{
  "inputs": {
    "m": 2,
    "r": "3/2",
    "J": "1",
    "reverse_budgets": [
      "2",
      "6"
    ],
    "equilibrium_constants": [
      "9/4",
      "14/9"
    ]
  },
  "unit_design": {
    "kp": [
      "3",
      "7"
    ],
    "km": [
      "2",
      "6"
    ],
    "g": [
      "1",
      "1"
    ],
    "f": [
      "1",
      "3"
    ],
    "u": [
      "1",
      "3/2"
    ],
    "q": [
      "3/2",
      "7/6"
    ],
    "phi": "7/4",
    "unattained_capacity": "3/2",
    "uniqueness": {
      "certified": true,
      "terminal": [
        0,
        1
      ],
      "transient_blocks": [],
      "reason": "Rooted with positive subcritical block vectors."
    },
    "curvature": {
      "J_second_log_control": "-33/10",
      "left_null": [
        "4",
        "1"
      ],
      "regular": true
    }
  },
  "budget_certificate": {
    "feasible": true,
    "f": [
      "1",
      "3"
    ],
    "D_f": [
      "0",
      "0"
    ],
    "D": [
      [
        "-3/2",
        "1/2"
      ],
      [
        "2",
        "-2/3"
      ]
    ],
    "q": [
      "3/2",
      "7/6"
    ],
    "reverse_one_way": [
      "2",
      "6"
    ]
  },
  "budget_optimum": {
    "feasible": true,
    "r_min": "3/2",
    "r_max": "3/2",
    "minimum_phi": "7/4",
    "maximum_current": "1",
    "maximum_current_numeric": 1.0
  },
  "higher_current_certificate": {
    "feasible": false,
    "dual_y": [
      "35/6",
      "25/6"
    ],
    "y_D": [
      "-1",
      "0"
    ],
    "D": [
      [
        "-8/5",
        "1/2"
      ],
      [
        "2",
        "-7/10"
      ]
    ]
  },
  "fixed_equilibrium_design": {
    "reference": [
      "2",
      "3"
    ],
    "kp": [
      "3/2",
      "7/9"
    ],
    "km": [
      "2/3",
      "1/2"
    ]
  },
  "rooted_counterexample": {
    "T": [
      [
        "0",
        "2",
        "0"
      ],
      [
        "1",
        "0",
        "0"
      ],
      [
        "1",
        "0",
        "2"
      ]
    ],
    "g": [
      "3/2",
      "1/2",
      "1/2"
    ],
    "weights": [
      "3",
      "1",
      "1"
    ],
    "uniqueness_criterion": {
      "certified": false,
      "terminal": [
        2
      ],
      "transient_blocks": [
        {
          "indices": [
            0,
            1
          ],
          "subcritical_certificate": {
            "feasible": false,
            "dual_y": [
              "1",
              "1"
            ],
            "y_D": [
              "0",
              "-1"
            ]
          }
        }
      ],
      "reason": "Sufficient uniqueness criterion fails; this alone does not prove nonuniqueness."
    },
    "maximizers": [
      [
        "1",
        "1",
        "1"
      ],
      [
        "5*sqrt(3)/3",
        "sqrt(3)",
        "1"
      ]
    ],
    "maximizer_currents": [
      [
        "3/2",
        "1/2",
        "1/2"
      ],
      [
        "3/2",
        "1/2",
        "1/2"
      ]
    ],
    "unit_phi": "32",
    "unattained_forward_capacity": "4",
    "second_flux_ratios": [
      "6/5",
      "10/9",
      "2"
    ],
    "second_phi": "96/25",
    "second_response_u": [
      "1",
      "17",
      "-6"
    ],
    "second_response_f": [
      "10",
      "18",
      "-6"
    ],
    "capacity_scope": "The second maximum has a negative reaction response and is outside the forward-response cone.",
    "stationary_monomial_equations": [
      "2*p1 - p2*p3 - t",
      "-p1**2 + 2*p2 - t",
      "-p3**2 + 2*p3 - t"
    ],
    "factor_at_maximum": "-(p1 - 3)*(p1 - 1)",
    "unit_internal_jacobian": [
      [
        "-15/2",
        "-45/2"
      ],
      [
        "-43/2",
        "-127/2"
      ]
    ],
    "unit_internal_determinant": "-15/2",
    "second_internal_determinant": "-5*sqrt(3)/2",
    "local_curvature": {
      "J_second_log_control": "-8/25",
      "left_null": [
        "0",
        "0",
        "1"
      ],
      "regular": true
    },
    "dynamical_scope": "The unit design is an internal saddle. Maxima occur at different X; this is not bistability at one control."
  },
  "scope": "Exact finite algebra/LP witnesses plus numerical illustrations. Global theorem is explained, not proved by sampling. Lean is not rerun."
}