{
  "parameters": {
    "recruitment": "4",
    "alpha1": "2",
    "alpha2": "1",
    "alpha3": "1",
    "eta1": "1/10",
    "eta2": "1/10",
    "gamma1": "1/10",
    "gamma2": "1/10",
    "beta1": "1/10",
    "beta2": "1",
    "mu0": "1",
    "mu1": "1",
    "mu2": "1",
    "mu3": "1"
  },
  "siphons": [
    [],
    [
      1,
      3
    ],
    [
      2,
      3
    ],
    [
      1,
      2,
      3
    ]
  ],
  "permanence": {
    "status": "uniform_permanence_by_paper_theorem",
    "residents": [
      [
        "4",
        "0",
        "0",
        "0"
      ],
      [
        "1/2",
        "7/2",
        "0",
        "0"
      ],
      [
        "1",
        "0",
        "3",
        "0"
      ]
    ],
    "invasion": [
      {
        "status": "strict_invasion",
        "matrix": [
          [
            "-17/20",
            "1/2"
          ],
          [
            "7/10",
            "-3/20"
          ]
        ],
        "left_weight": "191/84",
        "weighted_columns": [
          "89/120",
          "89/560"
        ],
        "relative_margin": "267/3820",
        "lambda_plus": "-1/2 + 3*sqrt(21)/20",
        "numeric_lambda_plus": 0.187386354243376
      },
      {
        "status": "strict_invasion",
        "matrix": [
          [
            "7/10",
            "1/10"
          ],
          [
            "3/5",
            "3/10"
          ]
        ],
        "left_weight": "1",
        "weighted_columns": [
          "13/10",
          "2/5"
        ],
        "relative_margin": "2/5",
        "lambda_plus": "sqrt(10)/10 + 1/2",
        "numeric_lambda_plus": 0.8162277660168379
      }
    ],
    "numerical_floor": null,
    "scope": "Existential floor depends on fixed parameters, not initial state. No global interior convergence claim."
  },
  "overlap": {
    "normal_indices": [
      1,
      2,
      3
    ],
    "union": [
      1,
      2,
      3
    ],
    "intersection": [
      3
    ],
    "normal_matrix": [
      [
        "7",
        "0",
        "2/5"
      ],
      [
        "0",
        "3",
        "4"
      ],
      [
        "0",
        "0",
        "3"
      ]
    ],
    "chi_union": "(z - 7)*(z - 3)**2",
    "chi_intersection": "z - 3",
    "chi_S1": "(z - 7)*(z - 3)",
    "chi_S2": "(z - 3)**2",
    "cross_multiplied_residual": "0",
    "chi_full_normal": "(z - 7)*(z - 3)**2",
    "signature_factors": [
      {
        "membership": [
          0
        ],
        "species": [
          1
        ],
        "factor": "z - 7"
      },
      {
        "membership": [
          1
        ],
        "species": [
          2
        ],
        "factor": "z - 3"
      },
      {
        "membership": [
          0,
          1
        ],
        "species": [
          3
        ],
        "factor": "z - 3"
      }
    ],
    "scope": "All factors evaluated at the same boundary point; no determinant division."
  },
  "zero_shared_mode_overlap": {
    "normal_indices": [
      1,
      2,
      3
    ],
    "union": [
      1,
      2,
      3
    ],
    "intersection": [
      3
    ],
    "normal_matrix": [
      [
        "1",
        "0",
        "1/10"
      ],
      [
        "0",
        "0",
        "1"
      ],
      [
        "0",
        "0",
        "0"
      ]
    ],
    "chi_union": "z**2*(z - 1)",
    "chi_intersection": "z",
    "chi_S1": "z*(z - 1)",
    "chi_S2": "z**2",
    "cross_multiplied_residual": "0",
    "chi_full_normal": "z**2*(z - 1)",
    "signature_factors": [
      {
        "membership": [
          0
        ],
        "species": [
          1
        ],
        "factor": "z - 1"
      },
      {
        "membership": [
          1
        ],
        "species": [
          2
        ],
        "factor": "z"
      },
      {
        "membership": [
          0,
          1
        ],
        "species": [
          3
        ],
        "factor": "z"
      }
    ],
    "scope": "All factors evaluated at the same boundary point; no determinant division."
