{
  "status": "PASS",
  "assertions": 25980,
  "checks": {
    "PB_full_enumeration": 1365,
    "PB_mass": 1365,
    "PB_mean": 1365,
    "PB_variance": 1365,
    "PB_order_invariance": 1365,
    "dependent_size_bias_law": 119,
    "dependent_size_bias_moment": 476,
    "pairwise_independence_insufficient": 1,
    "zero_density_nonnegative": 36,
    "zero_density_normalized": 36,
    "zero_polynomial_identity": 216,
    "zero_absolute_first_moment": 36,
    "Bernoulli_zero_uniform": 19,
    "Bernoulli_coupling_half_distance": 19,
    "zero_independent_sum_identity": 30,
    "exchange_independent_regression": 62,
    "exchange_independent_conditional_second": 62,
    "exchange_independent_symmetry": 5,
    "without_replacement_regression": 1002,
    "without_replacement_conditional_second": 1002,
    "without_replacement_variance": 35,
    "without_replacement_symmetry": 35,
    "without_replacement_jump_second": 35,
    "overlap_DP_enumeration": 24,
    "overlap_rigorous_Poisson_TV": 24,
    "Poisson_Stein_equation": 6080,
    "Poisson_Stein_factors": 6080,
    "Poisson_kernel_backward_identity": 90,
    "normal_Stein_bounded_solution": 605,
    "normal_Stein_first_derivative": 605,
    "normal_Stein_equation": 605,
    "normal_kernel_weight_identity": 605,
    "normal_kernel_second_weight": 605,
    "normal_Stein_second_derivative": 600,
    "capstone_independent_certificate": 1,
    "capstone_overlap_certificate": 1,
    "capstone_hypergeometric_law": 1,
    "capstone_hypergeometric_variance": 1,
    "capstone_conditional_second_average": 1,
    "capstone_zero_bias_payoff": 1
  },
  "precision_digits": 100,
  "rational_TV_enclosure_degree": 90,
  "independent": {
    "pmf": [
      "364021/500000",
      "122481/500000",
      "12981/500000",
      "511/500000",
      "3/250000"
    ],
    "lambda": "3/10",
    "budget": "159/5000",
    "TV_interval_rational": [
      "1280032023789964327239683767727445810398308478119791978138117218847089358396024447523842963206047664311865678982050691312054250535243756035869539309278712086693170530443137598852962835450137937873010059730831257609480151119640334581658370888260906924788636747086826804697489302126593962962762651342020118246162567569860470760437268758989702584276292019459735480098903536752169397651690081473884932452174777621922833826173/56348034225379753002654368242738334199858634057093940898056002999412740015808113753145682288953732125505282424085989559717196718476911202227481859326009155789495852485708486657636693875324787525709835647057998370555216472917884918786689878281598410053316711731048605156670052991726999072050302728746993791049071152137313014918384356589959677763393065126263401997448190073367172858042023176957589064639310495594920166500000",
      "1280032023789964327239683767727445810398308478119791978138117218847089358396024447523842963206047664311865678982050691312054250535243756035869539309278712086693170530443137598852962835450949009218832931098797614585395594132195914652947397711192078172739021556570336751086004805808667350827454426118140403839762567569860470760437268758989702584276292019459735480098903536752169397651690081473884932452174777621922833826173/56348034225379753002654368242738334199858634057093940898056002999412740015808113753145682288953732125505282424085989559717196718476911202227481859326009155789495852485708486657636693875324787525709835647057998370555216472917884918786689878281598410053316711731048605156670052991726999072050302728746993791049071152137313014918384356589959677763393065126263401997448190073367172858042023176957589064639310495594920166500000"
    ],
    "TV_decimal_approx": "0.022716533795484640179937866204654938345324630400298095511407"
  },
  "overlap": {
    "bit_count": 20,
    "indicator_count": 19,
    "pmf": [
      "83882575688449447359/100000000000000000000",
      "13626877217274569907/100000000000000000000",
      "107375529115579401/5000000000000000000",
      "299751219025271973/100000000000000000000",
      "1193862194026263/3125000000000000000",
      "4521360124562427/100000000000000000000",
      "62745230554461/12500000000000000000",
      "2104485633801/4000000000000000000",
      "2613457308321/50000000000000000000",
      "246662612397/50000000000000000000",
      "22136466267/50000000000000000000",
      "944173827/25000000000000000000",
      "1528713/500000000000000000",
      "23417667/100000000000000000000",
      "422091/25000000000000000000",
      "22761/20000000000000000000",
      "7047/100000000000000000000",
      "81/20000000000000000000",
      "9/50000000000000000000",
      "1/100000000000000000000"
    ],
    "lambda": "19/100",
    "b1": "11/2000",
    "b2": "9/250",
    "budget": "83/2000",
    "P0": "83882575688449447359/100000000000000000000",
    "TV_interval_rational": [
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      "8490233603420552775569090240408106337447653067441729641942183114153586816754368655460327753799547758889466169231366692998753804279613045846625931130690956300839797045657277984908588452507549347349785884061934598369100973068356175269036994668546567227373192369735059399615691834625046072768603853138079416603955104841574012037023278190156958493207524270739995447301705146087950311855929143544143517222047027394881006155494622775008767654339095412113013970717304415894291098897101426732997460430423125357055943964958053227676994155705815732993781994635570879641367993057661431716860473067388765591067246612497825661694367457288297265520051845662625633/407137821226610547140269306319643602657975012848352093267593586999890411628344816987678402628420515007181935840836106927629971194105283603903734542931676913426304873264524273179279662679124700869467861255676537746243578129234142198024118217079886142168993785669384878878636261689901862553875247697282542652770063955879347317278415692482362463759124433155590131560360975098077536228907363255474151862475102270455565008304885511780643206107184207367524513025698155021942654321827780941374617335585097177644761899694897246107412060185866694608325818559591334179534786334500091716555559891858969873444819572102807670761456072365991178100000000000000000000"
    ],
    "TV_decimal_approx": "0.020853463276493141256737890804584844253901364445359934993237"
  },
  "without_replacement": {
    "population_size": 200,
    "sample_size": 100,
    "sigma_squared": "10000/199",
    "lambda": "1/50",
    "conditional_variance_defect": "11596626418118939329703021858546330072877333027775008/2382514573074362016737713787223201833066650186799924875",
    "W1_budget": "0.28601833452729733560089319952312099892212516935326393380281",
    "positive_part": "0.396454211614766247766275184367121584930388297598599706325988",
    "actual_positive_error": "0.00248806878666643017367087556726028354547033356633495133993758"
  },
  "zero_bias": {
    "n": 400,
    "sigma": 10,
    "W1_budget": "1/10",
    "positive_part": "0.398693019637929277767349625746474453464881428272339010442972",
    "actual_positive_error": "0.000249260763503400172596434187907415010977202892595647222953882"
  },
  "normal_positive_part": "0.398942280401432677939946059934381868475858631164934657665926",
  "limitations": "Finite enumeration validates the specified constructions; universal conclusions require the proofs in the formal pages. Gaussian numerical checks are 100-digit diagnostics, not directed-rounding certificates."
}