{
  "proof_locators": [
    "CX.67",
    "CX.68",
    "CX.G--CX.M"
  ],
  "coordinates": "z=0, w=t real; full ambient space is C^2",
  "phi_plus": "|z|^2+|w|^2+(1/2)Re(w)",
  "phi_minus": "|z|^2+|w|^2-(1/2)Re(w)",
  "each_smoothing_radius": "1/5",
  "exact_deletion_threshold": "2/5",
  "exact_lower_envelope": "t^2+|t|/2",
  "exact_upper_envelope": "t^2+|t|/2+1/5",
  "levi_lower_bound": "identity matrix",
  "quadrature": "64-point Gauss-Legendre in each variable, even smooth bump reweighted and normalized",
  "sample_count": 401,
  "samples": [
    {
      "t": -1.0,
      "quadrature_value": 1.5,
      "exact_lower": 1.5
    },
    {
      "t": -0.995,
      "quadrature_value": 1.487525,
      "exact_lower": 1.487525
    },
    {
      "t": -0.99,
      "quadrature_value": 1.4750999999999999,
      "exact_lower": 1.4750999999999999
    },
    {
      "t": -0.985,
      "quadrature_value": 1.462725,
      "exact_lower": 1.462725
    },
    {
      "t": -0.98,
      "quadrature_value": 1.4503999999999997,
      "exact_lower": 1.4504
    },
    {
      "t": -0.975,
      "quadrature_value": 1.4381249999999999,
      "exact_lower": 1.4381249999999999
    },
    {
      "t": -0.97,
      "quadrature_value": 1.4259,
      "exact_lower": 1.4259
    },
    {
      "t": -0.965,
      "quadrature_value": 1.413725,
      "exact_lower": 1.413725
    },
    {
      "t": -0.96,
      "quadrature_value": 1.4016,
      "exact_lower": 1.4016
    },
    {
      "t": -0.955,
      "quadrature_value": 1.389525,
      "exact_lower": 1.389525
    },
    {
      "t": -0.95,
      "quadrature_value": 1.3774999999999997,
      "exact_lower": 1.3775
    },
    {
      "t": -0.945,
      "quadrature_value": 1.3655249999999999,
      "exact_lower": 1.3655249999999999
    },
    {
      "t": -0.94,
      "quadrature_value": 1.3536,
      "exact_lower": 1.3536
    },
    {
      "t": -0.935,
      "quadrature_value": 1.3417250000000003,
      "exact_lower": 1.3417250000000003
    },
    {
      "t": -0.9299999999999999,
      "quadrature_value": 1.3298999999999996,
      "exact_lower": 1.3298999999999999
    },
    {
      "t": -0.925,
      "quadrature_value": 1.3181250000000004,
      "exact_lower": 1.3181250000000002
    },
    {
      "t": -0.92,
      "quadrature_value": 1.3064,
      "exact_lower": 1.3064
    },
    {
      "t": -0.915,
      "quadrature_value": 1.2947250000000001,
      "exact_lower": 1.2947250000000001
    },
    {
      "t": -0.91,
      "quadrature_value": 1.2831,
      "exact_lower": 1.2831000000000001
    },
    {
      "t": -0.905,
      "quadrature_value": 1.271525,
      "exact_lower": 1.271525
    },
    {
      "t": -0.9,
      "quadrature_value": 1.26,
      "exact_lower": 1.26
    },
    {
      "t": -0.895,
      "quadrature_value": 1.2485249999999999,
      "exact_lower": 1.2485249999999999
    },
    {
      "t": -0.89,
      "quadrature_value": 1.2371,
      "exact_lower": 1.2371
    },
    {
      "t": -0.885,
      "quadrature_value": 1.225725,
      "exact_lower": 1.2257250000000002
    },
    {
      "t": -0.88,
      "quadrature_value": 1.2143999999999997,
      "exact_lower": 1.2144
    },
    {
      "t": -0.875,
      "quadrature_value": 1.2031250000000002,
      "exact_lower": 1.203125
    },
    {
      "t": -0.87,
      "quadrature_value": 1.1919,
      "exact_lower": 1.1919
    },
    {
      "t": -0.865,
      "quadrature_value": 1.180725,
      "exact_lower": 1.180725
    },
    {
      "t": -0.86,
      "quadrature_value": 1.1696,
      "exact_lower": 1.1696
    },
    {
      "t": -0.855,
      "quadrature_value": 1.158525,
      "exact_lower": 1.158525
    },
    {
      "t": -0.85,
      "quadrature_value": 1.1475,
      "exact_lower": 1.1475
    },
    {
      "t": -0.845,
      "quadrature_value": 1.1365249999999998,
      "exact_lower": 1.1365249999999998
    },
    {
      "t": -0.84,
      "quadrature_value": 1.1256,
      "exact_lower": 1.1256
    },
    {
      "t": -0.835,
      "quadrature_value": 1.114725,
      "exact_lower": 1.114725
    },
    {
      "t": -0.83,
      "quadrature_value": 1.1038999999999999,
      "exact_lower": 1.1038999999999999
    },
    {
      "t": -0.825,
      "quadrature_value": 1.093125,
      "exact_lower": 1.093125
    },
    {
      "t": -0.8200000000000001,
      "quadrature_value": 1.0824000000000003,
      "exact_lower": 1.0824000000000003
    },
    {
      "t": -0.815,
      "quadrature_value": 1.0717249999999998,
      "exact_lower": 1.0717249999999998
    },
    {
      "t": -0.81,
      "quadrature_value": 1.0611000000000004,
      "exact_lower": 1.0611000000000002
    },
    {
      "t": -0.8049999999999999,
      "quadrature_value": 1.050525,
      "exact_lower": 1.050525
    },
    {
      "t": -0.8,
      "quadrature_value": 1.04,
      "exact_lower": 1.04
    },
    {
      "t": -0.7949999999999999,
      "quadrature_value": 1.0295249999999998,
      "exact_lower": 1.0295249999999998
    },
    {
      "t": -0.79,
      "quadrature_value": 1.0191000000000001,
      "exact_lower": 1.0191000000000001
    },
    {
      "t": -0.785,
      "quadrature_value": 1.008725,
      "exact_lower": 1.008725
    },
    {
      "t": -0.78,
      "quadrature_value": 0.9984,
      "exact_lower": 0.9984000000000001
    },
    {
      "t": -0.775,
      "quadrature_value": 0.9881250000000003,
      "exact_lower": 0.9881250000000001
    },
    {
      "t": -0.77,
      "quadrature_value": 0.9779,
      "exact_lower": 0.9779
    },
    {
      "t": -0.765,
      "quadrature_value": 0.967725,
      "exact_lower": 0.967725
    },
    {
      "t": -0.76,
      "quadrature_value": 0.9576,
      "exact_lower": 0.9576
    },
    {
      "t": -0.755,
      "quadrature_value": 0.947525,
      "exact_lower": 0.947525
    },
    {
      "t": -0.75,
      "quadrature_value": 0.9375,
      "exact_lower": 0.9375
    },
    {
      "t": -0.745,
      "quadrature_value": 0.9275249999999999,
      "exact_lower": 0.9275249999999999
    },
    {
      "t": -0.74,
      "quadrature_value": 0.9176,
