{
  "results": {
    "lambda_margin": "0.00014908745",
    "g": "0.753771282058235",
    "exp_g": "2.124998894",
    "coef_necessary_1_over_g": "1.32666238",
    "coef_compiled_1_over_logR": "0.701114922",
    "coef_refined_1_over_logRstar": "0.979590633",
    "R": "4.1632653",
    "R_star": "2.7755102",
    "reduced_model_base": "2.515536575",
    "sandwich_eta_ceiling": "0.32967",
    "compiled": {
      "transfer": "0.00395635237364",
      "chem": "1.08420231578e-5",
      "service": "0.002",
      "total": "0.0059671943968",
      "confidence_replay": "0.9940328056032",
      "minority_floor_real": "1598082.2754"
    },
    "odds_10": "938.7654303",
    "fraction_10": "0.9989359046761",
    "refined": {
      "transfer": "0.000967176369129",
      "chem": "4.33680926314e-9",
      "service": "0.002",
      "total": "0.00296718070594",
      "confidence_replay": "0.9970328193",
      "total_fine_quotas": "0.0009871807059",
      "tau_last": "0.00096717510994",
      "tau_second_last": "1.25919e-9",
      "minority_floor_real": "36861.3907344",
      "minority_floor_int": 36862,
      "second_moment_only_at_same_M": "0.101884"
    },
    "required_M_K10_delta_0.004": {
      "compiled_second_moment": "9.8909e+12",
      "exponential_tail_original_floors": "2.087e+11",
      "minority_growth_second_moment": "1.0188e+11",
      "refined_theorem_B": "3.256e+9",
      "necessary_1_plus_exp(10g)/2": "939.765"
    },
    "simple_rule_M_K10": "4.8493e+9",
    "ceiling_K_M4e9": "30.2515",
    "ceiling_K_M1e13": "40.6314",
    "loss": {
      "1": "0.75",
      "4": "0.314817373",
      "20": "0.00268990773"
    },
    "heterogeneity": {
      "equal": {
        "1/50": "17/35",
        "1/2": "1/35"
      },
      "mixed": {
        "1/50": "27/35",
        "1/2": "13/35"
      }
    },
    "accounts_compiled": {
      "NM": "6.5536e+35",
      "operating_precursor": "4.980736e+37",
      "growth": "3.735552e+37",
      "residual": "1.245184e+37",
      "discard": "4.325376e+37",
      "terminal": "5.24288e+36",
      "total": "5.505024e+37",
      "duration": "8.0000001e+12"
    },
    "accounts_refined": {
      "NM": "2.62144e+32",
      "operating_precursor": "1.9922944e+34",
      "growth": "1.4942208e+34",
      "residual": "4.980736e+33",
      "discard": "1.7301504e+34",
      "terminal": "2.097152e+33",
      "total": "2.2020096e+34",
      "duration": "8.0000001e+12"
    },
    "quotas_compiled": {
      "qR": "2.228224e+27",
      "qB": "1.835008e+41",
      "JB": "1.4680064e+57",
      "JR": "1.1978932e+48",
      "exchange_allowance": "1.19804e+62"
    },
    "quotas_refined": {
      "qR": "2.228224e+27",
      "qB": "7.340032e+37",
      "JB": "5.8720256e+53",
      "JR": "4.7915729e+44",
      "exchange_allowance": "2.5038317e+55"
    },
    "N_over_NA_mol": "0.108825",
    "N0_over_NA_mol": "0.000232475",
    "pL_at_mM_scale": "6.022e+8",
    "fL_at_mM_scale": "6.022e+5",
    "sizing_rule_N_compiled": "1.42333e+23",
    "sizing_rule_N_refined": "1.2631e+23",
    "scalar_barrier_worst_over_N": "-3.04805e-5",
    "checks_passed": 2083
  },
  "checks": [
    [
      "rho = 49/204",
      true
    ],
    [
      "R = 204/49",
      true
    ],
    [
      "rho_* = 49/136",
      true
    ],
    [
      "R_* = 136/49",
      true
    ],
    [
      "g > 3/4",
      true
    ],
    [
      "g in (0.753771282, 0.753771283)",
      true
    ],
    [
      "b > 0.7937",
      true
    ],
    [
      "(8/25) log 4 - 19/500 > log(3/2)",
      true
    ],
    [
      "u = 128 for N = 6.5536e22",
      true
    ],
    [
      "N >= N0",
      true
    ],
    [
      "closed form of transfer sum",
      true
    ],
    [
      "compiled witness failure < 0.006",
      true
    ],
    [
      "exp(10g - log 2) > 938.76",
      true
    ],
    [
      "high fraction > 0.998935",
      true
    ],
    [
      "compiled minority floor 1598083",
      true
    ],
    [
      "refined witness failure < 0.003",
      true
    ],
    [
      "refined witness transfer < 0.00098",
      true
    ],
    [
      "refined witness with finer quotas < 0.001",
      true
    ],
    [
      "refined minority floor 36862",
      true
    ],
    [
      "M ratio 2500",
      true
    ],
    [
      "NM ratio 2500",
      true
    ],
    [
      "second-moment form alone does not close M = 4e9",
      true
    ],
    [
      "simple rule is sufficient at K=10 (diagnostic)",
      true
    ],
    [
      "gain table 9/10",
      true
    ],
    [
      "gain table minimal 9/10",
      true
    ],
    [
      "gain table 19/20",
      true
