{
  "modelVersion": "1.1.0",
  "illustrative": true,
  "risks": [
    {
      "name": "Dispatch interruption",
      "cause": "Safeguard does not affect the stated causal path",
      "event": "Dispatch cannot continue",
      "consequence": "One annual loss event affects contribution",
      "probability": 20,
      "impact": 1000,
      "prevention": 0,
      "mitigation": 0,
      "reliability": 90,
      "controlCost": 30,
      "grossLoss": 200,
      "residualLoss": 200,
      "residualProbability": 0.2,
      "residualImpact": 1000,
      "avoidedLoss": 0,
      "netControlValue": -30,
      "breakEvenReliability": null,
      "stressedGrossProbability": 0.3,
      "stressedReliability": 70,
      "stressedProbability": 0.3,
      "stressedImpact": 1250,
      "stressedLoss": 375
    }
  ],
  "grossLoss": 200,
  "residualLoss": 200,
  "stressedLoss": 375,
  "controlCost": 30,
  "avoidedLoss": 0,
  "netControlValue": -30,
  "operatingStates": [
    {
      "name": "Dispatch interruption",
      "state": "Controls unavailable",
      "stateProbability": 0.1,
      "eventProbability": 0.2,
      "eventSeverity": 1000,
      "weightedLoss": 20
    },
    {
      "name": "Dispatch interruption",
      "state": "Controls available",
      "stateProbability": 0.9,
      "eventProbability": 0.2,
      "eventSeverity": 1000,
      "weightedLoss": 180
    }
  ],
  "reliabilitySweep": [
    {
      "reliability": 0,
      "expectedLoss": 200,
      "totalCost": 230
    },
    {
      "reliability": 10,
      "expectedLoss": 200,
      "totalCost": 230
    },
    {
      "reliability": 20,
      "expectedLoss": 200,
      "totalCost": 230
    },
    {
      "reliability": 30,
      "expectedLoss": 200,
      "totalCost": 230
    },
    {
      "reliability": 40,
      "expectedLoss": 200,
      "totalCost": 230
    },
    {
      "reliability": 50,
      "expectedLoss": 200,
      "totalCost": 230
    },
    {
      "reliability": 60,
      "expectedLoss": 200,
      "totalCost": 230
    },
    {
      "reliability": 70,
      "expectedLoss": 200,
      "totalCost": 230
    },
    {
      "reliability": 80,
      "expectedLoss": 200,
      "totalCost": 230
    },
    {
      "reliability": 90,
      "expectedLoss": 200,
      "totalCost": 230
    },
    {
      "reliability": 100,
      "expectedLoss": 200,
      "totalCost": 230
    }
  ],
  "exactEvaluation": {
    "interpretation": "Rational evaluation of the canonical decimal spelling of validated Number inputs. Avoided loss is evaluated directly; net value is summed before numeric display conversion. Each decimal record has forty significant digits. JSON parsing can lose digits before evaluation; the record does not recover them.",
    "grossLoss": {
      "numerator": "200",
      "denominator": "1",
      "decimal": "2.000000000000000000000000000000000000000e2"
    },
    "residualLoss": {
      "numerator": "200",
      "denominator": "1",
      "decimal": "2.000000000000000000000000000000000000000e2"
    },
    "stressedLoss": {
      "numerator": "375",
      "denominator": "1",
      "decimal": "3.750000000000000000000000000000000000000e2"
    },
    "controlCost": {
      "numerator": "30",
      "denominator": "1",
      "decimal": "3.000000000000000000000000000000000000000e1"
    },
    "avoidedLoss": {
      "numerator": "0",
      "denominator": "1",
      "decimal": "0"
    },
    "netControlValue": {
      "numerator": "-30",
      "denominator": "1",
      "decimal": "-3.000000000000000000000000000000000000000e1"
    },
    "risks": [
      {
        "name": "Dispatch interruption",
        "grossLoss": {
          "numerator": "200",
          "denominator": "1",
          "decimal": "2.000000000000000000000000000000000000000e2"
        },
        "residualLoss": {
          "numerator": "200",
          "denominator": "1",
          "decimal": "2.000000000000000000000000000000000000000e2"