      "exact_lower": 0.9176
    },
    {
      "t": -0.735,
      "quadrature_value": 0.907725,
      "exact_lower": 0.9077249999999999
    },
    {
      "t": -0.73,
      "quadrature_value": 0.8978999999999999,
      "exact_lower": 0.8978999999999999
    },
    {
      "t": -0.725,
      "quadrature_value": 0.888125,
      "exact_lower": 0.888125
    },
    {
      "t": -0.72,
      "quadrature_value": 0.8784,
      "exact_lower": 0.8784
    },
    {
      "t": -0.715,
      "quadrature_value": 0.868725,
      "exact_lower": 0.868725
    },
    {
      "t": -0.71,
      "quadrature_value": 0.8591,
      "exact_lower": 0.8591
    },
    {
      "t": -0.7050000000000001,
      "quadrature_value": 0.8495250000000001,
      "exact_lower": 0.8495250000000001
    },
    {
      "t": -0.7,
      "quadrature_value": 0.8399999999999999,
      "exact_lower": 0.8399999999999999
    },
    {
      "t": -0.6950000000000001,
      "quadrature_value": 0.8305250000000001,
      "exact_lower": 0.8305250000000002
    },
    {
      "t": -0.69,
      "quadrature_value": 0.8210999999999999,
      "exact_lower": 0.8210999999999999
    },
    {
      "t": -0.685,
      "quadrature_value": 0.811725,
      "exact_lower": 0.811725
    },
    {
      "t": -0.6799999999999999,
      "quadrature_value": 0.8023999999999998,
      "exact_lower": 0.8023999999999999
    },
    {
      "t": -0.675,
      "quadrature_value": 0.7931250000000002,
      "exact_lower": 0.7931250000000001
    },
    {
      "t": -0.6699999999999999,
      "quadrature_value": 0.7838999999999998,
      "exact_lower": 0.7838999999999998
    },
    {
      "t": -0.665,
      "quadrature_value": 0.7747250000000002,
      "exact_lower": 0.7747250000000001
    },
    {
      "t": -0.6599999999999999,
      "quadrature_value": 0.7655999999999998,
      "exact_lower": 0.7655999999999998
    },
    {
      "t": -0.655,
      "quadrature_value": 0.7565250000000001,
      "exact_lower": 0.7565250000000001
    },
    {
      "t": -0.6499999999999999,
      "quadrature_value": 0.7474999999999998,
      "exact_lower": 0.7474999999999998
    },
    {
      "t": -0.645,
      "quadrature_value": 0.7385250000000001,
      "exact_lower": 0.7385250000000001
    },
    {
      "t": -0.64,
      "quadrature_value": 0.7296,
      "exact_lower": 0.7296
    },
    {
      "t": -0.635,
      "quadrature_value": 0.7207250000000001,
      "exact_lower": 0.7207250000000001
    },
    {
      "t": -0.63,
      "quadrature_value": 0.7118999999999999,
      "exact_lower": 0.7119
    },
    {
      "t": -0.625,
      "quadrature_value": 0.703125,
      "exact_lower": 0.703125
    },
    {
      "t": -0.62,
      "quadrature_value": 0.6943999999999999,
      "exact_lower": 0.6944
    },
    {
      "t": -0.615,
      "quadrature_value": 0.6857249999999999,
      "exact_lower": 0.6857249999999999
    },
    {
      "t": -0.61,
      "quadrature_value": 0.6771,
      "exact_lower": 0.6771
    },
    {
      "t": -0.605,
      "quadrature_value": 0.668525,
      "exact_lower": 0.668525
    },
    {
      "t": -0.6,
      "quadrature_value": 0.6599999999999999,
      "exact_lower": 0.6599999999999999
    },
    {
      "t": -0.595,
      "quadrature_value": 0.6515249999999999,
      "exact_lower": 0.6515249999999999
    },
    {
      "t": -0.59,
      "quadrature_value": 0.6431,
      "exact_lower": 0.6431
    },
    {
      "t": -0.585,
      "quadrature_value": 0.6347249999999999,
      "exact_lower": 0.634725
    },
    {
      "t": -0.5800000000000001,
      "quadrature_value": 0.6264000000000001,
      "exact_lower": 0.6264000000000001
    },
    {
      "t": -0.575,
      "quadrature_value": 0.6181249999999999,
      "exact_lower": 0.6181249999999999
    },
    {
      "t": -0.5700000000000001,
      "quadrature_value": 0.6099000000000001,
      "exact_lower": 0.6099000000000001
    },
    {
      "t": -0.565,
      "quadrature_value": 0.6017249999999998,
      "exact_lower": 0.6017249999999998
    },
    {
      "t": -0.56,
      "quadrature_value": 0.5936000000000001,
      "exact_lower": 0.5936000000000001
    },
    {
      "t": -0.5549999999999999,
      "quadrature_value": 0.5855249999999999,
      "exact_lower": 0.5855249999999999
    },
    {
      "t": -0.55,
      "quadrature_value": 0.5775000000000001,
      "exact_lower": 0.5775000000000001
    },
    {
      "t": -0.5449999999999999,
      "quadrature_value": 0.5695249999999998,
      "exact_lower": 0.5695249999999998
    },
    {
      "t": -0.54,
      "quadrature_value": 0.5616000000000001,
      "exact_lower": 0.5616000000000001
    },
    {
      "t": -0.5349999999999999,
      "quadrature_value": 0.5537249999999999,
      "exact_lower": 0.5537249999999998
    },
    {
      "t": -0.53,
      "quadrature_value": 0.5459,
      "exact_lower": 0.5459
    },
    {
      "t": -0.5249999999999999,
      "quadrature_value": 0.5381249999999999,
      "exact_lower": 0.5381249999999999
    },
    {
      "t": -0.52,
      "quadrature_value": 0.5303999999999999,
      "exact_lower": 0.5304
    },
    {
      "t": -0.515,
      "quadrature_value": 0.522725,
      "exact_lower": 0.522725
    },
    {
      "t": -0.51,
      "quadrature_value": 0.5150999999999999,
      "exact_lower": 0.5151
    },
    {
      "t": -0.505,
      "quadrature_value": 0.507525,
      "exact_lower": 0.507525
    },
    {
      "t": -0.5,
      "quadrature_value": 0.5,
      "exact_lower": 0.5
    },
    {
      "t": -0.495,
      "quadrature_value": 0.49252499999999994,
      "exact_lower": 0.492525
    },
    {
      "t": -0.49,
      "quadrature_value": 0.4851,
      "exact_lower": 0.4851
    },
    {
      "t": -0.485,
      "quadrature_value": 0.477725,
      "exact_lower": 0.47772499999999996
    },
    {
      "t": -0.48,
      "quadrature_value": 0.47039999999999993,
      "exact_lower": 0.4704
    },
    {
      "t": -0.475,
      "quadrature_value": 0.46312500000000006,
      "exact_lower": 0.463125
    },
    {
      "t": -0.47,
      "quadrature_value": 0.45589999999999997,
