{
  "inputs": {
    "menu_dependence": "0",
    "detection": "1/2",
    "seed": 56092026,
    "reference_rates": [
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      0.3,
      0.001,
      0.1,
      0.0,
      1e-05
    ],
    "rate_radius": "1/2000"
  },
  "calibration_rows": [
    {
      "event": "at_most_two",
      "n": 1024,
      "threshold": 607,
      "W_error": 0.01833462228214261,
      "I_error": 0.02336813372797641,
      "coverage_display": 0.9504153777178574,
      "exact_target": "19/20",
      "exact_comparison_passed": true
    },
    {
      "event": "at_most_two",
      "n": 1280,
      "threshold": 759,
      "W_error": 0.009946867493054016,
      "I_error": 0.012846126929679113,
      "coverage_display": 0.95703125,
      "exact_target": "245/256",
      "exact_comparison_passed": true
    },
    {
      "event": "at_most_two",
      "n": 4000,
      "threshold": 2374,
      "W_error": 2.262254576215986e-05,
      "I_error": 3.4565033319586767e-05,
      "coverage_display": 0.95703125,
      "exact_target": "245/256",
      "exact_comparison_passed": true
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    {
      "event": "three_or_four",
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      "threshold": 149,
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      "I_error": 0.019058141262992698,
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      "exact_target": "19/20",
      "exact_comparison_passed": true
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    {
      "event": "three_or_four",
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      "threshold": 165,
      "W_error": 0.010559295024741398,
      "I_error": 0.012841645642751346,
      "coverage_display": 0.95703125,
      "exact_target": "245/256",
      "exact_comparison_passed": true
    }
  ],
  "synthetic_menu": {
    "n": 640,
    "H": 188,
    "decision": {
      "cutoff": 6,
      "status": "CONDITIONAL_MENU_DECISION",
      "threshold": 165
    }
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    "cutoff": 6,
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    "coverage": "19/20",
    "meaning": "Seven is a fallback, not evidence that dependence exceeds 3/5"
  },
  "unknown_detector_rule": {
    "cutoff": 7,
    "retained_models": [
      "I",
      "W"
    ],
    "detector_interval": [
      "11963067088941783865754917462231490232848581/32667107224410092492483962313449748299776000",
      "20406973629146329348125518818930324418326331/32667107224410092492483962313449748299776000"
    ],
    "statistic_mean": "2961/2000",
    "statistic_pgf": "9453/20480",
    "mean_radius": "33265202610436774234287343515647684424727/87112285931760246646623899502532662132736",
    "pgf_radius": "53224324176698838774859749625036295079563/1393796574908163946345982392040522594123776",
    "model_ranges": {
      "I": [
        "46068812216022977842217131401680379615346917189734369878679687951052637050623053350950400662894029424295855123239719272298139833222910082602240453947948155018553692567165540721/125522139412449572852754417547667248081342549065799146119882305204618139092793021568677632833094857428769894929550970821885074466194219631803376335364903577410098247499776000000",
        "57948734098475506175542595219212726761528802682131264705486794985242488173902414403261630960644253606547804803568480193868337282976413736484373490726120974479525156873624164721/102016349698085874807926597751135297132168232958337334830245913353558254609723679769743229853141241034255306860168731893778403025431393011571703020467697171663570941771776000000"
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      "W": [
        "23454693832719289547277930627400906135651431190057653595572592771386616238301081565735580646651013405661165400698065933700435840574838816624129125419216107881509186154584676721/62761069706224786426377208773833624040671274532899573059941152602309069546396510784338816416547428714384947464775485410942537233097109815901688167682451788705049123749888000000",
        "29178197075011341461600662825652576541867442677225076901807159444177101235626953438986601355634533466425268039716125918286574903651415033995987266430868150816335590121331300721/51008174849042937403963298875567648566084116479168667415122956676779127304861839884871614926570620517127653430084365946889201512715696505785851510233848585831785470885888000000"
      ]
    },
    "status": "CONDITIONAL_FEASIBLE_SET",
    "uniform_coverage": "245/256"
  },
  "detector_half": {
    "low_count_gap": "0",
    "pgf_gap": "9/1600",