        },
        "residualProbability": {
          "numerator": "1",
          "denominator": "5",
          "decimal": "2.000000000000000000000000000000000000000e-1"
        },
        "residualImpact": {
          "numerator": "1000",
          "denominator": "1",
          "decimal": "1.000000000000000000000000000000000000000e3"
        },
        "avoidedLoss": {
          "numerator": "0",
          "denominator": "1",
          "decimal": "0"
        },
        "netControlValue": {
          "numerator": "-30",
          "denominator": "1",
          "decimal": "-3.000000000000000000000000000000000000000e1"
        },
        "breakEvenReliability": null,
        "stressedGrossProbability": {
          "numerator": "3",
          "denominator": "10",
          "decimal": "3.000000000000000000000000000000000000000e-1"
        },
        "stressedReliability": {
          "numerator": "70",
          "denominator": "1",
          "decimal": "7.000000000000000000000000000000000000000e1"
        },
        "stressedProbability": {
          "numerator": "3",
          "denominator": "10",
          "decimal": "3.000000000000000000000000000000000000000e-1"
        },
        "stressedImpact": {
          "numerator": "1250",
          "denominator": "1",
          "decimal": "1.250000000000000000000000000000000000000e3"
        },
        "stressedLoss": {
          "numerator": "375",
          "denominator": "1",
          "decimal": "3.750000000000000000000000000000000000000e2"
        }
      }
    ],
    "operatingStates": [
      {
        "name": "Dispatch interruption",
        "state": "Controls unavailable",
        "stateProbability": {
          "numerator": "1",
          "denominator": "10",
          "decimal": "1.000000000000000000000000000000000000000e-1"
        },
        "eventProbability": {
          "numerator": "1",
          "denominator": "5",
          "decimal": "2.000000000000000000000000000000000000000e-1"
        },
        "eventSeverity": {
          "numerator": "1000",
          "denominator": "1",
          "decimal": "1.000000000000000000000000000000000000000e3"
        },
        "weightedLoss": {
          "numerator": "20",
          "denominator": "1",
          "decimal": "2.000000000000000000000000000000000000000e1"
        }
      },
      {
        "name": "Dispatch interruption",
        "state": "Controls available",
        "stateProbability": {
          "numerator": "9",
          "denominator": "10",
          "decimal": "9.000000000000000000000000000000000000000e-1"
        },
        "eventProbability": {
          "numerator": "1",
          "denominator": "5",
          "decimal": "2.000000000000000000000000000000000000000e-1"
        },
        "eventSeverity": {
          "numerator": "1000",
          "denominator": "1",
          "decimal": "1.000000000000000000000000000000000000000e3"
        },
        "weightedLoss": {
          "numerator": "180",
          "denominator": "1",
          "decimal": "1.800000000000000000000000000000000000000e2"
        }
      }
    ],
    "reliabilitySweep": [
      {
        "reliability": 0,
        "expectedLoss": {
          "numerator": "200",
          "denominator": "1",
          "decimal": "2.000000000000000000000000000000000000000e2"
        },
        "totalCost": {
          "numerator": "230",
          "denominator": "1",
          "decimal": "2.300000000000000000000000000000000000000e2"
        }
      },
      {
        "reliability": 10,
        "expectedLoss": {
          "numerator": "200",
          "denominator": "1",
          "decimal": "2.000000000000000000000000000000000000000e2"
        },
        "totalCost": {
          "numerator": "230",
          "denominator": "1",
          "decimal": "2.300000000000000000000000000000000000000e2"
        }
      },
      {
        "reliability": 20,
        "expectedLoss": {