      "exact_lower": 0.45589999999999997
    },
    {
      "t": -0.46499999999999997,
      "quadrature_value": 0.4487249999999999,
      "exact_lower": 0.44872499999999993
    },
    {
      "t": -0.45999999999999996,
      "quadrature_value": 0.4415999999999999,
      "exact_lower": 0.44159999999999994
    },
    {
      "t": -0.45499999999999996,
      "quadrature_value": 0.43452499999999994,
      "exact_lower": 0.43452499999999994
    },
    {
      "t": -0.44999999999999996,
      "quadrature_value": 0.42749999999999994,
      "exact_lower": 0.42749999999999994
    },
    {
      "t": -0.44499999999999995,
      "quadrature_value": 0.4205249999999999,
      "exact_lower": 0.4205249999999999
    },
    {
      "t": -0.43999999999999995,
      "quadrature_value": 0.4136,
      "exact_lower": 0.41359999999999997
    },
    {
      "t": -0.43499999999999994,
      "quadrature_value": 0.4067249999999999,
      "exact_lower": 0.4067249999999999
    },
    {
      "t": -0.42999999999999994,
      "quadrature_value": 0.3998999999999999,
      "exact_lower": 0.3998999999999999
    },
    {
      "t": -0.42499999999999993,
      "quadrature_value": 0.39312499999999995,
      "exact_lower": 0.39312499999999995
    },
    {
      "t": -0.42000000000000004,
      "quadrature_value": 0.38640000000000013,
      "exact_lower": 0.3864000000000001
    },
    {
      "t": -0.41500000000000004,
      "quadrature_value": 0.37972500000000003,
      "exact_lower": 0.37972500000000003
    },
    {
      "t": -0.41000000000000003,
      "quadrature_value": 0.3731,
      "exact_lower": 0.37310000000000004
    },
    {
      "t": -0.405,
      "quadrature_value": 0.366525,
      "exact_lower": 0.36652500000000005
    },
    {
      "t": -0.4,
      "quadrature_value": 0.36,
      "exact_lower": 0.36000000000000004
    },
    {
      "t": -0.395,
      "quadrature_value": 0.35352500000000003,
      "exact_lower": 0.35352500000000003
    },
    {
      "t": -0.39,
      "quadrature_value": 0.3471000000000001,
      "exact_lower": 0.3471
    },
    {
      "t": -0.385,
      "quadrature_value": 0.340725,
      "exact_lower": 0.340725
    },
    {
      "t": -0.38,
      "quadrature_value": 0.3344000000000005,
      "exact_lower": 0.33440000000000003
    },
    {
      "t": -0.375,
      "quadrature_value": 0.32812500000005795,
      "exact_lower": 0.328125
    },
    {
      "t": -0.37,
      "quadrature_value": 0.3219000000029005,
      "exact_lower": 0.32189999999999996
    },
    {
      "t": -0.365,
      "quadrature_value": 0.31572500003517234,
      "exact_lower": 0.315725
    },
    {
      "t": -0.36,
      "quadrature_value": 0.30960000025305445,
      "exact_lower": 0.3096
    },
    {
      "t": -0.355,
      "quadrature_value": 0.3035250015142511,
      "exact_lower": 0.303525
    },
    {
      "t": -0.35,
      "quadrature_value": 0.29750000629704354,
      "exact_lower": 0.2975
    },
    {
      "t": -0.345,
      "quadrature_value": 0.29152502069202135,
      "exact_lower": 0.291525
    },
    {
      "t": -0.33999999999999997,
      "quadrature_value": 0.2856000572278141,
      "exact_lower": 0.28559999999999997
    },
    {
      "t": -0.33499999999999996,
      "quadrature_value": 0.2797251380831913,
      "exact_lower": 0.27972499999999995
    },
    {
      "t": -0.32999999999999996,
      "quadrature_value": 0.27390029920599657,
      "exact_lower": 0.2738999999999999
    },
    {
      "t": -0.32499999999999996,
      "quadrature_value": 0.2681256018070103,
      "exact_lower": 0.26812499999999995
    },
    {
      "t": -0.31999999999999995,
      "quadrature_value": 0.2624011453333263,
      "exact_lower": 0.26239999999999997
    },
    {
      "t": -0.31499999999999995,
      "quadrature_value": 0.2567270454603264,
      "exact_lower": 0.2567249999999999
    },
    {
      "t": -0.30999999999999994,
      "quadrature_value": 0.2511034506521464,
      "exact_lower": 0.25109999999999993
    },
    {
      "t": -0.30499999999999994,
      "quadrature_value": 0.24553053559830168,
      "exact_lower": 0.24552499999999994
    },
    {
      "t": -0.29999999999999993,
      "quadrature_value": 0.2400085331157171,
      "exact_lower": 0.23999999999999994
    },
    {
      "t": -0.29500000000000004,
      "quadrature_value": 0.2345378546255076,
      "exact_lower": 0.23452500000000004
    },
    {
      "t": -0.29000000000000004,
      "quadrature_value": 0.2291189064572875,
      "exact_lower": 0.22910000000000003
    },
    {
      "t": -0.28500000000000003,
      "quadrature_value": 0.22375187793703116,
      "exact_lower": 0.22372500000000003
    },
    {
      "t": -0.28,
      "quadrature_value": 0.21843724727080138,
      "exact_lower": 0.21840000000000004
    },
    {
      "t": -0.275,
      "quadrature_value": 0.2131760117326133,
      "exact_lower": 0.213125
    },
    {
      "t": -0.27,
      "quadrature_value": 0.20796856042873801,
      "exact_lower": 0.20790000000000003
    },
    {
      "t": -0.265,
      "quadrature_value": 0.202815049237908,
      "exact_lower": 0.20272500000000002
    },
    {
      "t": -0.26,
      "quadrature_value": 0.19771700700803926,
      "exact_lower": 0.1976
    },
    {
      "t": -0.255,
      "quadrature_value": 0.19267546365164628,
      "exact_lower": 0.192525
    },
    {
      "t": -0.25,
      "quadrature_value": 0.18769004806617579,
      "exact_lower": 0.1875
    },
    {
      "t": -0.245,
      "quadrature_value": 0.18276293746039102,
      "exact_lower": 0.182525
    },
    {
      "t": -0.24,
      "quadrature_value": 0.17789535792144837,
      "exact_lower": 0.17759999999999998
    },
    {
      "t": -0.235,
      "quadrature_value": 0.17308664027524656,
      "exact_lower": 0.172725
    },
    {
      "t": -0.22999999999999998,
      "quadrature_value": 0.16834062166741695,
      "exact_lower": 0.1679
    },
    {
      "t": -0.22499999999999998,
      "quadrature_value": 0.1636567768427167,
      "exact_lower": 0.16312499999999996
    },
    {
      "t": -0.21999999999999997,
