1"
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      [
        0,
        2,
        "1/2"
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      [
        0,
        4,
        "1"
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        1,
        2,
        "2"
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      [
        2,
        3,
        "3/2"
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    ],
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      "family": "none",
      "reason": "The proposed index is not integral."
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    "exact": {
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      "adjacency_dimension": 12,
      "adjacency_inertia": [
        6,
        6,
        0
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    },
    "ODE_multiplicity": 0,
    "passed": true
  },
  {
    "name": "atlas_13_2",
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        0,
        1,
        "3/2"
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        2,
        "1/2"
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        4,
        "2"
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        1,
        2,
        "1/2"
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        2,
        3,
        "1/2"
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    ],
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    "classification": {
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      "family": "excluded-topology",
      "reason": "The nonloop skeleton must be a tree."
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    "exact": {
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      "top_index": 5,
      "adjacency_dimension": 9,
      "adjacency_inertia": [
        4,
        4,
        1
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    },
    "ODE_multiplicity": 1,
    "passed": true
  },
  {
    "name": "atlas_14_0",
    "edges": [
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        0,
        4,
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        1,
        2,
        "1/2"
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        1,
        3,
        "3/2"
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        2,
        3,
        "1"
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        3,
        4,
        "1"
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    ],
    "Dirichlet": [
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    "classification": {
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      "saturated": false,
      "family": "lasso-tree",
      "reason": "An attached loop has incompatible phase."
    },
    "exact": {
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      "adjacency_inertia": [
        5,
        5,
        0
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    },
    "ODE_multiplicity": 0,
    "passed": true
  },
  {
    "name": "atlas_14_1",
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        0,
        4,
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        1,
        2,
        "3/2"
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        1,
        3,
        "2"
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        2,
        3,
        "2"
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        3,
        4,
        "1/2"
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    ],
    "Dirichlet": [
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    "classification": {
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    "exact": {
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      "adjacency_dimension": 14,
      "adjacency_inertia": [
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        7,
        0
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    },
    "ODE_multiplicity": 0,
    "passed": true
  },
  {
    "name": "atlas_14_2",
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        0,
        4,
        "3/2"
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        2,
        "1"
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        1,
        3,
        "3/2"
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        2,
        3,
        "3/2"
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      [
        3,
        4,
        "1"
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    ],
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      "family": "none",
      "reason": "The proposed index is not integral."
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    "exact": {
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      "adjacency_inertia": [
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        6,
        1
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    },
    "ODE_multiplicity": 1,
    "passed": true
  },
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    "name": "atlas_15_0",
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        0,
        1,
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        1,
        3,
        "1/2"
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        4,
        "2"
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        3,
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        "1"
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      "reason": "An attached loop has incompatible phase."
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    "exact": {
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      "adjacency_inertia": [
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        5,
        0
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    },
    "ODE_multiplicity": 0,
    "passed": true
  },
  {
    "name": "atlas_15_1",
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        0,
        1,
        "3/2"
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        1,
        3,
        "3/2"
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        1,
        4,
        "1"
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        2,
        3,
        "1"
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        4,
        "1"
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      "family": "lasso-tree",
      "reason": "An attached loop has incompatible phase."
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    "exact": {
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      "adjacency_dimension": 12,
      "adjacency_inertia": [
        6,
        6,
        0
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    },
    "ODE_multiplicity": 0,
    "passed": true
  },
  {
    "name": "atlas_15_2",
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        0,
        1,
        "2"
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        1,
        3,
        "1/2"
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        4,
        "1"
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        2,
        3,
        "3/2"
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        4,
        "2"
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      "family": "lasso-tree",
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    "exact": {
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      "adjacency_inertia": [
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        7,
        0
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    },
    "ODE_multiplicity": 0,
    "passed": true
  },
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    "name": "atlas_16_0",
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        0,
        1,
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        4,
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        2,
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        2,
        3,
        "3/2"
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        3,
        4,
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    ],
    "Dirichlet": [],
    "classification": {
      "saturated": false,
      "family": "excluded-circle",
      "reason": "The circle has a different bound."