    "sufficient_pgf_wells_numeric": 281067,
    "population_moment_efficiency": "E[Y]/3",
    "population_moment_dependence": "18 E[Y(Y-1)] / E[Y]^2 - 17; d>0 only"
  },
  "finite_scalar_certificate": {
    "rows": [
      1000000,
      1000000,
      1000000,
      1000000,
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      992141,
      983746,
      972743,
      959583,
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      928611,
      911617,
      894077,
      876268,
      858418,
      840711
    ],
    "lower": "3134312565151423153/3252877056000000000",
    "compiled_source_lower": "963/1000"
  },
  "compiled_recorded_floor": "952037/1000000",
  "demographic": [
    {
      "birth_cap": 0.1002,
      "death_floor": 0.05,
      "cutoff": 4,
      "source_lower": "8356410158013223257239768346421543794722591331282895231891557462457954928461446924767123431085534970224696180419859839134798459643/8646729503982049553835927946888271106476829048381821581853896986126193121098902165807581378667036762746386232414503039134798459643",
      "recorded_lower": "8261586452815389538444169298606239539863100449467794120841126935134235042321996456184280493867779067627007621915294948904315676586927/8646729503982049553835927946888271106476829048381821581853896986126193121098902165807581378667036762746386232414503039134798459643000",
      "numerical_full_cdf": 0.9664243769528964
    },
    {
      "birth_cap": 0.105,
      "death_floor": 0.05,
      "cutoff": 4,
      "source_lower": "9413600586810199714410273443573594919129799149078646490124679221628430850886337032630043/9792535295441821965256136362903890769084240215751786133017947634725566646321857032630043",
      "recorded_lower": "9306261633268971295043301806500982416519826947772049982304375066059546753572232125271112527/9792535295441821965256136362903890769084240215751786133017947634725566646321857032630043000",
      "numerical_full_cdf": 0.9613037218583843
    },
    {
      "birth_cap": 0.1,
      "death_floor": 0.0,
      "cutoff": 5,
      "source_lower": "77051749008111818500277258238036717453173452507/79626240000000000000000000000000000000000000000",
      "recorded_lower": "2821423513300137284510258554807358545767417742759/2949120000000000000000000000000000000000000000000",
      "numerical_full_cdf": 0.9676682323670306
    }
  ],
  "inherited_history_bounds": [
    {
      "cutoff": 2,
      "source_lower": "8557918717439/9091129500000",
      "recorded_lower": "313275907545243/336708500000000",
      "with_1pct_conditional_inference_failure": "31014314846979057/33670850000000000"
    },
    {
      "cutoff": 3,
      "source_lower": "176701212731773153/182749885209000000",
      "recorded_lower": "6470259728405606661/6768514267000000000",
      "with_1pct_conditional_inference_failure": "640555713112155059439/676851426700000000000"
    },
    {
      "cutoff": 4,
      "source_lower": "449814198567319619107/459204774058914750000",
      "recorded_lower": "16473049504746783406959/17007584224404250000000",
      "with_1pct_conditional_inference_failure": "1630831900969931557288941/1700758422440425000000000"
    },
    {
      "cutoff": 5,
      "source_lower": "18199913742084094881812203/18461868736264608609000000",
      "recorded_lower": "666559079295532025957051511/683772916157948467000000000",
      "with_1pct_conditional_inference_failure": "65989348850257670569748099589/68377291615794846700000000000"
    },
    {
      "cutoff": 8,
      "source_lower": "2322608975807863165105112502703311191/2343222294566537197795507107807375000",
      "recorded_lower": "85068671995792219628224159967501264067/86786010909871748066500263252125000000",
      "with_1pct_conditional_inference_failure": "8421798527583429743194191836782625142633/8678601090987174806650026325212500000000"
    }
  ],
  "reference_endpoint_two_failure_witness": "151415045117539070312500/3001800450060004500180003",
  "numerical_forward": [
    {
      "label": "reference",
      "in_rate_class": true,
      "cdf2": 0.947597717822017,
      "cdf3": 0.9738271217718986,
      "overflow": 1.890179870919209e-13,
      "normalization": 1.0000000000000002
    },
    {
      "label": "positive_example",
      "in_rate_class": true,
      "cdf2": 0.9475415601127161,
      "cdf3": 0.9737889160097194,
      "overflow": 1.9270588616379866e-13,
      "normalization": 1.0000000000000007
    }
  ],
  "unresolved_outcomes_example": [
    "17/25",
    "1"
  ],
  "evidence": "Exact source algebra and integer bounds; numeric branching/Monte Carlo illustrations; supplied contracts only; Lean not rerun"
}