      "quadrature_value": 0.15903540583388776,
      "exact_lower": 0.15839999999999999
    },
    {
      "t": -0.21499999999999997,
      "quadrature_value": 0.1544821947653936,
      "exact_lower": 0.15372499999999997
    },
    {
      "t": -0.20999999999999996,
      "quadrature_value": 0.1499932491219554,
      "exact_lower": 0.14909999999999995
    },
    {
      "t": -0.20499999999999996,
      "quadrature_value": 0.1455737150298684,
      "exact_lower": 0.14452499999999996
    },
    {
      "t": -0.19999999999999996,
      "quadrature_value": 0.1412246395603981,
      "exact_lower": 0.13999999999999996
    },
    {
      "t": -0.19499999999999995,
      "quadrature_value": 0.1369441103658055,
      "exact_lower": 0.13552499999999995
    },
    {
      "t": -0.18999999999999995,
      "quadrature_value": 0.13274123529880288,
      "exact_lower": 0.13109999999999994
    },
    {
      "t": -0.18499999999999994,
      "quadrature_value": 0.12860927197376254,
      "exact_lower": 0.12672499999999995
    },
    {
      "t": -0.17999999999999994,
      "quadrature_value": 0.12455674102051256,
      "exact_lower": 0.12239999999999995
    },
    {
      "t": -0.17499999999999993,
      "quadrature_value": 0.12058123014439373,
      "exact_lower": 0.11812499999999994
    },
    {
      "t": -0.16999999999999993,
      "quadrature_value": 0.11668470041022568,
      "exact_lower": 0.11389999999999995
    },
    {
      "t": -0.16500000000000004,
      "quadrature_value": 0.11287461651636421,
      "exact_lower": 0.10972500000000003
    },
    {
      "t": -0.16000000000000003,
      "quadrature_value": 0.10914226295376646,
      "exact_lower": 0.10560000000000003
    },
    {
      "t": -0.15500000000000003,
      "quadrature_value": 0.1055038101027347,
      "exact_lower": 0.10152500000000002
    },
    {
      "t": -0.15000000000000002,
      "quadrature_value": 0.10194575671356117,
      "exact_lower": 0.09750000000000002
    },
    {
      "t": -0.14500000000000002,
      "quadrature_value": 0.09848423825490911,
      "exact_lower": 0.09352500000000001
    },
    {
      "t": -0.14,
      "quadrature_value": 0.09510959333160934,
      "exact_lower": 0.08960000000000001
    },
    {
      "t": -0.135,
      "quadrature_value": 0.09183176841925872,
      "exact_lower": 0.08572500000000001
    },
    {
      "t": -0.13,
      "quadrature_value": 0.08864973148074487,
      "exact_lower": 0.0819
    },
    {
      "t": -0.125,
      "quadrature_value": 0.0855624939793206,
      "exact_lower": 0.078125
    },
    {
      "t": -0.12,
      "quadrature_value": 0.08258184646149018,
      "exact_lower": 0.0744
    },
    {
      "t": -0.11499999999999999,
      "quadrature_value": 0.07969336818118186,
      "exact_lower": 0.070725
    },
    {
      "t": -0.10999999999999999,
      "quadrature_value": 0.07692209780061579,
      "exact_lower": 0.06709999999999999
    },
    {
      "t": -0.10499999999999998,
      "quadrature_value": 0.07424291801021461,
      "exact_lower": 0.06352499999999998
    },
    {
      "t": -0.09999999999999998,
      "quadrature_value": 0.07168675924315684,
      "exact_lower": 0.059999999999999984
    },
    {
      "t": -0.09499999999999997,
      "quadrature_value": 0.0692253931804363,
      "exact_lower": 0.05652499999999998
    },
    {
      "t": -0.08999999999999997,
      "quadrature_value": 0.06689137674963236,
      "exact_lower": 0.05309999999999998
    },
    {
      "t": -0.08499999999999996,
      "quadrature_value": 0.06465649207588568,
      "exact_lower": 0.04972499999999998
    },
    {
      "t": -0.07999999999999996,
      "quadrature_value": 0.06255132114471586,
      "exact_lower": 0.046399999999999976
    },
    {
      "t": -0.07499999999999996,
      "quadrature_value": 0.060550493350188105,
      "exact_lower": 0.04312499999999997
    },
    {
      "t": -0.06999999999999995,
      "quadrature_value": 0.05868081391450092,
      "exact_lower": 0.03989999999999997
    },
    {
      "t": -0.06499999999999995,
      "quadrature_value": 0.05692176320439493,
      "exact_lower": 0.036724999999999966
    },
    {
      "t": -0.05999999999999994,
      "quadrature_value": 0.05529386354285785,
      "exact_lower": 0.03359999999999996
    },
    {
      "t": -0.05499999999999994,
      "quadrature_value": 0.05378398508197722,
      "exact_lower": 0.030524999999999962
    },
    {
      "t": -0.04999999999999993,
      "quadrature_value": 0.05240342747440204,
      "exact_lower": 0.027499999999999962
    },
    {
      "t": -0.04499999999999993,
      "quadrature_value": 0.05114861269277919,
      "exact_lower": 0.024524999999999957
    },
    {
      "t": -0.040000000000000036,
      "quadrature_value": 0.05002039281779313,
      "exact_lower": 0.021600000000000022
    },
    {
      "t": -0.03500000000000003,
      "quadrature_value": 0.04902698430367811,
      "exact_lower": 0.01872500000000002
    },
    {
      "t": -0.030000000000000027,
      "quadrature_value": 0.048154645853009194,
      "exact_lower": 0.015900000000000015
    },
    {
      "t": -0.025000000000000022,
      "quadrature_value": 0.047428058554076925,
      "exact_lower": 0.013125000000000012
    },
    {
      "t": -0.020000000000000018,
      "quadrature_value": 0.046813745047985224,
      "exact_lower": 0.01040000000000001
    },
    {
      "t": -0.015000000000000013,
      "quadrature_value": 0.046359486945110454,
      "exact_lower": 0.007725000000000007
    },
    {
      "t": -0.010000000000000009,
      "quadrature_value": 0.04600258902114773,
      "exact_lower": 0.005100000000000005
    },
    {
      "t": -0.0050000000000000044,
      "quadrature_value": 0.0458256642181108,
      "exact_lower": 0.002525000000000002
    },
    {
      "t": 0.0,
      "quadrature_value": 0.04572356521847359,
      "exact_lower": 0.0
    },
    {
      "t": 0.0050000000000001155,
      "quadrature_value": 0.045825664218110795,
      "exact_lower": 0.002525000000000059
    },
    {
      "t": 0.010000000000000009,
      "quadrature_value": 0.04600258902114773,
