{
  "schema": "scorecompute.engine-examples.v1",
  "recorded_on": "2026-11-06",
  "endpoint": "https://scorecompute.com/mcp",
  "service_release": "0.17.1",
  "note": "Each published example called once through the public MCP endpoint. response_sha256 covers the response serialized as sorted-key compact UTF-8 JSON. Elapsed times vary between runs. A recorded response shows what the tool returned for these inputs; it does not certify the model or other inputs.",
  "engines": {
    "propagate_uncertainty": {
      "tool": "propagate_uncertainty",
      "arguments": {
        "expression": "x1 * x2",
        "variables": [
          {
            "name": "x1",
            "value": 1,
            "distribution": "normal",
            "standard_uncertainty": 1,
            "unit": ""
          },
          {
            "name": "x2",
            "value": 1,
            "distribution": "normal",
            "standard_uncertainty": 1,
            "unit": ""
          }
        ],
        "coverage": 0.95,
        "samples": 200000,
        "seed": 7
      },
      "response_sha256": "1f2e79db5bfe4b9b8f01769842d90493a095a149c084bd501ac5e9896069e0d8",
      "response": {
        "contract_version": "0.1.0",
        "status": "evaluated",
        "verdict": "linearization_inadequate",
        "diagnostic": null,
        "unit": "1",
        "dimension": "1",
        "gum": {
          "value": 1,
          "standard_uncertainty": 1.4142135623730951,
          "coverage_factor": 1.959963986120195,
          "expanded_uncertainty": 2.7718076509340124,
          "interval": [
            -1.7718076509340124,
            3.7718076509340124
          ]
        },
        "monte_carlo": {
          "draws": 200000,
          "finite_draws": 200000,
          "nonfinite_fraction": 0,
          "mean": 0.9917114807823371,
          "standard_deviation": 1.731517193609199,
          "symmetric_interval": [
            -1.744741348335197,
            5.294808742654364
          ],
          "shortest_interval": [
            -1.998506604626448,
            4.9671020860898745
          ],
          "blocks": 10,
          "stability": {
            "mean_standard_error": 0.0035585134340418824,
            "standard_deviation_standard_error": 0.0027595699295887353,
            "low_standard_error": 0.011450522992292697,
            "high_standard_error": 0.01619590059392617,
            "numerical_tolerance": 0.05,
            "stable": true
          }
        },
        "validation": {
          "numerical_tolerance": 0.05,
          "low_difference": 0.027066302598815373,
          "high_difference": 1.523001091720352,
          "adequate": false
        },
        "budget": [
          {
            "name": "x1",
            "unit": "1",
            "value": 1,
            "distribution": "normal",
            "standard_uncertainty": 1,
            "sensitivity": 1,
            "contribution": 1,
            "variance_share": 0.5
          },
          {
            "name": "x2",
            "unit": "1",
            "value": 1,
            "distribution": "normal",
            "standard_uncertainty": 1,
            "sensitivity": 1,
            "contribution": 1,
            "variance_share": 0.5
          }
        ],
        "correlation_variance_share": 0,
        "recommended": {
          "method": "monte_carlo",
          "value": 0.9917114807823371,
          "standard_uncertainty": 1.731517193609199,
          "interval": [
            -1.744741348335197,
            5.294808742654364
          ]
        },
        "statement": "y = 1.0 1, standard uncertainty 1.7 1; 95% coverage interval [-1.7, 5.3] 1 (Monte Carlo, 200000 draws). The first-order GUM interval differs by more than the numerical tolerance and should not be used for this model.",
        "notes": [],
        "assumptions": [
          "The model is exactly the supplied expression; unlisted influences and definitional uncertainty are not included.",
          "Inputs are independent unless a correlation is declared; correlations are supported between normal inputs only.",
          "normal: standard_uncertainty is the standard deviation. uniform and triangular: half_width is the half-width of a symmetric distribution centred on value.",
          "The first-order coverage factor comes from the normal distribution; no Welch–Satterthwaite effective degrees of freedom are applied.",
          "Numeric literals are dimensionless. Affine temperature units (°C, °F) are refused; use K.",
          "The Monte Carlo interval is probabilistically symmetric; the shortest interval is reported separately."