  },
  "independent_parameter_box": {
    "certified": true,
    "resident_s_intervals": [
      [
        "99/202",
        "101/198"
      ],
      [
        "99/101",
        "101/99"
      ]
    ],
    "resident_u_intervals": [
      [
        "68207/19998",
        "71807/19998"
      ],
      [
        "29003/9999",
        "31003/9999"
      ]
    ],
    "weights": [
      "2",
      "1"
    ],
    "weighted_relative_column_intervals": [
      [
        "98611/202000",
        "121411/198000"
      ],
      [
        "5601/101000",
        "14401/99000"
      ],
      [
        "123013/101000",
        "45671/33000"
      ],
      [
        "8701/25250",
        "3767/8250"
      ]
    ],
    "relative_margins": [
      "5601/101000",
      "8701/25250"
    ],
    "scope": "Independent continuous parameter box; permanence at each parameter, no common numerical floor over the box. Failure is inconclusive."
  },
  "fixed_obstruction": {
    "complete_DFE_jacobians_equal_under_eta1_change": true,
    "low_beta2": {
      "status": "permanence_fails_resident_sink",
      "residents": [
        [
          "4",
          "0",
          "0",
          "0"
        ],
        [
          "1/2",
          "7/2",
          "0",
          "0"
        ],
        [
          "1",
          "0",
          "3",
          "0"
        ]
      ],
      "invasion": [
        {
          "status": "strict_decay",
          "matrix": [
            [
              "-17/20",
              "1/20"
            ],
            [
              "7/10",
              "-3/20"
            ]
          ],
          "left_weight": "65/84",
          "weighted_columns": [
            "-37/120",
            "-37/560"
          ],
          "relative_margin": "111/1300",
          "lambda_plus": "-1/2 + 3*sqrt(7)/20",
          "numeric_lambda_plus": -0.10313730334031142
        },
        {
          "status": "strict_invasion",
          "matrix": [
            [
              "7/10",
              "1/10"
            ],
            [
              "3/5",
              "3/10"
            ]
          ],
          "left_weight": "1",
          "weighted_columns": [
            "13/10",
            "2/5"
          ],
          "relative_margin": "2/5",
          "lambda_plus": "sqrt(10)/10 + 1/2",
          "numeric_lambda_plus": 0.8162277660168379
        }
      ],
      "numerical_floor": null,
      "scope": "Existential floor depends on fixed parameters, not initial state. No global interior convergence claim."
    },
    "changed_eta1": {
      "status": "uniform_permanence_by_paper_theorem",
      "residents": [
        [
          "4",
          "0",
          "0",
          "0"
        ],
        [
          "1/2",
          "7/2",
          "0",
          "0"
        ],
        [
          "1",
          "0",
          "3",
          "0"
        ]
      ],
      "invasion": [
        {
          "status": "strict_invasion",
          "matrix": [
            [
              "-17/20",
              "1/20"
            ],
            [
              "7/10",
              "1/5"
            ]
          ],
          "left_weight": "31/14",
          "weighted_columns": [
            "7/10",
            "69/140"
          ],
          "relative_margin": "69/310",
          "lambda_plus": "-13/40 + sqrt(497)/40",
          "numeric_lambda_plus": 0.23233742024019885
        },
        {
          "status": "strict_invasion",
          "matrix": [
            [
              "7/10",
              "1/10"
            ],
            [
              "3/5",
              "3/10"
            ]
          ],
          "left_weight": "1",
          "weighted_columns": [
            "13/10",
            "2/5"
          ],
          "relative_margin": "2/5",
          "lambda_plus": "sqrt(10)/10 + 1/2",
          "numeric_lambda_plus": 0.8162277660168379
        }
      ],
      "numerical_floor": null,
      "scope": "Existential floor depends on fixed parameters, not initial state. No global interior convergence claim."
    },
    "beta2_threshold": "51/140"
  },
  "normalized_weights": {
    "ru": "1",
    "rv": "191/84",
    "rj": "1",
    "k": 1,
    "fibre_growth_lower_bounds": [
      "47/5",
      "267/3820",
      "2/5"
    ],
    "product_floor": null
  },
  "absorbing_total_bound_and_eventual_s_floor": [
    "5",
    "4/53"
  ],
  "scope": "Fixed literal positive-rate model; theorem floor existential, sampled minima never promoted to a guarantee. No Lean rerun."
}