      "exact_lower": 0.005100000000000005
    },
    {
      "t": 0.015000000000000124,
      "quadrature_value": 0.046359486945110454,
      "exact_lower": 0.007725000000000066
    },
    {
      "t": 0.020000000000000018,
      "quadrature_value": 0.04681374504798524,
      "exact_lower": 0.01040000000000001
    },
    {
      "t": 0.02499999999999991,
      "quadrature_value": 0.04742805855407691,
      "exact_lower": 0.013124999999999951
    },
    {
      "t": 0.030000000000000027,
      "quadrature_value": 0.048154645853009194,
      "exact_lower": 0.015900000000000015
    },
    {
      "t": 0.03499999999999992,
      "quadrature_value": 0.04902698430367809,
      "exact_lower": 0.018724999999999953
    },
    {
      "t": 0.040000000000000036,
      "quadrature_value": 0.05002039281779313,
      "exact_lower": 0.021600000000000022
    },
    {
      "t": 0.04499999999999993,
      "quadrature_value": 0.051148612692779184,
      "exact_lower": 0.024524999999999957
    },
    {
      "t": 0.050000000000000044,
      "quadrature_value": 0.05240342747440207,
      "exact_lower": 0.027500000000000028
    },
    {
      "t": 0.05499999999999994,
      "quadrature_value": 0.05378398508197722,
      "exact_lower": 0.030524999999999962
    },
    {
      "t": 0.06000000000000005,
      "quadrature_value": 0.05529386354285789,
      "exact_lower": 0.03360000000000003
    },
    {
      "t": 0.06499999999999995,
      "quadrature_value": 0.05692176320439493,
      "exact_lower": 0.036724999999999966
    },
    {
      "t": 0.07000000000000006,
      "quadrature_value": 0.058680813914500966,
      "exact_lower": 0.03990000000000004
    },
    {
      "t": 0.07499999999999996,
      "quadrature_value": 0.0605504933501881,
      "exact_lower": 0.04312499999999997
    },
    {
      "t": 0.08000000000000007,
      "quadrature_value": 0.0625513211447159,
      "exact_lower": 0.046400000000000045
    },
    {
      "t": 0.08499999999999996,
      "quadrature_value": 0.06465649207588568,
      "exact_lower": 0.04972499999999998
    },
    {
      "t": 0.09000000000000008,
      "quadrature_value": 0.0668913767496324,
      "exact_lower": 0.05310000000000006
    },
    {
      "t": 0.09499999999999997,
      "quadrature_value": 0.0692253931804363,
      "exact_lower": 0.05652499999999998
    },
    {
      "t": 0.10000000000000009,
      "quadrature_value": 0.0716867592431569,
      "exact_lower": 0.06000000000000006
    },
    {
      "t": 0.10499999999999998,
      "quadrature_value": 0.07424291801021463,
      "exact_lower": 0.06352499999999998
    },
    {
      "t": 0.1100000000000001,
      "quadrature_value": 0.07692209780061586,
      "exact_lower": 0.06710000000000008
    },
    {
      "t": 0.11499999999999999,
      "quadrature_value": 0.07969336818118188,
      "exact_lower": 0.070725
    },
    {
      "t": 0.1200000000000001,
      "quadrature_value": 0.08258184646149025,
      "exact_lower": 0.07440000000000008
    },
    {
      "t": 0.125,
      "quadrature_value": 0.0855624939793206,
      "exact_lower": 0.078125
    },
    {
      "t": 0.13000000000000012,
      "quadrature_value": 0.08864973148074495,
      "exact_lower": 0.08190000000000008
    },
    {
      "t": 0.135,
      "quadrature_value": 0.09183176841925872,
      "exact_lower": 0.08572500000000001
    },
    {
      "t": 0.14000000000000012,
      "quadrature_value": 0.09510959333160943,
      "exact_lower": 0.0896000000000001
    },
    {
      "t": 0.14500000000000002,
      "quadrature_value": 0.09848423825490911,
      "exact_lower": 0.09352500000000001
    },
    {
      "t": 0.15000000000000013,
      "quadrature_value": 0.10194575671356125,
      "exact_lower": 0.09750000000000011
    },
    {
      "t": 0.15500000000000003,
      "quadrature_value": 0.1055038101027347,
      "exact_lower": 0.10152500000000002
    },
    {
      "t": 0.15999999999999992,
      "quadrature_value": 0.10914226295376636,
      "exact_lower": 0.10559999999999993
    },
    {
      "t": 0.16500000000000004,
      "quadrature_value": 0.1128746165163642,
      "exact_lower": 0.10972500000000003
    },
    {
      "t": 0.16999999999999993,
      "quadrature_value": 0.11668470041022569,
      "exact_lower": 0.11389999999999995
    },
    {
      "t": 0.17500000000000004,
      "quadrature_value": 0.12058123014439381,
      "exact_lower": 0.11812500000000004
    },
    {
      "t": 0.17999999999999994,
      "quadrature_value": 0.12455674102051259,
      "exact_lower": 0.12239999999999995
    },
    {
      "t": 0.18500000000000005,
      "quadrature_value": 0.12860927197376265,
      "exact_lower": 0.12672500000000003
    },
    {
      "t": 0.18999999999999995,
      "quadrature_value": 0.13274123529880288,
      "exact_lower": 0.13109999999999994
    },
    {
      "t": 0.19500000000000006,
      "quadrature_value": 0.13694411036580562,
      "exact_lower": 0.13552500000000006
    },
    {
      "t": 0.19999999999999996,
      "quadrature_value": 0.1412246395603981,
      "exact_lower": 0.13999999999999996
    },
    {
      "t": 0.20500000000000007,
      "quadrature_value": 0.14557371502986852,
      "exact_lower": 0.14452500000000007
    },
    {
      "t": 0.20999999999999996,
      "quadrature_value": 0.14999324912195544,
      "exact_lower": 0.14909999999999995
    },
    {
      "t": 0.21500000000000008,
      "quadrature_value": 0.15448219476539374,
      "exact_lower": 0.15372500000000008
    },
    {
      "t": 0.21999999999999997,
      "quadrature_value": 0.15903540583388776,
      "exact_lower": 0.15839999999999999
    },
    {
      "t": 0.2250000000000001,
      "quadrature_value": 0.16365677684271682,
      "exact_lower": 0.16312500000000008
    },
    {
      "t": 0.22999999999999998,
      "quadrature_value": 0.16834062166741695,
      "exact_lower": 0.1679
    },
    {
      "t": 0.2350000000000001,
      "quadrature_value": 0.17308664027524664,
      "exact_lower": 0.1727250000000001
    },
    {
      "t": 0.24,
      "quadrature_value": 0.17789535792144834,
