{
  "decisions": {
    "weighted_private": {
      "status": "SAT",
      "activities": {
        "A": "3789/4096",
        "B": "6746098527/7381975040",
        "C": "18433/20480"
      },
      "currents_and_residuals": [
        [
          "743299497/7381975040",
          "429229287/7381975040",
          "10469007/671088640",
          "31407021/738197504"
        ],
        [
          "917644887/7381975040",
          "3537015424212349631/54493555491183001600",
          "149999598503539391/27246777745591500800",
          "3237016227205270849/54493555491183001600"
        ],
        [
          "1/20",
          "3718963/83886080",
          "1621811/41943040",
          "475341/83886080"
        ]
      ],
      "queries": 31,
      "normalized_response_slack": "1/512",
      "brackets": {
        "A": [
          "37/40",
          "9473/10240"
        ],
        "C": [
          "9/10",
          "9217/10240"
        ]
      },
      "reconstruction": [
        {
          "iterations": 2,
          "proved_budget": 21,
          "interpolation_parameter": "1/4",
          "certified_parameter_radius": "4137432795063009099/4219980937237211643904000"
        },
        {
          "iterations": 0,
          "proved_budget": 0
        }
      ],
      "scope": "Exact rational literal-current witness; Z3 QF_NRA used for decisions. No claim of the manuscript backend complexity or rerun Lean verification."
    },
    "weighted_junctions": {
      "status": "SAT",
      "activities": {
        "A": "37859/40960",
        "B": "37379/40960",
        "C": "7373/8192"
      },
      "currents_and_residuals": [
        [
          "27/256",
          "97739959/1677721600",
          "9266359/838860800",
          "79207241/1677721600"
        ],
        [
          "2313/20480",
          "112800759/1677721600",
          "18060279/838860800",
          "76680201/1677721600"
        ],
        [
          "497/10240",
          "76686519/1677721600",
          "35972279/838860800",
          "4741961/1677721600"
        ]
      ],
      "queries": 45,
      "normalized_response_slack": "1/1024",
      "brackets": {
        "A": [
          "18929/20480",
          "1893/2048"
        ],
        "B": [
          "18689/20480",
          "1869/2048"
        ],
        "C": [
          "9/10",
          "18433/20480"
        ]
      },
      "reconstruction": [
        {
          "iterations": 0,
          "proved_budget": 0
        },
        {
          "iterations": 0,
          "proved_budget": 0
        },
        {
          "iterations": 0,
          "proved_budget": 0
        }
      ],
      "scope": "Exact rational literal-current witness; Z3 QF_NRA used for decisions. No claim of the manuscript backend complexity or rerun Lean verification."
    },
    "unit_incompatible": {
      "status": "UNSAT",
      "queries": 1,
      "scope": "Exact nonlinear real-arithmetic backend verdict for the validated reduction; no independent UNSAT proof export."
    },
    "singleton_junctions": {
      "status": "SAT",
      "activities": {
        "A": "99/100",
        "B": "395361/400000",
        "C": "3551/3600"
      },
      "currents_and_residuals": [
        [
          "5751/400000",
          "3321/400000",
          "891/400000",
          "243/40000"
        ],
        [
          "7249/400000",
          "13607117111/1440000000000",
          "558917111/720000000000",
          "12489282889/1440000000000"
        ],
        [
          "13/1800",
          "283/45000",
          "241/45000",
          "7/7500"
        ]
      ],
      "queries": 14,
      "normalized_response_slack": "1/4096",
      "brackets": {
        "A": [
          "99/100",
          "99/100"
        ],
        "C": [
          "3551/3600",
          "3551/3600"
        ]
      },
      "reconstruction": [
        {
          "iterations": 2,
          "proved_budget": 27,
          "interpolation_parameter": "1/4",
          "certified_parameter_radius": "1147263/60500000000000"
        },
        {
          "iterations": 0,
          "proved_budget": 0
        }
      ],
      "scope": "Exact rational literal-current witness; Z3 QF_NRA used for decisions. No claim of the manuscript backend complexity or rerun Lean verification."
    },
    "cycle": {
      "status": "UNSAT",
      "queries": 1,
      "scope": "Exact nonlinear real-arithmetic backend verdict for the validated reduction; no independent UNSAT proof export."
