{
  "status": "PASS exact rational outward-rounded enclosure; not Lean",
  "bits": 100,
  "t": {
    "lower": "620773913352840272667917871074087/649037107316853453566312041152512",
    "upper": "2483095653411361090671671484296349/2596148429267413814265248164610048"
  },
  "omega": {
    "lower": "1000243249191158591026197561/9903520314283042199192993792",
    "upper": "500121624595579295513098781/4951760157141521099596496896"
  },
  "l1_q4_equal_one": {
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    "upper": "-4452492920187474771918547733137511/1267650600228229401496703205376"
  },
  "q_norm_squared": {
    "lower": "99387345143695994816299950801841237/633825300114114700748351602688",
    "upper": "198774690287391989632599901616613509/1267650600228229401496703205376"
  },
  "l1_unit_norm": {
    "lower": "-28394989898498152149303450903/1267650600228229401496703205376",
    "upper": "-28394989898498152148662113303/1267650600228229401496703205376"
  },
  "checked_pivots": [
    {
      "dimension": 3,
      "column": 0,
      "real": {
        "lower": "-1",
        "upper": "-1"
      },
      "imaginary": {
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        "upper": "-1000243249191158591026197561/9903520314283042199192993792"
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      "modulus_squared_lower": "640290792954172009313064207649/633825300114114700748351602688"
    },
    {
      "dimension": 3,
      "column": 1,
      "real": {
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      "modulus_squared_lower": "5260987380393821324751027609/316912650057057350374175801344"
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    {
      "dimension": 3,
      "column": 2,
      "real": {
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      "imaginary": {
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        "upper": "-66483526672056990286883410579/633825300114114700748351602688"
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      "modulus_squared_lower": "1277376589584543837950572594517/316912650057057350374175801344"
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      "column": 0,
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      "imaginary": {
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        "upper": "-1000243249191158591026197561/9903520314283042199192993792"
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      "modulus_squared_lower": "640290792954172009313064207649/633825300114114700748351602688"
    },
    {
      "dimension": 3,
      "column": 1,
      "real": {
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      "imaginary": {
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        "upper": "-1000243249191158591026197561/9903520314283042199192993792"
      },
      "modulus_squared_lower": "5260987380393821324751027609/316912650057057350374175801344"
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    {
      "dimension": 3,
      "column": 2,
      "real": {
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      "imaginary": {
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      "modulus_squared_lower": "1277376589584543837950572594517/316912650057057350374175801344"
    },
    {
      "dimension": 4,
      "column": 0,
      "real": {
        "lower": "-1",
        "upper": "-1"
      },
      "imaginary": {
        "lower": "0",
        "upper": "0"
      },
      "modulus_squared_lower": "1"
    },
    {
      "dimension": 4,
      "column": 1,
      "real": {
        "lower": "-101412048018258352119736256431/1267650600228229401496703205376",
        "upper": "-50706024009129176059868128215/633825300114114700748351602688"
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      "imaginary": {
        "lower": "0",
        "upper": "0"
      },
      "modulus_squared_lower": "4056481920730334084789450257/633825300114114700748351602688"
    },
    {
      "dimension": 4,
      "column": 2,
      "real": {
        "lower": "14208387299030462783842114358625/79228162514264337593543950336",
        "upper": "56833549196121851135368457434875/316912650057057350374175801344"
      },
      "imaginary": {
        "lower": "0",
        "upper": "0"
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      "modulus_squared_lower": "40768991880210020620904218917989865/1267650600228229401496703205376"
    },
    {
      "dimension": 4,
      "column": 3,
      "real": {
        "lower": "-20282409603651670423947252169/1267650600228229401496703205376",
        "upper": "-20282409603651670423947251035/1267650600228229401496703205376"
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      "imaginary": {
        "lower": "0",
        "upper": "0"
      },
      "modulus_squared_lower": "81129638414606681695789003/316912650057057350374175801344"
    },
    {
      "dimension": 4,
      "column": 0,
      "real": {
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      },
      "imaginary": {
        "lower": "1000243249191158591026197561/4951760157141521099596496896",
        "upper": "500121624595579295513098781/2475880078570760549798248448"
      },
      "modulus_squared_lower": "1319374542948687870014404045065/1267650600228229401496703205376"
    },
    {
      "dimension": 4,
      "column": 1,
      "real": {
        "lower": "50706024009129176059868128215/633825300114114700748351602688",
        "upper": "101412048018258352119736256431/1267650600228229401496703205376"
      },
      "imaginary": {
        "lower": "1000243249191158591026197561/4951760157141521099596496896",
        "upper": "500121624595579295513098781/2475880078570760549798248448"
      },
      "modulus_squared_lower": "59836906561919136687279740203/1267650600228229401496703205376"
    },
    {
      "dimension": 4,
      "column": 2,
      "real": {
        "lower": "-56833549196121851135368457434875/316912650057057350374175801344",
        "upper": "-14208387299030462783842114358625/79228162514264337593543950336"
      },
      "imaginary": {
        "lower": "0",
        "upper": "0"
      },
      "modulus_squared_lower": "40768991880210020620904218917989865/1267650600228229401496703205376"
    },
    {
      "dimension": 4,
      "column": 3,
      "real": {
        "lower": "-41777238221865851367294216651/1267650600228229401496703205376",
        "upper": "-41777238221865851367294210915/1267650600228229401496703205376"
      },
      "imaginary": {
        "lower": "7383225713299475301205761063/633825300114114700748351602688",
        "upper": "1845806428324868825301442155/158456325028528675187087900672"
      },
      "modulus_squared_lower": "774419118654282482107841815/633825300114114700748351602688"
    }
  ],
  "binding": "Jets are constructed from the supplied literal S,Y,flux. The exact quartic crossing identity implies det(A-i*omega I)=0; checked leading-block pivots make its Schur complement zero, completing the omitted eigenvector equations. Checked pairing and resolvents justify each division.",
  "scope": "Together with the exact crossing and conventional nondegenerate Hopf theorem this certifies supercritical local attraction. No explicit decimal orbit or size of its parameter neighborhood is validated."
}