          "numerator": "200",
          "denominator": "1",
          "decimal": "2.000000000000000000000000000000000000000e2"
        },
        "totalCost": {
          "numerator": "230",
          "denominator": "1",
          "decimal": "2.300000000000000000000000000000000000000e2"
        }
      },
      {
        "reliability": 30,
        "expectedLoss": {
          "numerator": "200",
          "denominator": "1",
          "decimal": "2.000000000000000000000000000000000000000e2"
        },
        "totalCost": {
          "numerator": "230",
          "denominator": "1",
          "decimal": "2.300000000000000000000000000000000000000e2"
        }
      },
      {
        "reliability": 40,
        "expectedLoss": {
          "numerator": "200",
          "denominator": "1",
          "decimal": "2.000000000000000000000000000000000000000e2"
        },
        "totalCost": {
          "numerator": "230",
          "denominator": "1",
          "decimal": "2.300000000000000000000000000000000000000e2"
        }
      },
      {
        "reliability": 50,
        "expectedLoss": {
          "numerator": "200",
          "denominator": "1",
          "decimal": "2.000000000000000000000000000000000000000e2"
        },
        "totalCost": {
          "numerator": "230",
          "denominator": "1",
          "decimal": "2.300000000000000000000000000000000000000e2"
        }
      },
      {
        "reliability": 60,
        "expectedLoss": {
          "numerator": "200",
          "denominator": "1",
          "decimal": "2.000000000000000000000000000000000000000e2"
        },
        "totalCost": {
          "numerator": "230",
          "denominator": "1",
          "decimal": "2.300000000000000000000000000000000000000e2"
        }
      },
      {
        "reliability": 70,
        "expectedLoss": {
          "numerator": "200",
          "denominator": "1",
          "decimal": "2.000000000000000000000000000000000000000e2"
        },
        "totalCost": {
          "numerator": "230",
          "denominator": "1",
          "decimal": "2.300000000000000000000000000000000000000e2"
        }
      },
      {
        "reliability": 80,
        "expectedLoss": {
          "numerator": "200",
          "denominator": "1",
          "decimal": "2.000000000000000000000000000000000000000e2"
        },
        "totalCost": {
          "numerator": "230",
          "denominator": "1",
          "decimal": "2.300000000000000000000000000000000000000e2"
        }
      },
      {
        "reliability": 90,
        "expectedLoss": {
          "numerator": "200",
          "denominator": "1",
          "decimal": "2.000000000000000000000000000000000000000e2"
        },
        "totalCost": {
          "numerator": "230",
          "denominator": "1",
          "decimal": "2.300000000000000000000000000000000000000e2"
        }
      },
      {
        "reliability": 100,
        "expectedLoss": {
          "numerator": "200",
          "denominator": "1",
          "decimal": "2.000000000000000000000000000000000000000e2"
        },
        "totalCost": {
          "numerator": "230",
          "denominator": "1",
          "decimal": "2.300000000000000000000000000000000000000e2"
        }
      }
    ]
  },
  "metrics": [
    {
      "key": "gross",
      "label": "Gross annual expected loss",
      "value": 200,
      "unit": "USDk/year",
      "detail": ""
    },
    {
      "key": "residual",
      "label": "Residual annual expected loss",
      "value": 200,
      "unit": "USDk/year",
      "detail": ""
    },
    {
      "key": "stress",
      "label": "Stressed annual expected loss",
      "value": 375,
      "unit": "USDk/year",
      "detail": ""
    },
    {
      "key": "controls",
      "label": "Net annual control value",
      "value": -30,
      "unit": "USDk/year",
      "detail": "Avoided expected loss less annual control cost."
