{
  "inputs": {
    "a1, b1": {
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        0,
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      "rank9": true,
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      "rank9": true,
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      "rank9": true,
      "scaled_determinant": "[-1.874029873154807011480186485211321910636008664826669745668607427970190254126812935787313124943e-46, -1.8740298731548060777066613415695040550028371244091814496962111322315796870586695828761100479994e-46]",
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    "a2, b2": {
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      "scaled_determinant": "[1.5196265238696106005228242425586443144320111880630938153879186333425176055149165989982895119003e-47, 1.5196265238696149647115273889722326872995263803387589030106952018054461952683639369040231064624e-47]",
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      "rank9": true,
      "scaled_determinant": "[8.8512777050179203125678045864695728431070411369260000542934086261390340929288308990800267037623e-52, 8.8512777050212928173981539118934001269686716942470815913325802099028571488491523394022585698539e-52]",
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    "alpha2, beta2": {
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      "scaled_determinant": "[-8.4685093495898844880437408721896258395814118712170552742840155223477838694899394269788655482577e-51, -8.4685093495898364026989548916911257384002242100028763221679302384188096254277026775008745007555e-51]",
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      "pivots": 9
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    "a3, b3": {
      "direction": [
        0,
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        1,
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        0
      ],
      "rank9": true,
      "scaled_determinant": "[8.0610461348465087207749584934705909972404675902464223110830481160408731612912792117011198544034e-46, 8.0610461348465133771736081229002293163693792938912965743301827878354451020278981607231276875883e-46]",
      "pivots": 9
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    "c3": {
      "direction": [
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        1,
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        -1,
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        0
      ],
      "rank9": true,
      "scaled_determinant": "[1.6196491560092325518074817767465556985555204454189361980847237683228946811682475333917463694957e-44, 1.6196491560092332148786994867827568239089428781998568012744666475340659049164689913496728508065e-44]",
      "pivots": 9
    },
    "alpha3, beta3": {
      "direction": [
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        1
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      "rank9": true,
      "scaled_determinant": "[-4.1696260198223918242687881399733411581515234231583715747033338991533555383865870387439905321619e-49, -4.1696260198223331342983437756604113274386242034911131554456123556942604804065039281598386239313e-49]",
      "pivots": 9
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    "gamma3": {
      "direction": [
        0,
        0,
        -1,
        0,
        0,
        0,
        0,
        0,
        -1
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      "rank9": true,
      "scaled_determinant": "[-4.33621433279436022871488852032030889240577458400628755144378424328923023412559979363535876417e-43, -4.3362143327943543792099697648461425676299054966884419263888207935110436964890091673529811094661e-43]",
      "pivots": 9
    }
  },
  "all_eighteen_rates": true,
  "alpha1_full_box": "[-1.8740313792411374217180956508612891913014554732872065727620907396087562542197329743114646791893e-46, -1.8740283670684756680348122454681762802640855455578506944123193258978830972621900332602574264496e-46]",
  "scope": "Fresh directed intervals over the freshly certified generalized-Hopf root box; rank is not a conditioning or finite-witness switching certificate."
}