    ],
    [
      "gain table minimal 19/20",
      true
    ],
    [
      "gain table 99/100",
      true
    ],
    [
      "gain table minimal 99/100",
      true
    ],
    [
      "gain table 999/1000",
      true
    ],
    [
      "gain table minimal 999/1000",
      true
    ],
    [
      "loss c=1 is 3/4",
      true
    ],
    [
      "loss c=4",
      true
    ],
    [
      "loss bounds c=1 (diagnostic)",
      true
    ],
    [
      "loss bounds c=4 (diagnostic)",
      true
    ],
    [
      "loss bounds c=20 (diagnostic)",
      true
    ],
    [
      "exact variance identity equal",
      true
    ],
    [
      "variance <= (n-m)/(n-1) mean equal",
      true
    ],
    [
      "exact variance identity equal",
      true
    ],
    [
      "variance <= (n-m)/(n-1) mean equal",
      true
    ],
    [
      "exact variance identity mixed",
      true
    ],
    [
      "variance <= (n-m)/(n-1) mean mixed",
      true
    ],
    [
      "exact variance identity mixed",
      true
    ],
    [
      "variance <= (n-m)/(n-1) mean mixed",
      true
    ],
    [
      "hetero equal 17/35",
      true
    ],
    [
      "hetero mixed 27/35",
      true
    ],
    [
      "hetero equal 1/35",
      true
    ],
    [
      "hetero mixed 13/35",
      true
    ],
    [
      "normalization closed form j=0",
      true
    ],
    [
      "normalization cap j=0",
      true
    ],
    [
      "normalization closed form j=1",
      true
    ],
    [
      "normalization cap j=1",
      true
    ],
    [
      "normalization closed form j=2",
      true
    ],
    [
      "normalization cap j=2",
      true
    ],
    [
      "normalization closed form j=3",
      true
    ],
    [
      "normalization cap j=3",
      true
    ],
    [
      "normalization closed form j=4",
      true
    ],
    [
      "normalization cap j=4",
      true
    ],
    [
      "normalization closed form j=5",
      true
    ],
    [
      "normalization cap j=5",
      true
    ],
    [
      "normalization closed form j=6",
      true
    ],
    [
      "normalization cap j=6",
      true
    ],
    [
      "normalization closed form j=7",
      true
    ],
    [
      "normalization cap j=7",
      true
    ],
    [
      "normalization closed form j=8",
      true
    ],
    [
      "normalization cap j=8",
      true
    ],
    [
      "normalization closed form j=9",
      true
    ],
    [
      "normalization cap j=9",
      true
    ],
    [
      "normalization closed form j=10",
      true
    ],
    [
      "normalization cap j=10",
      true
    ],
    [
      "normalization closed form j=11",
      true
    ],
    [
      "normalization cap j=11",
      true
    ],
    [
      "compiled operating precursor",
      true
    ],
    [
      "compiled total precursor",
      true
    ],
    [
      "duration",
      true
    ],
    [
      "refined NM",
      true
    ],
    [
      "quota allowances compiled",
      true
    ],
    [
      "quota allowances refined",
      true
    ],
    [
      "scalar minority barrier negative on random grid (diagnostic)",
      true
    ],
    [
      "Chernoff upper exponent (diagnostic)",
      true
    ],
    [
      "Chernoff lower exponent (diagnostic)",
      true
    ],
    [
      "Chernoff upper exponent (diagnostic)",
      true
    ],
    [
      "Chernoff lower exponent (diagnostic)",
      true
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      "Chernoff lower exponent (diagnostic)",
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    ],
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    ],
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    ],
    [
      "exponential tail dominates exact law equal 1/4 (diagnostic)",
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    ],
    [
      "exponential tail dominates exact law equal 1/2 (diagnostic)",
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    ],
    [
      "exponential tail dominates exact law equal 9/10 (diagnostic)",
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    ],
    [
      "exponential tail dominates exact law mixed 1/4 (diagnostic)",
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    ],
    [
      "exponential tail dominates exact law mixed 1/2 (diagnostic)",
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    ],
    [
      "exponential tail dominates exact law mixed 9/10 (diagnostic)",
      true
    ]
  ],
  "scope": "Exact enclosures and explicitly labeled numerical diagnostics from the source. Neither the process theorem nor Lean is reproved."
}