    }
  },
  "reference_state": {
    "A": "99/100",
    "B": "593/600",
    "C": "3551/3600"
  },
  "relative_radius": "43/943",
  "edge_relative_radii": [
    "11/236",
    "43/943",
    "21/304"
  ],
  "margin_at_configured_relative_radius": "77/375000",
  "joint_rectangle": {
    "productive_throughout": true,
    "minimum_residual": "847959991/4687500000000",
    "corners": [
      {
        "edge": 0,
        "side": "source",
        "a": "216/25",
        "b": "24/25",
        "x": "990001/1000000",
        "y": "2964997/3000000",
        "food": "1",
        "residual": "2164059997/1562500000000"
      },
      {
        "edge": 0,
        "side": "target",
        "a": "216/25",
        "b": "24/25",
        "x": "989999/1000000",
        "y": "2965003/3000000",
        "food": "1",
        "residual": "20237060003/3125000000000"
      },
      {
        "edge": 0,
        "side": "source",
        "a": "216/25",
        "b": "26/25",
        "x": "990001/1000000",
        "y": "2964997/3000000",
        "food": "1",
        "residual": "50659779961/18750000000000"
      },
      {
        "edge": 0,
        "side": "target",
        "a": "216/25",
        "b": "26/25",
        "x": "989999/1000000",
        "y": "2965003/3000000",
        "food": "1",
        "residual": "218135780039/37500000000000"
      },
      {
        "edge": 0,
        "side": "source",
        "a": "234/25",
        "b": "24/25",
        "x": "990001/1000000",
        "y": "2964997/3000000",
        "food": "1",
        "residual": "286809997/1562500000000"
      },
      {
        "edge": 0,
        "side": "target",
        "a": "234/25",
        "b": "24/25",
        "x": "989999/1000000",
        "y": "2965003/3000000",
        "food": "1",
        "residual": "23982560003/3125000000000"
      },
      {
        "edge": 0,
        "side": "source",
        "a": "234/25",
        "b": "26/25",
        "x": "990001/1000000",
        "y": "2964997/3000000",
        "food": "1",
        "residual": "28132779961/18750000000000"
      },
      {
        "edge": 0,
        "side": "target",
        "a": "234/25",
        "b": "26/25",
        "x": "989999/1000000",
        "y": "2965003/3000000",
        "food": "1",
        "residual": "263081780039/37500000000000"
      },
      {
        "edge": 1,
        "side": "source",
        "a": "216/25",
        "b": "24/25",
        "x": "2965003/3000000",
        "y": "8877491/9000000",
        "food": "1",
        "residual": "7417209991/4687500000000"
      },
      {
        "edge": 1,
        "side": "target",
        "a": "216/25",
        "b": "24/25",
        "x": "2964997/3000000",
        "y": "8877509/9000000",
        "food": "1",
        "residual": "71036210009/9375000000000"
      },
      {
        "edge": 1,
        "side": "source",
        "a": "216/25",
        "b": "26/25",
        "x": "2965003/3000000",
        "y": "8877491/9000000",
        "food": "1",
        "residual": "175254729883/56250000000000"
      },
      {
        "edge": 1,
        "side": "target",
        "a": "216/25",
        "b": "26/25",
        "x": "2964997/3000000",
        "y": "8877509/9000000",
        "food": "1",
        "residual": "766132730117/112500000000000"
      },
      {
        "edge": 1,
        "side": "source",
        "a": "234/25",
        "b": "24/25",
        "x": "2965003/3000000",
        "y": "8877491/9000000",
        "food": "1",
        "residual": "847959991/4687500000000"
      },
      {
        "edge": 1,
        "side": "target",
        "a": "234/25",
        "b": "24/25",
        "x": "2964997/3000000",
        "y": "8877509/9000000",
        "food": "1",
        "residual": "84147710009/9375000000000"
      },
      {
        "edge": 1,
        "side": "source",
        "a": "234/25",
        "b": "26/25",
        "x": "2965003/3000000",
        "y": "8877491/9000000",
        "food": "1",
        "residual": "96423729883/56250000000000"
      },
      {
        "edge": 1,
        "side": "target",
        "a": "234/25",
        "b": "26/25",
        "x": "2964997/3000000",
