{
  "precision_decimal_digits": 70,
  "exact_arithmetic": "fractions.Fraction",
  "numeric_claim": "70-digit cross-checks; no certified directed-rounding quadrature",
  "bernoulli_identity_checks": 920,
  "finite_euler_maclaurin_exact_cases": 390,
  "B0_through_B20": [
    "1",
    "-1/2",
    "1/6",
    "0",
    "-1/30",
    "0",
    "1/42",
    "0",
    "-1/30",
    "0",
    "5/66",
    "0",
    "-691/2730",
    "0",
    "7/6",
    "0",
    "-3617/510",
    "0",
    "43867/798",
    "0",
    "-174611/330"
  ],
  "zeta2_enclosure_20": {
    "lower_exact": "713143079493440020951/433539007930828800000",
    "upper_exact": "445714429975624231/270961879956768000",
    "width_exact": "1/51200000",
    "lower_decimal_display_only": "1.644934057715106649974212205390976553837",
    "upper_decimal_display_only": "1.644934077246356649974212205390976553837"
  },
  "zeta2_enclosure_100": {
    "lower_exact": "499744408842221210425246429860601211375973527484183079235282641283975567840250726685771/303808170135744072059268117710194732550617369998670700557100110845474370676640000000000",
    "upper_exact": "199897763537648004595437932124388654844664897825049775119109733264982977413213976601/121523268054297628823707247084077893020246947999468280222840044338189748270656000000",
    "width_exact": "1/160000000000",
    "lower_decimal_display_only": "1.64493406684530953174383616484699043335",
    "upper_decimal_display_only": "1.64493406685155953174383616484699043335"
  },
  "zeta2_enclosure_200": {
    "lower_exact": "91287393425335596305637838934064174880813685776570258599546972860257075677096604363613843968985428182500206572511517860976354643183008256990559480389710717003621369922959541741463391/55496080520875668962503430291248779024997961187389707583601710800729307690063426881021016672582320297521160821843416964443845564866198363786963829827545528318975329877038080000000000",
    "upper_exact": "4564369671267321769193228623157920691602122265186178925692069245625974894311868590326102974102406379990953515347231373134968546777943809778872370487881892918831728120447967080529/2774804026043783448125171514562438951249898059369485379180085540036465384503171344051050833629116014876058041092170848222192278243309918189348191491377276415948766493851904000000",
    "width_exact": "1/5120000000000",
    "lower_decimal_display_only": "1.644934066848135288779027886161519465624",
    "upper_decimal_display_only": "1.644934066848330601279027886161519465624"
  },
  "tail_enclosure_N_through": 1000,
  "beta_regularized_integral_cases": 49,
  "reflection_regularized_integral_cases": 36,
  "gamma_regularized_integral_cases": 9,
  "bohr_mollerup_enclosures": 60,
  "mellin_inverse_checks": [
    {
      "x": "0.1",
      "T": 2,
      "error": "0.00152050745520462451631852530264",
      "analytic_tail_bound": "0.00375947685348456181084831683551"
    },
    {
      "x": "0.1",
      "T": 4,
      "error": "0.00000517487750700925682003509890929",
      "analytic_tail_bound": "0.00000702060772506416453476524847239"
    },
    {
      "x": "0.1",
      "T": 8,
      "error": "1.93392329674003373181990294859e-11",
      "analytic_tail_bound": "2.44832626859443391639009039186e-11"
    },
    {
      "x": "0.25",
      "T": 2,
      "error": "0.00217296485044812533307131372123",
      "analytic_tail_bound": "0.00237770193353886823411796213469"
    },
    {
      "x": "0.25",
      "T": 4,
      "error": "0.00000385295051290123731298800367669",
      "analytic_tail_bound": "0.00000444022219395519096276500285592"
    },
    {
      "x": "0.25",
      "T": 8,
      "error": "6.92017190594916922377077866439e-12",
      "analytic_tail_bound": "1.54845749279591710315359301782e-11"
    },
    {
      "x": "1.0",
      "T": 2,
      "error": "0.00118884958479554855385942751274",
      "analytic_tail_bound": "0.00118885096676943411705898106735"
    },
    {
      "x": "1.0",
      "T": 4,
      "error": "0.00000222011109696859547904687312169",
      "analytic_tail_bound": "0.00000222011109697759548138250142796"
    },
    {
      "x": "1.0",
      "T": 8,
      "error": "7.74228746397958551576758338538e-12",
      "analytic_tail_bound": "7.74228746397958551576796508908e-12"
    },
    {
      "x": "4.0",
      "T": 2,
      "error": "0.000543241212612031333267828430308",
      "analytic_tail_bound": "0.000594425483384717058529490533674"
    },
    {
      "x": "4.0",
      "T": 4,
      "error": "0.000000963237628225309328247000919172",
      "analytic_tail_bound": "0.00000111005554848879774069125071398"
    },
    {
      "x": "4.0",
      "T": 8,
      "error": "1.7300429764872923059426946661e-12",
      "analytic_tail_bound": "3.87114373198979275788398254454e-12"
    },
    {
      "x": "10.0",
      "T": 2,
      "error": "0.000152050745520462451631852530264",
      "analytic_tail_bound": "0.000375947685348456181084831683551"
    },
    {
      "x": "10.0",
      "T": 4,
      "error": "0.000000517487750700925682003509890929",
      "analytic_tail_bound": "0.000000702060772506416453476524847239"
    },
    {
      "x": "10.0",
      "T": 8,
      "error": "1.93392329674003373181990294859e-12",
      "analytic_tail_bound": "2.44832626859443391639009039186e-12"
    }
  ],
  "capstone_integral": {
    "exact": "2*pi/sqrt(3)",
    "numeric": "3.6275987284684357011881565152843114645681324961855",
    "U": 1000,
    "actual_cutoff_error": "0.000001499999999400000000374999999727272727487",
    "analytic_tail_bound": "3/2000000"
  },
  "status": "PASS",
  "assertions": 6616
}