    }
  ],
  "tables": [
    {
      "title": "Risk and control expected-loss ledger",
      "columns": [
        {
          "key": "name",
          "label": "Risk",
          "unit": ""
        },
        {
          "key": "probability",
          "label": "Gross annual probability",
          "unit": "%"
        },
        {
          "key": "impact",
          "label": "Gross event severity",
          "unit": "USDk"
        },
        {
          "key": "grossLoss",
          "label": "Gross expected loss",
          "unit": "USDk/year"
        },
        {
          "key": "residualProbability",
          "label": "Residual event probability",
          "unit": ""
        },
        {
          "key": "residualImpact",
          "label": "Event-conditional severity",
          "unit": "USDk"
        },
        {
          "key": "residualLoss",
          "label": "Residual expected loss",
          "unit": "USDk/year"
        },
        {
          "key": "controlCost",
          "label": "Annual control cost",
          "unit": "USDk"
        },
        {
          "key": "netControlValue",
          "label": "Net control value",
          "unit": "USDk/year"
        },
        {
          "key": "breakEvenReliability",
          "label": "Break-even shared availability",
          "unit": "%"
        }
      ],
      "rows": [
        {
          "name": "Dispatch interruption",
          "cause": "Safeguard does not affect the stated causal path",
          "event": "Dispatch cannot continue",
          "consequence": "One annual loss event affects contribution",
          "probability": 20,
          "impact": 1000,
          "prevention": 0,
          "mitigation": 0,
          "reliability": 90,
          "controlCost": 30,
          "grossLoss": 200,
          "residualLoss": 200,
          "residualProbability": 0.2,
          "residualImpact": 1000,
          "avoidedLoss": 0,
          "netControlValue": -30,
          "breakEvenReliability": null,
          "stressedGrossProbability": 0.3,
          "stressedReliability": 70,
          "stressedProbability": 0.3,
          "stressedImpact": 1250,
          "stressedLoss": 375
        }
      ]
    },
    {
      "title": "Shared control availability mixture",
      "columns": [
        {
          "key": "name",
          "label": "Risk",
          "unit": ""
        },
        {
          "key": "state",
          "label": "Shared control state",
          "unit": ""
        },
        {
          "key": "stateProbability",
          "label": "State weight",
          "unit": ""
        },
        {
          "key": "eventProbability",
          "label": "Event probability in state",
          "unit": ""
        },
        {
          "key": "eventSeverity",
          "label": "Severity in state",
          "unit": "USDk"
        },
        {
          "key": "weightedLoss",
          "label": "Expected-loss contribution",
          "unit": "USDk/year"
        }
      ],
      "rows": [
        {
          "name": "Dispatch interruption",
          "state": "Controls unavailable",
          "stateProbability": 0.1,
          "eventProbability": 0.2,
          "eventSeverity": 1000,
          "weightedLoss": 20
        },
        {
          "name": "Dispatch interruption",
          "state": "Controls available",
          "stateProbability": 0.9,
          "eventProbability": 0.2,
          "eventSeverity": 1000,
          "weightedLoss": 180
        }
      ]
    },
    {
      "title": "Stress mechanism ledger",
      "columns": [
        {
          "key": "name",
          "label": "Risk",
          "unit": ""
        },
        {
          "key": "stressedGrossProbability",
          "label": "Stressed gross probability",
          "unit": ""
        },
        {
          "key": "stressedReliability",
          "label": "Stressed shared availability",
          "unit": "%"
        },
        {
          "key": "stressedProbability",
          "label": "Residual event probability",
          "unit": ""
        },
        {
          "key": "stressedImpact",
          "label": "Event-conditional severity",
          "unit": "USDk"
        },
        {
          "key": "stressedLoss",
          "label": "Expected loss",
          "unit": "USDk/year"
        }
      ],
      "rows": [
        {
          "name": "Dispatch interruption",
          "cause": "Safeguard does not affect the stated causal path",
          "event": "Dispatch cannot continue",
          "consequence": "One annual loss event affects contribution",
          "probability": 20,
          "impact": 1000,
          "prevention": 0,
          "mitigation": 0,
          "reliability": 90,
          "controlCost": 30,
          "grossLoss": 200,
          "residualLoss": 200,
          "residualProbability": 0.2,
          "residualImpact": 1000,
          "avoidedLoss": 0,