      "exact_lower": 0.17759999999999998
    },
    {
      "t": 0.2450000000000001,
      "quadrature_value": 0.18276293746039113,
      "exact_lower": 0.1825250000000001
    },
    {
      "t": 0.25,
      "quadrature_value": 0.18769004806617579,
      "exact_lower": 0.1875
    },
    {
      "t": 0.2550000000000001,
      "quadrature_value": 0.1926754636516464,
      "exact_lower": 0.1925250000000001
    },
    {
      "t": 0.26,
      "quadrature_value": 0.19771700700803926,
      "exact_lower": 0.1976
    },
    {
      "t": 0.2650000000000001,
      "quadrature_value": 0.2028150492379081,
      "exact_lower": 0.20272500000000013
    },
    {
      "t": 0.27,
      "quadrature_value": 0.20796856042873801,
      "exact_lower": 0.20790000000000003
    },
    {
      "t": 0.27500000000000013,
      "quadrature_value": 0.21317601173261344,
      "exact_lower": 0.21312500000000012
    },
    {
      "t": 0.28,
      "quadrature_value": 0.21843724727080138,
      "exact_lower": 0.21840000000000004
    },
    {
      "t": 0.2849999999999999,
      "quadrature_value": 0.223751877937031,
      "exact_lower": 0.2237249999999999
    },
    {
      "t": 0.29000000000000004,
      "quadrature_value": 0.2291189064572875,
      "exact_lower": 0.22910000000000003
    },
    {
      "t": 0.29499999999999993,
      "quadrature_value": 0.2345378546255075,
      "exact_lower": 0.23452499999999993
    },
    {
      "t": 0.30000000000000004,
      "quadrature_value": 0.24000853311571724,
      "exact_lower": 0.24000000000000005
    },
    {
      "t": 0.30499999999999994,
      "quadrature_value": 0.24553053559830162,
      "exact_lower": 0.24552499999999994
    },
    {
      "t": 0.31000000000000005,
      "quadrature_value": 0.25110345065214656,
      "exact_lower": 0.25110000000000005
    },
    {
      "t": 0.31499999999999995,
      "quadrature_value": 0.2567270454603264,
      "exact_lower": 0.2567249999999999
    },
    {
      "t": 0.32000000000000006,
      "quadrature_value": 0.2624011453333264,
      "exact_lower": 0.2624000000000001
    },
    {
      "t": 0.32499999999999996,
      "quadrature_value": 0.2681256018070102,
      "exact_lower": 0.26812499999999995
    },
    {
      "t": 0.33000000000000007,
      "quadrature_value": 0.27390029920599673,
      "exact_lower": 0.2739000000000001
    },
    {
      "t": 0.33499999999999996,
      "quadrature_value": 0.2797251380831913,
      "exact_lower": 0.27972499999999995
    },
    {
      "t": 0.3400000000000001,
      "quadrature_value": 0.28560005722781423,
      "exact_lower": 0.2856000000000001
    },
    {
      "t": 0.345,
      "quadrature_value": 0.2915250206920213,
      "exact_lower": 0.291525
    },
    {
      "t": 0.3500000000000001,
      "quadrature_value": 0.29750000629704365,
      "exact_lower": 0.2975000000000001
    },
    {
      "t": 0.355,
      "quadrature_value": 0.3035250015142511,
      "exact_lower": 0.303525
    },
    {
      "t": 0.3600000000000001,
      "quadrature_value": 0.30960000025305456,
      "exact_lower": 0.3096000000000001
    },
    {
      "t": 0.365,
      "quadrature_value": 0.31572500003517234,
      "exact_lower": 0.315725
    },
    {
      "t": 0.3700000000000001,
      "quadrature_value": 0.3219000000029006,
      "exact_lower": 0.32190000000000013
    },
    {
      "t": 0.375,
      "quadrature_value": 0.32812500000005795,
      "exact_lower": 0.328125
    },
    {
      "t": 0.3800000000000001,
      "quadrature_value": 0.33440000000000064,
      "exact_lower": 0.33440000000000014
    },
    {
      "t": 0.385,
      "quadrature_value": 0.34072499999999994,
      "exact_lower": 0.340725
    },
    {
      "t": 0.3900000000000001,
      "quadrature_value": 0.3471000000000002,
      "exact_lower": 0.3471000000000002
    },
    {
      "t": 0.395,
      "quadrature_value": 0.353525,
      "exact_lower": 0.35352500000000003
    },
    {
      "t": 0.40000000000000013,
      "quadrature_value": 0.3600000000000002,
      "exact_lower": 0.3600000000000002
    },
    {
      "t": 0.405,
      "quadrature_value": 0.36652500000000005,
      "exact_lower": 0.36652500000000005
    },
    {
      "t": 0.4099999999999999,
      "quadrature_value": 0.3730999999999999,
      "exact_lower": 0.3730999999999999
    },
    {
      "t": 0.41500000000000004,
      "quadrature_value": 0.37972500000000003,
      "exact_lower": 0.37972500000000003
    },
    {
      "t": 0.41999999999999993,
      "quadrature_value": 0.3863999999999999,
      "exact_lower": 0.3863999999999999
    },
    {
      "t": 0.42500000000000004,
      "quadrature_value": 0.393125,
      "exact_lower": 0.39312500000000006
    },
    {
      "t": 0.42999999999999994,
      "quadrature_value": 0.3998999999999999,
      "exact_lower": 0.3998999999999999
    },
    {
      "t": 0.43500000000000005,
      "quadrature_value": 0.40672500000000017,
      "exact_lower": 0.4067250000000001
    },
    {
      "t": 0.43999999999999995,
      "quadrature_value": 0.41359999999999997,
      "exact_lower": 0.41359999999999997
    },
    {
      "t": 0.44500000000000006,
      "quadrature_value": 0.4205250000000001,
      "exact_lower": 0.4205250000000001
    },
    {
      "t": 0.44999999999999996,
      "quadrature_value": 0.42749999999999994,
      "exact_lower": 0.42749999999999994
    },
    {
      "t": 0.45500000000000007,
      "quadrature_value": 0.4345250000000001,
      "exact_lower": 0.4345250000000001
    },
    {
      "t": 0.45999999999999996,
      "quadrature_value": 0.4416,
      "exact_lower": 0.44159999999999994
    },
    {
      "t": 0.4650000000000001,
      "quadrature_value": 0.44872500000000015,
      "exact_lower": 0.44872500000000015
    },
    {
      "t": 0.47,
      "quadrature_value": 0.45589999999999997,
      "exact_lower": 0.45589999999999997
    },
    {
      "t": 0.4750000000000001,
      "quadrature_value": 0.4631250000000001,
      "exact_lower": 0.4631250000000001
    },
    {
      "t": 0.48,
      "quadrature_value": 0.4704,
      "exact_lower": 0.4704
    },
    {