        ],
        "coverage": 0.95,
        "samples": 200000,
        "seed": 7,
        "method": "First-order GUM propagation (JCGM 100:2008) with exact forward-mode derivatives; Monte Carlo propagation (JCGM 101:2008) with SplitMix64, Box–Muller and 10 independently seeded blocks; JCGM 101 §8 validation of the first-order interval; block spread checked against the 2-significant-digit numerical tolerance.",
        "engine": "rust-cpu",
        "elapsed_ms": 158.301476,
        "provenance": {
          "tool": "propagate_uncertainty",
          "server": "scorecompute",
          "client": {
            "name": "scorecompute-docs-recording",
            "version": "1.0"
          },
          "identity_source": "MCP clientInfo (self-reported)",
          "model": null
        }
      }
    },
    "propagate_uncertainty_product": {
      "tool": "propagate_uncertainty",
      "arguments": {
        "expression": "x1 * x2",
        "variables": [
          {
            "name": "x1",
            "value": 10,
            "distribution": "normal",
            "standard_uncertainty": 0.2,
            "unit": ""
          },
          {
            "name": "x2",
            "value": 5,
            "distribution": "normal",
            "standard_uncertainty": 0.1,
            "unit": ""
          }
        ],
        "coverage": 0.95,
        "samples": 200000,
        "seed": 7
      },
      "response_sha256": "9b429a4649afb19e4fedd7737c06e853dbbfb25ab8b1c233c8af51e444d12fb6",
      "response": {
        "contract_version": "0.1.0",
        "status": "evaluated",
        "verdict": "linearization_adequate",
        "diagnostic": null,
        "unit": "1",
        "dimension": "1",
        "gum": {
          "value": 50,
          "standard_uncertainty": 1.4142135623730951,
          "coverage_factor": 1.959963986120195,
          "expanded_uncertainty": 2.7718076509340124,
          "interval": [
            47.228192349065985,
            52.771807650934015
          ]
        },
        "monte_carlo": {
          "draws": 200000,
          "finite_draws": 200000,
          "nonfinite_fraction": 0,
          "mean": 49.99478371659442,
          "standard_deviation": 1.4140172815916268,
          "symmetric_interval": [
            47.25631579953347,
            52.79365035288087
          ],
          "shortest_interval": [
            47.249695328298095,
            52.78476287308614
          ],
          "blocks": 10,
          "stability": {
            "mean_standard_error": 0.00296630163347803,
            "standard_deviation_standard_error": 0.0020765268817084202,
            "low_standard_error": 0.006926486576880078,
            "high_standard_error": 0.00651865382354911,
            "numerical_tolerance": 0.05,
            "stable": true
          }
        },
        "validation": {
          "numerical_tolerance": 0.05,
          "low_difference": 0.02812345046748277,
          "high_difference": 0.021842701946852117,
          "adequate": true
        },
        "budget": [
          {
            "name": "x1",
            "unit": "1",
            "value": 10,
            "distribution": "normal",
            "standard_uncertainty": 0.2,
            "sensitivity": 5,
            "contribution": 1,
            "variance_share": 0.5
          },
          {
            "name": "x2",
            "unit": "1",
            "value": 5,
            "distribution": "normal",
            "standard_uncertainty": 0.1,
            "sensitivity": 10,
            "contribution": 1,
            "variance_share": 0.5
          }
        ],
        "correlation_variance_share": 0,
        "recommended": {
          "method": "gum_first_order",
          "value": 50,
          "standard_uncertainty": 1.4142135623730951,
          "interval": [
            47.228192349065985,
            52.771807650934015
          ]
        },
        "statement": "y = 50.0 1, standard uncertainty 1.4 1; 95% coverage interval [47.2, 52.8] 1 (first-order GUM, k = 1.960; confirmed by 200000 Monte Carlo draws).",
        "notes": [],
        "assumptions": [
          "The model is exactly the supplied expression; unlisted influences and definitional uncertainty are not included.",
          "Inputs are independent unless a correlation is declared; correlations are supported between normal inputs only.",
          "normal: standard_uncertainty is the standard deviation. uniform and triangular: half_width is the half-width of a symmetric distribution centred on value.",
          "The first-order coverage factor comes from the normal distribution; no Welch–Satterthwaite effective degrees of freedom are applied.",
          "Numeric literals are dimensionless. Affine temperature units (°C, °F) are refused; use K.",
          "The Monte Carlo interval is probabilistically symmetric; the shortest interval is reported separately."
