{
  "status": "feasible",
  "state": {
    "u": {
      "exact": "(root-obj (+ (* 25 (^ x 2)) (* (- 25) x) 3) 1)",
      "approximation": 0.13944487245360107
    },
    "v": {
      "exact": "(root-obj (+ (* 10000 (^ x 2)) (* (- 8600) x) 549) 1)",
      "approximation": 0.06944487245360106
    }
  },
  "trace": [
    {
      "root_vertex": "u",
      "cycle_arcs": [
        0,
        1
      ],
      "before": {
        "exact": "(/ 1.0 10.0)",
        "approximation": 0.1
      },
      "cycle_value_before": {
        "exact": "(root-obj (+ (* 25 (^ x 2)) (* 25 x) (- 3)) 2)",
        "approximation": 0.10827625302982197
      },
      "phase_round": 2,
      "root": {
        "exact": "(root-obj (+ (* 25 (^ x 2)) (* (- 25) x) 3) 1)",
        "approximation": 0.13944487245360107
      }
    }
  ],
  "jumps": 1,
  "rounds": 4,
  "max_simple_transport": 1,
  "labels": {
    "u": {
      "seed": "u",
      "seed_description": {
        "kind": "cycle_root",
        "cycle_arcs": [
          0,
          1
        ],
        "value": {
          "exact": "(root-obj (+ (* 25 (^ x 2)) (* (- 25) x) 3) 1)",
          "approximation": 0.13944487245360107
        }
      },
      "path": [
        "u"
      ],
      "arcs": []
    },
    "v": {
      "seed": "u",
      "seed_description": {
        "kind": "cycle_root",
        "cycle_arcs": [
          0,
          1
        ],
        "value": {
          "exact": "(root-obj (+ (* 25 (^ x 2)) (* (- 25) x) 3) 1)",
          "approximation": 0.13944487245360107
        }
      },
      "path": [
        "u",
        "v"
      ],
      "arcs": [
        0
      ]
    }
  },
  "independent_leastness_check": true,
  "rounded_half_margin_witness": {
    "u": "71/512",
    "v": "35/512"
  },
  "scope": "Exact fixed-margin Algorithm 1 with general QF_NRA algebraic roots. No projected-CAD, positive-infinitesimal or FPT implementation claim."
}