{
  "generatedAt": "2026-10-02T10:00:00+02:00",
  "method": "Exact negative-binomial arrival count combined with gambler's-ruin catch-up probability",
  "assumptions": [
    "Attacker and honest miners find blocks independently at constant relative shares q and p=1-q.",
    "Block discoveries are memoryless; network delay, stale blocks, eclipse attacks and difficulty changes are excluded.",
    "The attacker begins a private competing branch when the payment is broadcast and continues indefinitely.",
    "A tie is counted as attacker success, making the result conservative for tie-breaking but not a universal security bound."
  ],
  "sixConfirmations": {
    "0.05": 0.000011602690117462622,
    "0.10": 0.0005914121599998046,
    "0.20": 0.023308410879999575,
    "0.30": 0.15644958192000047,
    "0.40": 0.49300373504000017
  },
  "comparisonAtQ10Z6": {
    "exact": 0.0005914121599998046,
    "nakamotoPoisson": 0.00024280274536281864,
    "ratio": 2.4357721290015113
  },
  "independentIdentityCheck": {
    "identity": "P(z,q) = 2 * Pr[Binomial(2z-1,q) >= z]",
    "maximumAbsoluteDifference": 5.0790450268961215e-15,
    "grid": "z=1..60; q=0.05,0.1,0.2,0.3,0.4"
  },
  "thresholds": [
    {
      "attackerShare": 0.05,
      "confirmations": {
        "0.001": 4,
        "0.0001": 5,
        "0.000001": 8
      }
    },
    {
      "attackerShare": 0.1,
      "confirmations": {
        "0.001": 6,
        "0.0001": 8,
        "0.000001": 12
      }
    },
    {
      "attackerShare": 0.2,
      "confirmations": {
        "0.001": 13,
        "0.0001": 18,
        "0.000001": 28
      }
    },
    {
      "attackerShare": 0.3,
      "confirmations": {
        "0.001": 32,
        "0.0001": 44,
        "0.000001": 69
      }
    },
    {
      "attackerShare": 0.4,
      "confirmations": {
        "0.001": 133,
        "0.0001": 186,
        "0.000001": 294
      }
    }
  ]
}