        ],
        "coverage": 0.95,
        "samples": 200000,
        "seed": 7,
        "method": "First-order GUM propagation (JCGM 100:2008) with exact forward-mode derivatives; Monte Carlo propagation (JCGM 101:2008) with SplitMix64, Box–Muller and 10 independently seeded blocks; JCGM 101 §8 validation of the first-order interval; block spread checked against the 2-significant-digit numerical tolerance.",
        "engine": "rust-cpu",
        "elapsed_ms": 34.904956,
        "provenance": {
          "tool": "propagate_uncertainty",
          "server": "scorecompute",
          "client": {
            "name": "scorecompute-docs-recording",
            "version": "1.0"
          },
          "identity_source": "MCP clientInfo (self-reported)",
          "model": null
        }
      }
    },
    "simulate_plan": {
      "tool": "simulate_plan",
      "arguments": {
        "durations": [
          60,
          30
        ],
        "budget": 100,
        "samples": 100000,
        "seed": 42,
        "uncertainty": 0.25
      },
      "response_sha256": "b558af85cb81716f6ca8b67ee9d2e60862dc97a7acc97d6d568ed5bd7869d8a8",
      "response": {
        "success_rate": 0.8254,
        "mean_duration": 89.96684030406585,
        "p95_duration": 105.77462346362617,
        "samples": 100000,
        "elapsed_ms": 8.803649,
        "method": "Durées indépendantes, variations uniformes symétriques ; quantile empirique à 95 %. Modèle illustratif, pas une prévision.",
        "provenance": {
          "tool": "simulate_plan",
          "server": "scorecompute",
          "client": {
            "name": "scorecompute-docs-recording",
            "version": "1.0"
          },
          "identity_source": "MCP clientInfo (self-reported)",
          "model": null
        }
      }
    },
    "audit_statistics_grimmer_reachable": {
      "tool": "audit_statistics",
      "arguments": {
        "n": 5,
        "mean": 3,
        "sd": 1,
        "decimals": 2,
        "min_value": 1,
        "max_value": 5
      },
      "response_sha256": "c42330dd3a7060ae0256bcdad73f83ea811fd0f6691821950bc5f367a68f47ee",
      "response": {
        "n": 5,
        "min_value": 1,
        "max_value": 5,
        "decimals": 2,
        "sum_needed": 15,
        "sum_round": 15,
        "mean_reported": 3,
        "mean_nearest_attainable": 3,
        "mean_consistent": true,
        "sd_reported": 1,
        "sd_attainable_min": 0,
        "sd_attainable_max": 2,
        "sd_nearest_attainable": 1,
        "sd_consistent": true,
        "verdict": "consistant",
        "issues": [],
        "elapsed_ms": 0.001142,
        "method": "Contrôles nécessaires GRIM (moyenne) et GRIMMER (écart-type d’échantillon, diviseur n−1) pour des valeurs entières bornées. Toutes les sommes compatibles avec les intervalles de demi-arrondi sont examinées ; les sommes des carrés sont filtrées par leurs bornes exactes et leur parité. Consistant signifie que ces filtres ne détectent pas d’incohérence : ce n’est pas une preuve d’existence d’un jeu de données. sd_nearest_attainable désigne le candidat le plus proche passant ces filtres. Les arrondis aux frontières sont acceptés dans les deux sens. Une incohérence ne prouve jamais une fraude.",
        "engine": "rust-cpu",
        "provenance": {
          "tool": "audit_statistics",
          "server": "scorecompute",
          "client": {
            "name": "scorecompute-docs-recording",
            "version": "1.0"
          },
          "identity_source": "MCP clientInfo (self-reported)",
          "model": null
        }
      }
    },
    "audit_statistics_grimmer_unreachable": {
      "tool": "audit_statistics",
      "arguments": {
        "n": 5,
        "mean": 3,
        "sd": 0.8,
        "decimals": 2,
        "min_value": 1,
        "max_value": 5
      },
      "response_sha256": "ed75bf7d7dcc5bbd031a025246a21ba11bc637159fa2a84d04ade370984b9564",
      "response": {
        "n": 5,
        "min_value": 1,
        "max_value": 5,
        "decimals": 2,
        "sum_needed": 15,
        "sum_round": 15,
        "mean_reported": 3,
        "mean_nearest_attainable": 3,
        "mean_consistent": true,
        "sd_reported": 0.8,
        "sd_attainable_min": 0,
        "sd_attainable_max": 2,
        "sd_nearest_attainable": 0.7071067811865476,
        "sd_consistent": false,
        "verdict": "inconsistant",
        "issues": [
          "L’écart-type 0.8 échoue aux contraintes de bornes et de parité pour toutes les sommes compatibles avec l’arrondi de la moyenne : n = 5, bornes d’écart-type 0.0000 à 2.0000, candidat le plus proche 0.7071."
        ],
        "elapsed_ms": 0.170734,
        "method": "Contrôles nécessaires GRIM (moyenne) et GRIMMER (écart-type d’échantillon, diviseur n−1) pour des valeurs entières bornées. Toutes les sommes compatibles avec les intervalles de demi-arrondi sont examinées ; les sommes des carrés sont filtrées par leurs bornes exactes et leur parité. Consistant signifie que ces filtres ne détectent pas d’incohérence : ce n’est pas une preuve d’existence d’un jeu de données. sd_nearest_attainable désigne le candidat le plus proche passant ces filtres. Les arrondis aux frontières sont acceptés dans les deux sens. Une incohérence ne prouve jamais une fraude.",
        "engine": "rust-cpu",
        "provenance": {
          "tool": "audit_statistics",
          "server": "scorecompute",
          "client": {
            "name": "scorecompute-docs-recording",
            "version": "1.0"
          },
          "identity_source": "MCP clientInfo (self-reported)",
          "model": null
        }
      }
    }
  }
}