{
  "schemaVersion": 1,
  "generatedOn": "2026-10-15",
  "kind": "printed-count arithmetic and synthetic counterexamples",
  "sourceCodeSha256": "32858230b5b2611f200bc20f25f37f1e87ddcfa9669c5781efedb348b71fc270",
  "runtime": "Python 3.12+ standard library; no random seed or third-party data",
  "observed_counts": [
    {
      "medium": "HDD",
      "drives": 458482,
      "groups": 38029,
      "drive_hours": 857183442,
      "slow_drive_hours": 1885804,
      "group_hours": 72046373,
      "tail_group_hours": 1109514,
      "slow_drive_hour_percent": 0.2200000498843047,
      "tail_group_hour_percent": 1.539999799851132,
      "slow_drives_per_tail_group_hour": 1.6996667009158966,
      "source": "https://www.usenix.org/system/files/conference/fast16/fast16-papers-hao.pdf",
      "locator": "Table 1, printed page 265"
    },
    {
      "medium": "SSD",
      "drives": 4069,
      "groups": 572,
      "drive_hours": 7481055,
      "slow_drive_hours": 43016,
      "group_hours": 1072690,
      "tail_group_hours": 23964,
      "slow_drive_hour_percent": 0.5749991144297162,
      "tail_group_hour_percent": 2.2340098257651326,
      "slow_drives_per_tail_group_hour": 1.7950258721415457,
      "source": "https://www.usenix.org/system/files/conference/fast16/fast16-papers-hao.pdf",
      "locator": "Table 1, printed page 265"
    }
  ],
  "fanout": [
    {
      "p": 0.01,
      "n": 100,
      "independent_any_slow": 0.6339676587267705,
      "equal_marginal_lower_bound": 0.01,
      "equal_marginal_upper_bound": 1.0,
      "independent_conditional_count": 1.5773675300856054
    },
    {
      "p": 0.0001,
      "n": 2000,
      "independent_any_slow": 0.1812774347344685,
      "equal_marginal_lower_bound": 0.0001,
      "equal_marginal_upper_bound": 0.2,
      "independent_conditional_count": 1.1032812787369588
    }
  ],
  "same_mean": [
    {
      "scenario": "Uniform",
      "observations": 1000,
      "mean_ms": 10.0,
      "p99_ms": 10,
      "p999_ms": 10
    },
    {
      "scenario": "Bursty",
      "observations": 1000,
      "mean_ms": 10.0,
      "p99_ms": 1,
      "p999_ms": 901
    }
  ],
  "common_mode": [
    {
      "latencies_ms": [
        10,
        10,
        10
      ],
      "ratios_to_group_median": [
        1,
        1,
        1
      ]
    },
    {
      "latencies_ms": [
        100,
        100,
        100
      ],
      "ratios_to_group_median": [
        1,
        1,
        1
      ]
    }
  ],
  "limitations": [
    "No request traces or joint group histories were analyzed.",
    "Hourly co-classification is not necessarily simultaneous request delay.",
    "The conditional multiplicity is not a test of drive independence.",
    "Fanout examples require equal marginals, a fixed event and wait-for-all completion.",
    "Probability bounds permit arbitrary dependence, not an estimated confidence interval.",
    "Synthetic nearest-rank percentiles are examples, not observed device performance.",
    "No fleet confidence intervals are inferred from correlated aggregate counts."
  ]
}