{
  "schemaVersion": 1,
  "kind": "deterministic-model-arithmetic",
  "generatedOn": "2026-10-15",
  "generatorSha256": "b35fd7bd12cf9f29a98e244f1a37560b91eb7a9ca59d78a1c83b0f8ea0fa5e50",
  "precisionDecimalDigits": 70,
  "notebookCommit": "37f758d64240cfb42a6d6fd41ff4ca16b8499bb3",
  "assumptions": [
    "20 shards; recovery requires 17; constant independent per-shard hazard.",
    "Fixed windows are treated as independent, with no repair dynamics across window boundaries.",
    "Poisson counts events; binomial counts distinct shards failing at least once.",
    "Fractional 8760/hours exponent is a window-model convention, not a simulated partial window.",
    "No observed loss sample, confidence interval, S3 implementation or provider certification."
  ],
  "rows": [
    {
      "id": "historical-inputs",
      "rate_per_drive_year": "0.0041",
      "window_hours": "156",
      "periods_per_365_day_year": "56.15384615384615384615384615384615384615384615384615384615384615384615",
      "poisson_exact_four_per_window": "1.891872862585546783341124876402997022257090526425627833342309612036068E-13",
      "poisson_at_least_four_per_window": "1.892425527628073899415548077502106898309593273012678282935712790812434E-13",
      "binomial_distinct_at_least_four_per_window": "1.375440753109179637583228851346200822705778334937284714037595442254618E-13",
      "poisson_exact_four_annual": "1.06235937667711064893996808057501793590669255862544969311127E-11",
      "poisson_at_least_four_annual": "1.06266971935483417540558634586586040994078059516732681151002E-11",
      "binomial_distinct_at_least_four_annual": "7.7236288443530203748598086020142115410624674257139613042758E-12",
      "printed_periods": "56",
      "printed_poisson_annual": "1.05944880304239425696163974897267244383844660428055106857209E-11"
    },
    {
      "id": "without-recovery-credit",
      "rate_per_drive_year": "0.0081",
      "window_hours": "156",
      "periods_per_365_day_year": "56.15384615384615384615384615384615384615384615384615384615384615384615",
      "poisson_exact_four_per_window": "2.877914420736210899925502462427574262478458922435266622792669951382075E-12",
      "poisson_at_least_four_per_window": "2.879575736675724956156827003148388183880513478435290261839668323043393E-12",
      "binomial_distinct_at_least_four_per_window": "2.093093911319857040550860935492336200260779662125958624877580808544588E-12",
      "poisson_exact_four_annual": "1.616059636131307585541132780807585658865405556004990233843918E-10",
      "poisson_at_least_four_annual": "1.616992528927963513508523195654072119485354924863571055525233E-10",
      "binomial_distinct_at_least_four_annual": "1.175352734750230928191511705799854480906137068418221357759054E-10",
      "printed_periods": "56",
      "printed_poisson_annual": "1.611632075484729276203434540860822281805743277400976635507183E-10"
    },
    {
      "id": "illustrative-two-percent",
      "rate_per_drive_year": "0.02",
      "window_hours": "156",
      "periods_per_365_day_year": "56.15384615384615384615384615384615384615384615384615384615384615384615",
      "poisson_exact_four_per_window": "1.065165491001289954008471371492815152659565647433443143786097739846597E-10",
      "poisson_at_least_four_per_window": "1.066684790471696673115853886839517524034652205879575675860060479596884E-10",
      "binomial_distinct_at_least_four_per_window": "7.755444986724465386016000433480498217837473402154373163443878832004607E-11",
      "poisson_exact_four_annual": "5.9813138934377400291138269888299812384649058445597602669989218E-9",
      "poisson_at_least_four_annual": "5.9898453442598676236636796932708610215195891029055258780439849E-9",
      "binomial_distinct_at_least_four_annual": "4.3549806370773764248406860540286319720238749550724359402841685E-9",
      "printed_periods": "56",
      "printed_poisson_annual": "5.9649267321347299183591208371429800780147590017386169777586444E-9"
    },
    {
      "id": "double-window",
      "rate_per_drive_year": "0.0041",
      "window_hours": "312",
      "periods_per_365_day_year": "28.07692307692307692307692307692307692307692307692307692307692307692308",
      "poisson_exact_four_per_window": "3.022579561629229269973041452637392478725107216130455949774712488910992E-12",
      "poisson_at_least_four_per_window": "3.024345939073350122913213117414950839694317675916467823931545667532449E-12",
      "binomial_distinct_at_least_four_per_window": "2.198328564717680599820250662814096691140675228131349777044075511309549E-12",
      "poisson_exact_four_annual": "8.48647338422709885674540285114422208937264963631089913942780E-11",
      "poisson_at_least_four_annual": "8.49143282858903216440491819489347207586221144721336282125096E-11",
      "binomial_distinct_at_least_four_annual": "6.17223020075440538928825804498845052971500169738660161936826E-11",
      "printed_periods": "28",
      "printed_poisson_annual": "8.46322277221650163953244598011419828357165467270037860150917E-11"
    }
  ],
  "expectationExample": {
    "objects": "10000000",
    "annual_probability_per_object": "1E-11",
    "expected_losses_in_one_year": "0.00010000000",
    "probability_any_loss_one_year_if_independent": "0.0000999950001671624500858351940080646150886042206173162910924636504754",
    "probability_any_loss_10000_years_if_independent": "0.6321205588303970756103411056015411947741378689578164380524741452016891",
    "note": "Same object-year independence assumption throughout; extrapolation illustrates expectation, not a forecast."
  }
}