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    "exact": {
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      "top_index": 7,
      "adjacency_dimension": 12,
      "adjacency_inertia": [
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        5,
        2
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    },
    "ODE_multiplicity": 2,
    "passed": true
  },
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    "name": "atlas_16_1",
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        0,
        1,
        "1"
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        4,
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        2,
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        3,
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        4,
        "1"
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    ],
    "Dirichlet": [],
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      "family": "excluded-circle",
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        4,
        0
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    },
    "ODE_multiplicity": 0,
    "passed": true
  },
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    "name": "atlas_16_2",
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        0,
        1,
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        2,
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        2,
        3,
        "3/2"
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        3,
        4,
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    ],
    "Dirichlet": [],
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      "adjacency_inertia": [
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        7,
        0
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    },
    "ODE_multiplicity": 0,
    "passed": true
  },
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    "name": "atlas_17_0",
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        0,
        1,
        "1"
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        2,
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        1,
        3,
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        4,
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        3,
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    ],
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      "family": "none",
      "reason": "The proposed index is not integral."
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        1
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    },
    "ODE_multiplicity": 1,
    "passed": true
  },
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    "name": "atlas_17_1",
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        0,
        1,
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        1,
        3,
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        1,
        4,
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        3,
        "2"
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        2,
        4,
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    ],
    "Dirichlet": [],
    "classification": {
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      "saturated": false,
      "family": "excluded-topology",
      "reason": "The nonloop skeleton must be a tree."
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    "exact": {
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      "adjacency_dimension": 18,
      "adjacency_inertia": [
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        9,
        0
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    },
    "ODE_multiplicity": 0,
    "passed": true
  },
  {
    "name": "atlas_17_2",
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        0,
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        1,
        2,
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        1,
        3,
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        1,
        4,
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        2,
        3,
        "3/2"
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        2,
        4,
        "3/2"
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    ],
    "Dirichlet": [],
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      "saturated": false,
      "family": "none",
      "reason": "The proposed index is not integral."
    },
    "exact": {
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        1
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    },
    "ODE_multiplicity": 1,
    "passed": true
  },
  {
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        1,
        4,
        "3/2"
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        2,
        4,
        "1/2"
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        3,
        4,
        "1/2"
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    ],
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      5
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    "classification": {
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      "reason": "A nonexceptional loop must be pendant at a degree-three vertex."
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        1
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    "ODE_multiplicity": 1,
    "passed": true
  },
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    "name": "atlas_40_0",
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        "1/2"
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        3,
        "2"
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    ],
    "Dirichlet": [],
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      "family": "none",
      "reason": "The proposed index is not integral."
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    "exact": {
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        8,
        2
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    },
    "ODE_multiplicity": 2,
    "passed": true
  },
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    "name": "atlas_40_1",
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        "1"
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    ],
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      "reason": "The proposed index is not integral."
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        6,
        2
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    },
    "ODE_multiplicity": 2,
    "passed": true
  },
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    "name": "atlas_40_2",
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      "reason": "The proposed index is not integral."
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        0
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    },
    "ODE_multiplicity": 0,
    "passed": true
  },
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    "name": "atlas_41_0",
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        5,
        0
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    },
    "ODE_multiplicity": 0,
    "passed": true
  },
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    "name": "atlas_41_1",
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        0,
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    "name": "atlas_41_2",
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      "reason": "The nonloop skeleton must be a tree."
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    "exact": {
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        8,
        0
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    },
    "ODE_multiplicity": 0,
    "passed": true
  },
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    "name": "atlas_42_0",
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    "classification": {
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        5,
        1
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    },
    "ODE_multiplicity": 1,
    "passed": true
  },
  {
    "name": "atlas_42_1",
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        0,
        2,
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    "classification": {
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        6,
        1
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    },
    "ODE_multiplicity": 1,
    "passed": true
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    "name": "atlas_42_2",
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      "reason": "The proposed index is not integral."