          "netControlValue": -30,
          "breakEvenReliability": null,
          "stressedGrossProbability": 0.3,
          "stressedReliability": 70,
          "stressedProbability": 0.3,
          "stressedImpact": 1250,
          "stressedLoss": 375
        }
      ]
    },
    {
      "title": "Uniform shared-availability sensitivity",
      "columns": [
        {
          "key": "reliability",
          "label": "Shared availability for every risk",
          "unit": "%"
        },
        {
          "key": "expectedLoss",
          "label": "Residual expected loss",
          "unit": "USDk/year"
        },
        {
          "key": "totalCost",
          "label": "Loss plus control cost",
          "unit": "USDk/year"
        }
      ],
      "rows": [
        {
          "reliability": 0,
          "expectedLoss": 200,
          "totalCost": 230
        },
        {
          "reliability": 10,
          "expectedLoss": 200,
          "totalCost": 230
        },
        {
          "reliability": 20,
          "expectedLoss": 200,
          "totalCost": 230
        },
        {
          "reliability": 30,
          "expectedLoss": 200,
          "totalCost": 230
        },
        {
          "reliability": 40,
          "expectedLoss": 200,
          "totalCost": 230
        },
        {
          "reliability": 50,
          "expectedLoss": 200,
          "totalCost": 230
        },
        {
          "reliability": 60,
          "expectedLoss": 200,
          "totalCost": 230
        },
        {
          "reliability": 70,
          "expectedLoss": 200,
          "totalCost": 230
        },
        {
          "reliability": 80,
          "expectedLoss": 200,
          "totalCost": 230
        },
        {
          "reliability": 90,
          "expectedLoss": 200,
          "totalCost": 230
        },
        {
          "reliability": 100,
          "expectedLoss": 200,
          "totalCost": 230
        }
      ]
    }
  ],
  "warnings": [
    "At least one control cannot recover its annual cost through expected-loss reduction even at 100% shared availability. Other objectives may still justify it.",
    "Prevention and mitigation share one Bernoulli availability state. Residual loss is a mixture of available and unavailable controls; multiplying their marginal effects would incorrectly imply independent operation."
  ],
  "summary": "The supplied controls reduce annual expected loss from 200 to 200 USDk, at a cost of 30 USDk/year. Net control value is -30 USDk/year. The stressed control system produces 375 USDk/year of expected loss. These sums describe expectations, not a maximum loss or tail confidence level.",
  "methods": [
    "Gross expected loss = probability × event impact.",
    "Controls share one Bernoulli availability state. Residual expected loss = gross expected loss × [(1 − reliability) + reliability × (1 − prevention) × (1 − mitigation)].",
    "Expected avoided loss = gross expected loss × shared availability × (prevention + mitigation − prevention × mitigation). Net control value = avoided expected loss − annual control cost.",
    "Stress changes gross probability and impact and reduces control reliability; probabilities cap at one with an explicit warning.",
    "Residual event probability is a marginal; severity is conditional on an event. Break-even availability = annual control cost / [gross expected loss × (prevention + mitigation − prevention × mitigation)], if attainable.",
    "Event-conditional severity is unavailable when the marginal event probability is zero. A zero monetary severity remains meaningful when the event population exists.",
    "Complements, stress clipping, control-value sums and break-even comparisons use exact rational arithmetic for canonical decimal input numbers. JSON exports retain numerator, denominator and a forty-significant-digit decimal; metrics and charts use numeric approximations.",
    "Equal exact residual losses use literal name order independent of browser language for consistent display; this name order is not a causal risk distinction."
  ],
  "limitations": [
    "One annual event per risk model, additive expected losses and one shared Bernoulli availability state for prevention and mitigation.",
    "No tail distribution, correlation, causal estimation, insurance recovery or regulatory adequacy is inferred.",
    "Effectiveness and reliability can double count uncertainty unless users define them separately.",
    "Numerical input precision: use zero or absolute values of at least 0.000000001. Smaller nonzero inputs are rejected explicitly.",
    "Canonical decimal evaluation begins after JSON numbers have been parsed. Digits already lost during parsing cannot be recovered. Equal rounded gross and residual means do not establish zero avoided loss; retain the direct avoided-loss and net-value outputs."
  ]
}