        "y": "8877509/9000000",
        "food": "1",
        "residual": "923470730117/112500000000000"
      },
      {
        "edge": 2,
        "side": "source",
        "a": "48/25",
        "b": "24/25",
        "x": "990001/1000000",
        "y": "8877491/9000000",
        "food": "1",
        "residual": "24055179991/4687500000000"
      },
      {
        "edge": 2,
        "side": "target",
        "a": "48/25",
        "b": "24/25",
        "x": "989999/1000000",
        "y": "8877509/9000000",
        "food": "1",
        "residual": "2779060003/3125000000000"
      },
      {
        "edge": 2,
        "side": "source",
        "a": "48/25",
        "b": "26/25",
        "x": "990001/1000000",
        "y": "8877491/9000000",
        "food": "1",
        "residual": "345235339883/56250000000000"
      },
      {
        "edge": 2,
        "side": "target",
        "a": "48/25",
        "b": "26/25",
        "x": "989999/1000000",
        "y": "8877509/9000000",
        "food": "1",
        "residual": "43419340117/112500000000000"
      },
      {
        "edge": 2,
        "side": "source",
        "a": "52/25",
        "b": "24/25",
        "x": "990001/1000000",
        "y": "8877491/9000000",
        "food": "1",
        "residual": "64036039973/14062500000000"
      },
      {
        "edge": 2,
        "side": "target",
        "a": "52/25",
        "b": "24/25",
        "x": "989999/1000000",
        "y": "8877509/9000000",
        "food": "1",
        "residual": "41252540027/28125000000000"
      },
      {
        "edge": 2,
        "side": "source",
        "a": "52/25",
        "b": "26/25",
        "x": "990001/1000000",
        "y": "8877491/9000000",
        "food": "1",
        "residual": "312717339883/56250000000000"
      },
      {
        "edge": 2,
        "side": "target",
        "a": "52/25",
        "b": "26/25",
        "x": "989999/1000000",
        "y": "8877509/9000000",
        "food": "1",
        "residual": "36127780039/37500000000000"
      }
    ]
  },
  "food_window_open": [
    "14814/14825",
    "88859/88775"
  ],
  "instantaneous_loss_budget": {
    "production": {
      "A": "307/45000",
      "B": "1519/180000",
      "C": "637/72000"
    },
    "food_consumption": "2893/120000",
    "strict_dilution_upper": "307/44550",
    "scope": "Only the instantaneous field P_s-(D+d_s)*x_s at this prepared state. No persistence, invariant-region or steady-state conclusion."
  },
  "nongraded_four_five_explicit": {
    "status": "SAT",
    "activities": {
      "A": "9999/10000",
      "u1": "499917/500000",
      "u2": "249931/250000",
      "u3": "999541/1000000",
      "Z": "249809/250000",
      "v1": "9998499/10000000",
      "v2": "4998873/5000000",
      "v3": "9996617/10000000",
      "v4": "2498731/2500000"
    },
    "deficits": {
      "A": "1",
      "u1": "83/50",
      "u2": "69/25",
      "u3": "459/100",
      "Z": "191/25",
      "v1": "1501/1000",
      "v2": "1127/500",
      "v3": "3383/1000",
      "v4": "1269/250"
    },
    "epsilon": "1/10000",
    "minimum_residual": "21/100000000"
  },
  "nongraded_four_five_linear_program": {
    "status": "SAT",
    "activities": {
      "A": "17098586149/17101771682",
      "u1": "34192958417/34203543364",
      "u2": "17092967641/17101771682",
      "u3": "369567/369884",
      "Z": "51232082023/51305315046",
      "v1": "51290929903/51305315046",
      "v2": "51283687087/51305315046",
      "v3": "51272822863/51305315046",
      "v4": "51256526527/51305315046"
    },
    "deficits": {
      "A": "30147/903290",
      "u1": "100173/1806580",
      "u2": "83319/903290",
      "u3": "277413/1806580",
      "Z": "231019/903290",
      "v1": "45379/903290",
      "v2": "68227/903290",
      "v3": "102499/903290",
      "v4": "153907/903290"
    },
    "epsilon": "143171465/25652657523",
    "minimum_residual": "100489/68407086728",
    "linear_margin": "317/1806580"
  },
  "scope": "Static common-activity compatibility and fixed-state tolerances. No claim of global dynamics, automatic decomposition, or Z3 complexity bound; Lean not rerun."
}