{
  "$schema": "https://json-schema.org/draft/2020-12/schema",
  "$id": "https://www.calculatorx.com/schemas/engineering.uncertainty.pooled_sd.output.json",
  "title": "Pooled standard deviation — success output",
  "type": "object",
  "additionalProperties": false,
  "required": [
    "status",
    "capability_id",
    "engine",
    "inputs",
    "result",
    "result_detail",
    "calculation_version",
    "verification"
  ],
  "properties": {
    "id": {
      "type": "string",
      "description": "Requested tool id"
    },
    "status": {
      "const": "success"
    },
    "capability_id": {
      "const": "engineering.uncertainty.pooled_sd"
    },
    "tool": {
      "type": "string",
      "description": "Requested tool id"
    },
    "engine": {
      "type": "string"
    },
    "inputs": {
      "type": "object",
      "description": "Normalized calculation inputs (aliases resolved)"
    },
    "result": {
      "type": "object",
      "additionalProperties": false,
      "required": [
        "s_p",
        "nu",
        "k",
        "s",
        "nu_i"
      ],
      "properties": {
        "s_p": {
          "type": "number",
          "description": "Pooled standard deviation √(Σ ν_i s_i² / Σ ν_i)"
        },
        "nu": {
          "type": "number",
          "description": "Pooled degrees of freedom Σ ν_i"
        },
        "k": {
          "type": "integer",
          "description": "Number of groups"
        },
        "s": {
          "type": "array",
          "items": {
            "type": "number"
          }
        },
        "nu_i": {
          "type": "array",
          "items": {
            "type": "number"
          }
        }
      }
    },
    "result_detail": {
      "type": "object",
      "additionalProperties": false,
      "required": [
        "value",
        "unit",
        "formatted"
      ],
      "properties": {
        "value": {
          "type": "object",
          "additionalProperties": false,
          "required": [
            "s_p",
            "nu",
            "k",
            "s",
            "nu_i"
          ],
          "properties": {
            "s_p": {
              "type": "number",
              "description": "Pooled standard deviation √(Σ ν_i s_i² / Σ ν_i)"
            },
            "nu": {
              "type": "number",
              "description": "Pooled degrees of freedom Σ ν_i"
            },
            "k": {
              "type": "integer",
              "description": "Number of groups"
            },
            "s": {
              "type": "array",
              "items": {
                "type": "number"
              }
            },
            "nu_i": {
              "type": "array",
              "items": {
                "type": "number"
              }
            }
          }
        },
        "unit": {
          "type": [
            "string",
            "null"
          ]
        },
        "formatted": {
          "type": [
            "string",
            "null"
          ]
        }
      }
    },
    "formula": {
      "anyOf": [
        {
          "type": "null"
        },
        {
          "type": "string"
        },
        {
          "type": "object",
          "additionalProperties": false,
          "properties": {
            "id": {
              "type": "string"
            },
            "expression": {
              "type": "string"
            },
            "label": {
              "type": "string"
            }
          }
        }
      ]
    },
    "assumptions": {
      "type": "array",
      "items": {
        "type": "string"
      }
    },
    "warnings": {
      "type": "array",
      "items": {
        "type": "object",
        "additionalProperties": false,
        "required": [
          "code"
        ],
        "properties": {
          "code": {
            "type": "string"
          },
          "severity": {
            "type": "string"
          },
          "detail": {
            "type": "string"
          },
          "suggestion": {
            "type": "string"
          }
        }
      }
    },
    "verification": {
      "type": "object",
      "additionalProperties": false,
      "required": [
        "tier",
        "engine_tested",
        "expert_reviewed",
        "source_checked",
        "reviewed_by",
        "reviewer_role",
        "last_reviewed"
      ],
      "properties": {
        "tier": {
          "type": "string",
          "enum": [
            "candidate",
            "engine_tested",
            "internally_reviewed",
            "expert_verified"
          ]
        },
        "engine_tested": {
          "type": "boolean"
        },
        "expert_reviewed": {
          "type": "boolean"
        },
        "internally_reviewed": {
          "type": "boolean"
        },
        "review_kind": {
          "type": [
            "string",
            "null"
          ]
        },
        "source_checked": {
          "type": "boolean"
        },
        "reviewed_by": {
          "type": [
            "string",
            "null"
          ]
        },
        "reviewer_role": {
          "type": [
            "string",
            "null"
          ]
        },
        "last_reviewed": {
          "type": [
            "string",
            "null"
          ]
        }
      },
      "allOf": [
        {
          "if": {
            "properties": {
              "tier": {
                "const": "expert_verified"
              }
            },
            "required": [
              "tier"
            ]
          },
          "then": {
            "properties": {
              "engine_tested": {
                "const": true
              },
              "expert_reviewed": {
                "const": true
              },
              "source_checked": {
                "const": true
              },
              "reviewed_by": {
                "type": "string",
                "minLength": 1
              },
              "reviewer_role": {
                "type": "string",
                "minLength": 1
              },
              "last_reviewed": {
                "type": "string",
                "minLength": 1
              }
            }
          }
        },
        {
          "if": {
            "properties": {
              "tier": {
                "const": "internally_reviewed"
              }
            },
            "required": [
              "tier"
            ]
          },
          "then": {
            "properties": {
              "engine_tested": {
                "const": true
              },
              "internally_reviewed": {
                "const": true
              },
              "source_checked": {
                "const": true
              }
            }
          }
        },
        {
          "if": {
            "properties": {
              "tier": {
                "const": "engine_tested"
              }
            },
            "required": [
              "tier"
            ]
          },
          "then": {
            "properties": {
              "engine_tested": {
                "const": true
              }
            }
          }
        }
      ]
    },
    "calculation_version": {
      "type": "string",
      "const": "1.0.0"
    },
    "api_version": {
      "type": "string"
    },
    "api_contract_version": {
      "type": "string"
    },
    "spec_version": {
      "type": "string"
    },
    "page": {
      "type": [
        "string",
        "null"
      ],
      "description": "Canonical calculator page URL"
    },
    "links": {
      "type": "object",
      "additionalProperties": false,
      "properties": {
        "schema_input": {
          "type": "string",
          "format": "uri"
        },
        "schema_output": {
          "type": "string",
          "format": "uri"
        },
        "evidence": {
          "type": "string",
          "format": "uri"
        },
        "openapi": {
          "type": "string",
          "format": "uri"
        },
        "capabilities": {
          "type": "string",
          "format": "uri"
        },
        "mcp": {
          "type": "string",
          "format": "uri"
        }
      }
    }
  }
}