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        10,
        0
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    },
    "ODE_multiplicity": 0,
    "passed": true
  },
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    "name": "atlas_43_0",
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        2
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    },
    "ODE_multiplicity": 2,
    "passed": true
  },
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    "name": "atlas_43_1",
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        1
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    "ODE_multiplicity": 1,
    "passed": true
  },
  {
    "name": "atlas_43_2",
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        9,
        0
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    "ODE_multiplicity": 0,
    "passed": true
  },
  {
    "name": "atlas_44_0",
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        1
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    },
    "ODE_multiplicity": 1,
    "passed": true
  },
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    "name": "atlas_44_1",
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    "classification": {
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    "ODE_multiplicity": 0,
    "passed": true
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    "name": "atlas_44_2",
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        0
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    },
    "ODE_multiplicity": 0,
    "passed": true
  },
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    "name": "atlas_45_0",
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    "ODE_multiplicity": 0,
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    },
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    "name": "atlas_45_2",
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    "ODE_multiplicity": 0,
    "passed": true
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    "name": "atlas_46_0",
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    },
    "ODE_multiplicity": 1,
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    "name": "atlas_46_1",
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    "ODE_multiplicity": 0,
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    "name": "atlas_46_2",
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    "ODE_multiplicity": 1,
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    "name": "atlas_47_0",
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        4,
        "1/2"
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        "2"
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      "reason": "The proposed index is not integral."
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        4,
        5
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        6,
        7
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    "ODE_multiplicity": 7,
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    "name": "compatible_star_2",
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    "ODE_multiplicity": 3,
    "passed": true
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    "name": "compatible_star_3",
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        4
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    "ODE_multiplicity": 4,
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    "name": "compatible_star_4",
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    "classification": {
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    "exact": {
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        6,
        7
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    },
    "ODE_multiplicity": 7,
    "passed": true
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    "name": "compatible_star_5",
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      "reason": "All exact topology and metric conditions hold."
    },
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        3
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    "ODE_multiplicity": 3,
    "passed": true
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    "name": "compatible_star_6",
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    "classification": {
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    "exact": {
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        6
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    },
    "ODE_multiplicity": 6,
    "passed": true
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    "name": "compatible_star_7",
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    "classification": {
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    "exact": {
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        6,
        6
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    },
    "ODE_multiplicity": 6,
    "passed": true
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    "name": "compatible_star_8",
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    "classification": {
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      "reason": "All exact topology and metric conditions hold."
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    "exact": {
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        5,
        7
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    },
    "ODE_multiplicity": 7,
    "passed": true
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    "name": "compatible_star_9",
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    "ODE_multiplicity": 3,
    "passed": true
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    "name": "compatible_star_10",
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      "family": "lasso-tree",
      "reason": "All exact topology and metric conditions hold."
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        3,
        6
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    },
    "ODE_multiplicity": 6,
    "passed": true
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  {
    "name": "compatible_star_11",
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      6
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      "family": "lasso-tree",
      "reason": "All exact topology and metric conditions hold."
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        7
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    },
    "ODE_multiplicity": 7,
    "passed": true
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    "name": "compatible_star_12",
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      "family": "tree",
      "reason": "All exact topology and metric conditions hold."
    },
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        4,
        5
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    },
    "ODE_multiplicity": 5,
    "passed": true
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    "name": "compatible_star_13",
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      "reason": "All exact topology and metric conditions hold."
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        4,
        3
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    "ODE_multiplicity": 3,
    "passed": true
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    "name": "compatible_star_14",
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        1,
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        2,
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        3,
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        3,
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        5,
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    ],
    "Dirichlet": [],
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      "family": "lasso-tree",
      "reason": "All exact topology and metric conditions hold."
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        8,
        8
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    "ODE_multiplicity": 8,
    "passed": true
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        2,
        "3/2"
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    "classification": {
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      "family": "tree",
      "reason": "All exact topology and metric conditions hold."
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    "exact": {
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        2,
        2
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    "ODE_multiplicity": 2,
    "passed": true
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    "name": "compatible_star_16",
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      "family": "lasso-tree",
      "reason": "All exact topology and metric conditions hold."
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        4,
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    "ODE_multiplicity": 3,
    "passed": true
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  {
    "name": "compatible_star_17",
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    "Dirichlet": [],
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      "family": "lasso-tree",
      "reason": "All exact topology and metric conditions hold."
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    "exact": {
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      "adjacency_inertia": [
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        6,
        6
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    },
    "ODE_multiplicity": 6,
    "passed": true
  },
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    "name": "compatible_star_18",
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        1,
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    "ODE_multiplicity": 7,
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    "ODE_multiplicity": 3,
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