      "t": 0.4850000000000001,
      "quadrature_value": 0.47772500000000007,
      "exact_lower": 0.4777250000000002
    },
    {
      "t": 0.49,
      "quadrature_value": 0.4851,
      "exact_lower": 0.4851
    },
    {
      "t": 0.4950000000000001,
      "quadrature_value": 0.4925250000000002,
      "exact_lower": 0.49252500000000016
    },
    {
      "t": 0.5,
      "quadrature_value": 0.5,
      "exact_lower": 0.5
    },
    {
      "t": 0.5050000000000001,
      "quadrature_value": 0.5075250000000002,
      "exact_lower": 0.5075250000000002
    },
    {
      "t": 0.51,
      "quadrature_value": 0.5151,
      "exact_lower": 0.5151
    },
    {
      "t": 0.5150000000000001,
      "quadrature_value": 0.5227250000000003,
      "exact_lower": 0.5227250000000002
    },
    {
      "t": 0.52,
      "quadrature_value": 0.5304,
      "exact_lower": 0.5304
    },
    {
      "t": 0.5250000000000001,
      "quadrature_value": 0.5381250000000002,
      "exact_lower": 0.5381250000000002
    },
    {
      "t": 0.53,
      "quadrature_value": 0.5459,
      "exact_lower": 0.5459
    },
    {
      "t": 0.5350000000000001,
      "quadrature_value": 0.5537250000000002,
      "exact_lower": 0.5537250000000002
    },
    {
      "t": 0.54,
      "quadrature_value": 0.5616000000000001,
      "exact_lower": 0.5616000000000001
    },
    {
      "t": 0.5449999999999999,
      "quadrature_value": 0.5695249999999998,
      "exact_lower": 0.5695249999999998
    },
    {
      "t": 0.55,
      "quadrature_value": 0.5775000000000001,
      "exact_lower": 0.5775000000000001
    },
    {
      "t": 0.5549999999999999,
      "quadrature_value": 0.5855249999999999,
      "exact_lower": 0.5855249999999999
    },
    {
      "t": 0.56,
      "quadrature_value": 0.5936000000000001,
      "exact_lower": 0.5936000000000001
    },
    {
      "t": 0.565,
      "quadrature_value": 0.6017249999999998,
      "exact_lower": 0.6017249999999998
    },
    {
      "t": 0.5700000000000001,
      "quadrature_value": 0.6099000000000001,
      "exact_lower": 0.6099000000000001
    },
    {
      "t": 0.575,
      "quadrature_value": 0.6181249999999998,
      "exact_lower": 0.6181249999999999
    },
    {
      "t": 0.5800000000000001,
      "quadrature_value": 0.6264000000000001,
      "exact_lower": 0.6264000000000001
    },
    {
      "t": 0.585,
      "quadrature_value": 0.634725,
      "exact_lower": 0.634725
    },
    {
      "t": 0.5900000000000001,
      "quadrature_value": 0.6431,
      "exact_lower": 0.6431000000000001
    },
    {
      "t": 0.595,
      "quadrature_value": 0.6515249999999999,
      "exact_lower": 0.6515249999999999
    },
    {
      "t": 0.6000000000000001,
      "quadrature_value": 0.66,
      "exact_lower": 0.6600000000000001
    },
    {
      "t": 0.605,
      "quadrature_value": 0.668525,
      "exact_lower": 0.668525
    },
    {
      "t": 0.6100000000000001,
      "quadrature_value": 0.6771000000000001,
      "exact_lower": 0.6771000000000001
    },
    {
      "t": 0.615,
      "quadrature_value": 0.6857249999999999,
      "exact_lower": 0.6857249999999999
    },
    {
      "t": 0.6200000000000001,
      "quadrature_value": 0.6944000000000001,
      "exact_lower": 0.6944000000000001
    },
    {
      "t": 0.625,
      "quadrature_value": 0.703125,
      "exact_lower": 0.703125
    },
    {
      "t": 0.6300000000000001,
      "quadrature_value": 0.7119000000000002,
      "exact_lower": 0.7119000000000002
    },
    {
      "t": 0.635,
      "quadrature_value": 0.720725,
      "exact_lower": 0.7207250000000001
    },
    {
      "t": 0.6400000000000001,
      "quadrature_value": 0.7296000000000002,
      "exact_lower": 0.7296000000000002
    },
    {
      "t": 0.645,
      "quadrature_value": 0.7385250000000001,
      "exact_lower": 0.7385250000000001
    },
    {
      "t": 0.6500000000000001,
      "quadrature_value": 0.7475000000000003,
      "exact_lower": 0.7475000000000003
    },
    {
      "t": 0.655,
      "quadrature_value": 0.7565250000000001,
      "exact_lower": 0.7565250000000001
    },
    {
      "t": 0.6600000000000001,
      "quadrature_value": 0.7656000000000003,
      "exact_lower": 0.7656000000000003
    },
    {
      "t": 0.665,
      "quadrature_value": 0.7747250000000001,
      "exact_lower": 0.7747250000000001
    },
    {
      "t": 0.6699999999999999,
      "quadrature_value": 0.7838999999999998,
      "exact_lower": 0.7838999999999998
    },
    {
      "t": 0.675,
      "quadrature_value": 0.7931250000000001,
      "exact_lower": 0.7931250000000001
    },
    {
      "t": 0.6799999999999999,
      "quadrature_value": 0.8023999999999999,
      "exact_lower": 0.8023999999999999
    },
    {
      "t": 0.685,
      "quadrature_value": 0.811725,
      "exact_lower": 0.811725
    },
    {
      "t": 0.69,
      "quadrature_value": 0.8210999999999999,
      "exact_lower": 0.8210999999999999
    },
    {
      "t": 0.6950000000000001,
      "quadrature_value": 0.8305250000000002,
      "exact_lower": 0.8305250000000002
    },
    {
      "t": 0.7,
      "quadrature_value": 0.8399999999999999,
      "exact_lower": 0.8399999999999999
    },
    {
      "t": 0.7050000000000001,
      "quadrature_value": 0.8495250000000001,
      "exact_lower": 0.8495250000000001
    },
    {
      "t": 0.71,
      "quadrature_value": 0.8591,
      "exact_lower": 0.8591
    },
    {
      "t": 0.7150000000000001,
      "quadrature_value": 0.8687250000000002,
      "exact_lower": 0.8687250000000002
    },
    {
      "t": 0.72,
      "quadrature_value": 0.8784,
      "exact_lower": 0.8784
    },
    {
      "t": 0.7250000000000001,
      "quadrature_value": 0.888125,
      "exact_lower": 0.8881250000000002
    },
    {
      "t": 0.73,
      "quadrature_value": 0.8978999999999999,
      "exact_lower": 0.8978999999999999
    },
    {
      "t": 0.7350000000000001,
      "quadrature_value": 0.9077250000000001,
      "exact_lower": 0.9077250000000002
    },
    {
      "t": 0.74,
      "quadrature_value": 0.9176,
      "exact_lower": 0.9176
