{
  "status": "passed",
  "precision_decimal_digits": 70,
  "assertions": 27809,
  "scope": "Exact identities and sampled verification of analytic bounds; grid maxima are NOT certified suprema. Boundary sup error has independent exact proof.",
  "regular": [
    {
      "epsilon": "0.1",
      "proven_bound": "0.02"
    },
    {
      "epsilon": "0.25",
      "proven_bound": "0.125"
    },
    {
      "epsilon": "0.5",
      "proven_bound": "0.5"
    }
  ],
  "boundary": [
    {
      "epsilon": "0.2",
      "exact_sup_error": "0.006737946999085467096636048423",
      "outer_error_at_left": "1"
    },
    {
      "epsilon": "0.1",
      "exact_sup_error": "0.00004539992976248485153559151556",
      "outer_error_at_left": "1"
    },
    {
      "epsilon": "0.05",
      "exact_sup_error": "2.06115362243855782796594038e-9",
      "outer_error_at_left": "1"
    },
    {
      "epsilon": "0.025",
      "exact_sup_error": "4.248354255291588995329234783e-18",
      "outer_error_at_left": "1"
    }
  ],
  "slow_fast": [
    {
      "epsilon": "0.25",
      "T": "1.0",
      "layer_cutoff": "0.3465735902799726547086160607",
      "sampled_max_slow_error": "0.7627168379968067751197978364",
      "slow_proven_bound": "2.526834481847423865647678733",
      "sampled_max_fast_error_all": "1.10486541173080068778828209",
      "sampled_max_fast_error_after_layer": "1.10486541173080068778828209",
      "fast_after_layer_proven_bound": "3.456404938962185174487750601"
    },
    {
      "epsilon": "0.125",
      "T": "1.0",
      "layer_cutoff": "0.2599301927099794910314620455",
      "sampled_max_slow_error": "0.4866175761056565163090763805",
      "slow_proven_bound": "1.263417240923711932823839366",
      "sampled_max_fast_error_all": "1.0",
      "sampled_max_fast_error_after_layer": "0.7121841829585419649415676335",
      "fast_after_layer_proven_bound": "1.7282024694810925872438753"
    },
    {
      "epsilon": "0.0625",
      "T": "1.0",
      "layer_cutoff": "0.1732867951399863273543080304",
      "sampled_max_slow_error": "0.2830517275826954747098035768",
      "slow_proven_bound": "0.6317086204618559664119196832",
      "sampled_max_fast_error_all": "1.0",
      "sampled_max_fast_error_after_layer": "0.4187624911497431485083595436",
      "fast_after_layer_proven_bound": "0.8641012347405462936219376502"
    },
    {
      "epsilon": "0.03125",
      "T": "1.0",
      "layer_cutoff": "0.108304246962491454596442519",
      "sampled_max_slow_error": "0.1543281999546377809197599353",
      "slow_proven_bound": "0.3158543102309279832059598416",
      "sampled_max_fast_error_all": "1.0",
      "sampled_max_fast_error_after_layer": "0.2298039478098747272865156673",
      "fast_after_layer_proven_bound": "0.4320506173702731468109688251"
    }
  ],
  "oscillator": [
    {
      "epsilon": "0.2",
      "physical_horizon": "10.0",
      "sampled_max_error": "0.03710677541957451065457550466",
      "proven_bound": "0.2020410288672876072108637012"
    },
    {
      "epsilon": "0.1",
      "physical_horizon": "20.0",
      "sampled_max_error": "0.01834843689750244811010784843",
      "proven_bound": "0.10025125786760090531040358"
    },
    {
      "epsilon": "0.05",
      "physical_horizon": "40.0",
      "sampled_max_error": "0.009200138785172465436606144292",
      "proven_bound": "0.05003128912364216843923534388"
    },
    {
      "epsilon": "0.025",
      "physical_horizon": "80.0",
      "sampled_max_error": "0.004597151509553168629179628149",
      "proven_bound": "0.02500390747118017087229675492"
    }
  ],
  "secular_failure": [
    {
      "n": 5,
      "epsilon": "0.03183098861837906715377675267",
      "time": "31.41592653589793238462643383",
      "ordinary_first_order": "0",
      "truth": "0.3678328260614290365162204467",
      "multiple_scales": "0.3678794411714423215955237702"
    },
    {
      "n": 20,
      "epsilon": "0.007957747154594766788444188169",
      "time": "125.6637061435917295385057353",
      "ordinary_first_order": "0",
      "truth": "0.3678765290533574044631308419",
      "multiple_scales": "0.3678794411714423215955237702"
    },
    {
      "n": 80,
      "epsilon": "0.001989436788648691697111047042",
      "time": "502.6548245743669181540229413",
      "ordinary_first_order": "0",
      "truth": "0.3678792591692396532527052815",
      "multiple_scales": "0.3678794411714423215955237702"
    }
  ],
  "averaging": [
    {
      "epsilon": "0.2",
      "sampled_max_error": "1.084434471273432975097197463",
      "proven_bound": "1.635957400503470699241349706"
    },
    {
      "epsilon": "0.1",
      "sampled_max_error": "0.7063319680207562977390842483",
      "proven_bound": "0.7771138136369998462192999499"
    },
    {
      "epsilon": "0.05",
      "sampled_max_error": "0.3656450046424698180733067784",
      "proven_bound": "0.3788450073761215890142366847"
    }
  ],
  "negative_cases": {
    "initial_fast_error": 1,
    "varying_period_error_at_pi_over_2epsilon": 1
  }
}