    },
    {
      "t": 0.7450000000000001,
      "quadrature_value": 0.9275250000000003,
      "exact_lower": 0.9275250000000003
    },
    {
      "t": 0.75,
      "quadrature_value": 0.9375,
      "exact_lower": 0.9375
    },
    {
      "t": 0.7550000000000001,
      "quadrature_value": 0.9475250000000002,
      "exact_lower": 0.9475250000000003
    },
    {
      "t": 0.76,
      "quadrature_value": 0.9576,
      "exact_lower": 0.9576
    },
    {
      "t": 0.7650000000000001,
      "quadrature_value": 0.9677250000000002,
      "exact_lower": 0.9677250000000003
    },
    {
      "t": 0.77,
      "quadrature_value": 0.9779,
      "exact_lower": 0.9779
    },
    {
      "t": 0.7750000000000001,
      "quadrature_value": 0.9881250000000001,
      "exact_lower": 0.9881250000000003
    },
    {
      "t": 0.78,
      "quadrature_value": 0.9984000000000001,
      "exact_lower": 0.9984000000000001
    },
    {
      "t": 0.7850000000000001,
      "quadrature_value": 1.0087250000000003,
      "exact_lower": 1.0087250000000003
    },
    {
      "t": 0.79,
      "quadrature_value": 1.0191000000000001,
      "exact_lower": 1.0191000000000001
    },
    {
      "t": 0.7949999999999999,
      "quadrature_value": 1.0295249999999998,
      "exact_lower": 1.0295249999999998
    },
    {
      "t": 0.8,
      "quadrature_value": 1.04,
      "exact_lower": 1.04
    },
    {
      "t": 0.8049999999999999,
      "quadrature_value": 1.050525,
      "exact_lower": 1.050525
    },
    {
      "t": 0.81,
      "quadrature_value": 1.0611000000000002,
      "exact_lower": 1.0611000000000002
    },
    {
      "t": 0.815,
      "quadrature_value": 1.0717249999999998,
      "exact_lower": 1.0717249999999998
    },
    {
      "t": 0.8200000000000001,
      "quadrature_value": 1.0824000000000003,
      "exact_lower": 1.0824000000000003
    },
    {
      "t": 0.825,
      "quadrature_value": 1.0931249999999997,
      "exact_lower": 1.093125
    },
    {
      "t": 0.8300000000000001,
      "quadrature_value": 1.1039,
      "exact_lower": 1.1039
    },
    {
      "t": 0.835,
      "quadrature_value": 1.114725,
      "exact_lower": 1.114725
    },
    {
      "t": 0.8400000000000001,
      "quadrature_value": 1.1256000000000002,
      "exact_lower": 1.1256000000000002
    },
    {
      "t": 0.845,
      "quadrature_value": 1.1365249999999998,
      "exact_lower": 1.1365249999999998
    },
    {
      "t": 0.8500000000000001,
      "quadrature_value": 1.1475000000000002,
      "exact_lower": 1.1475000000000002
    },
    {
      "t": 0.855,
      "quadrature_value": 1.1585249999999998,
      "exact_lower": 1.158525
    },
    {
      "t": 0.8600000000000001,
      "quadrature_value": 1.1696000000000002,
      "exact_lower": 1.1696000000000002
    },
    {
      "t": 0.865,
      "quadrature_value": 1.180725,
      "exact_lower": 1.180725
    },
    {
      "t": 0.8700000000000001,
      "quadrature_value": 1.1919000000000004,
      "exact_lower": 1.1919000000000004
    },
    {
      "t": 0.875,
      "quadrature_value": 1.2031249999999998,
      "exact_lower": 1.203125
    },
    {
      "t": 0.8800000000000001,
      "quadrature_value": 1.2144000000000004,
      "exact_lower": 1.2144000000000004
    },
    {
      "t": 0.885,
      "quadrature_value": 1.2257250000000002,
      "exact_lower": 1.2257250000000002
    },
    {
      "t": 0.8900000000000001,
      "quadrature_value": 1.2371000000000003,
      "exact_lower": 1.2371000000000003
    },
    {
      "t": 0.895,
      "quadrature_value": 1.2485249999999999,
      "exact_lower": 1.2485249999999999
    },
    {
      "t": 0.9000000000000001,
      "quadrature_value": 1.2600000000000002,
      "exact_lower": 1.2600000000000002
    },
    {
      "t": 0.905,
      "quadrature_value": 1.271525,
      "exact_lower": 1.271525
    },
    {
      "t": 0.9100000000000001,
      "quadrature_value": 1.2831000000000006,
      "exact_lower": 1.2831000000000004
    },
    {
      "t": 0.915,
      "quadrature_value": 1.2947250000000001,
      "exact_lower": 1.2947250000000001
    },
    {
      "t": 0.9199999999999999,
      "quadrature_value": 1.3063999999999996,
      "exact_lower": 1.3063999999999998
    },
    {
      "t": 0.925,
      "quadrature_value": 1.318125,
      "exact_lower": 1.3181250000000002
    },
    {
      "t": 0.9299999999999999,
      "quadrature_value": 1.3298999999999999,
      "exact_lower": 1.3298999999999999
    },
    {
      "t": 0.935,
      "quadrature_value": 1.3417250000000003,
      "exact_lower": 1.3417250000000003
    },
    {
      "t": 0.94,
      "quadrature_value": 1.3535999999999997,
      "exact_lower": 1.3536
    },
    {
      "t": 0.9450000000000001,
      "quadrature_value": 1.365525,
      "exact_lower": 1.365525
    },
    {
      "t": 0.95,
      "quadrature_value": 1.3775,
      "exact_lower": 1.3775
    },
    {
      "t": 0.9550000000000001,
      "quadrature_value": 1.389525,
      "exact_lower": 1.3895250000000001
    },
    {
      "t": 0.96,
      "quadrature_value": 1.4015999999999997,
      "exact_lower": 1.4016
    },
    {
      "t": 0.9650000000000001,
      "quadrature_value": 1.4137250000000003,
      "exact_lower": 1.4137250000000003
    },
    {
      "t": 0.97,
      "quadrature_value": 1.4259,
      "exact_lower": 1.4259
    },
    {
      "t": 0.9750000000000001,
      "quadrature_value": 1.4381250000000003,
      "exact_lower": 1.4381250000000003
    },
    {
      "t": 0.98,
      "quadrature_value": 1.4504,
      "exact_lower": 1.4504
    },
    {
      "t": 0.9850000000000001,
      "quadrature_value": 1.4627250000000003,
      "exact_lower": 1.4627250000000003
    },
    {
      "t": 0.99,
      "quadrature_value": 1.4750999999999999,
      "exact_lower": 1.4750999999999999
    },
    {
      "t": 0.9950000000000001,
      "quadrature_value": 1.4875250000000002,
      "exact_lower": 1.4875250000000002
    },
    {
      "t": 1.0,
      "quadrature_value": 1.5,
      "exact_lower": 1.5
    }
  ],
  "finite_quadrature_is_not_the_proof": true
}