{
  "$schema": "https://json-schema.org/draft/2020-12/schema",
  "$id": "https://www.calculatorx.com/schemas/math.prime_factorization/1.0.1/output.json",
  "title": "Prime factorization — success output",
  "type": "object",
  "additionalProperties": false,
  "required": [
    "status",
    "capability_id",
    "engine",
    "inputs",
    "result",
    "result_detail",
    "calculation_version",
    "verification",
    "review"
  ],
  "properties": {
    "id": {
      "type": "string",
      "description": "Requested tool id"
    },
    "status": {
      "const": "success"
    },
    "capability_id": {
      "const": "math.prime_factorization"
    },
    "tool": {
      "type": "string",
      "description": "Requested tool id"
    },
    "engine": {
      "type": "string"
    },
    "inputs": {
      "description": "Normalized calculation inputs (aliases resolved to canonical form)",
      "type": "object",
      "additionalProperties": false,
      "required": [
        "mode",
        "n"
      ],
      "properties": {
        "mode": {
          "enum": [
            "factorize",
            "is_prime"
          ]
        },
        "n": {
          "type": "integer",
          "minimum": 1,
          "maximum": 1000000000000
        }
      }
    },
    "result": {
      "type": "object",
      "additionalProperties": false,
      "properties": {
        "n": {
          "type": "integer",
          "minimum": 1,
          "maximum": 1000000000000
        },
        "mode": {
          "enum": [
            "factorize",
            "is_prime"
          ]
        },
        "is_prime": {
          "type": "boolean"
        },
        "factors": {
          "type": "array",
          "maxItems": 11,
          "items": {
            "type": "object",
            "additionalProperties": false,
            "required": [
              "p",
              "e"
            ],
            "properties": {
              "p": {
                "type": "integer",
                "minimum": 2,
                "maximum": 1000000000000
              },
              "e": {
                "type": "integer",
                "minimum": 1,
                "maximum": 39
              }
            }
          }
        },
        "canonical": {
          "type": "string"
        },
        "omega": {
          "type": "integer",
          "minimum": 0,
          "maximum": 11
        },
        "big_omega": {
          "type": "integer",
          "minimum": 0,
          "maximum": 39
        },
        "max_n": {
          "const": 1000000000000
        },
        "value": {
          "type": "string"
        },
        "display": {
          "type": "object",
          "additionalProperties": false,
          "required": [
            "value"
          ],
          "properties": {
            "value": {
              "type": "string"
            }
          }
        },
        "identity": {
          "type": "string"
        },
        "classification": {
          "enum": [
            "prime",
            "composite",
            "neither prime nor composite"
          ]
        },
        "algorithm": {
          "const": "trial_division"
        },
        "numeric_domain": {
          "const": "integer"
        },
        "exactness": {
          "const": "exact"
        },
        "numeric_backend": {
          "const": "bigint"
        },
        "formula": {
          "type": "string"
        },
        "work": {
          "type": "string"
        },
        "calculation_version": {
          "const": "1.0.1"
        }
      },
      "required": [
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        "mode",
        "is_prime",
        "factors",
        "canonical",
        "omega",
        "big_omega",
        "max_n",
        "value",
        "display",
        "identity",
        "classification",
        "algorithm",
        "numeric_domain",
        "exactness",
        "numeric_backend",
        "formula",
        "work",
        "calculation_version"
      ]
    },
    "result_detail": {
      "type": "object",
      "additionalProperties": false,
      "required": [
        "value",
        "unit",
        "formatted"
      ],
      "properties": {
        "value": {
          "type": "object",
          "additionalProperties": false,
          "properties": {
            "n": {
              "type": "integer",
              "minimum": 1,
              "maximum": 1000000000000
            },
            "mode": {
              "enum": [
                "factorize",
                "is_prime"
              ]
            },
            "is_prime": {
              "type": "boolean"
            },
            "factors": {
              "type": "array",
              "maxItems": 11,
              "items": {
                "type": "object",
                "additionalProperties": false,
                "required": [
                  "p",
                  "e"
                ],
                "properties": {
                  "p": {
                    "type": "integer",
                    "minimum": 2,
                    "maximum": 1000000000000
                  },
                  "e": {
                    "type": "integer",
                    "minimum": 1,
                    "maximum": 39
                  }
                }
              }
            },
            "canonical": {
              "type": "string"
            },
            "omega": {
              "type": "integer",
              "minimum": 0,
              "maximum": 11
            },
            "big_omega": {
              "type": "integer",
              "minimum": 0,
              "maximum": 39
            },
            "max_n": {
              "const": 1000000000000
            },
            "value": {
              "type": "string"
            },
            "display": {
              "type": "object",
              "additionalProperties": false,
              "required": [
                "value"
              ],
              "properties": {
                "value": {
                  "type": "string"
                }
              }
            },
            "identity": {
              "type": "string"
            },
            "classification": {
              "enum": [
                "prime",
                "composite",
                "neither prime nor composite"
              ]
            },
            "algorithm": {
              "const": "trial_division"
            },
            "numeric_domain": {
              "const": "integer"
            },
            "exactness": {
              "const": "exact"
            },
            "numeric_backend": {
              "const": "bigint"
            },
            "formula": {
              "type": "string"
            },
            "work": {
              "type": "string"
            },
            "calculation_version": {
              "const": "1.0.1"
            }
          },
          "required": [
            "n",
            "mode",
            "is_prime",
            "factors",
            "canonical",
            "omega",
            "big_omega",
            "max_n",
            "value",
            "display",
            "identity",
            "classification",
            "algorithm",
            "numeric_domain",
            "exactness",
            "numeric_backend",
            "formula",
            "work",
            "calculation_version"
          ]
        },
        "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,
      "description": "Computational verification under CVP. Review-policy tiers live on `review`, not here.",
      "required": [
        "cvp"
      ],
      "properties": {
        "cvp": {
          "type": "object",
          "additionalProperties": false,
          "required": [
            "status",
            "protocol",
            "profile",
            "verified_scope",
            "verification_revision",
            "evidence_digest"
          ],
          "properties": {
            "status": {
              "type": "string",
              "description": "CVP verification status (e.g. VERIFIED)"
            },
            "protocol": {
              "type": "string",
              "description": "CVP protocol id, e.g. 1.0.0-proposed"
            },
            "profile": {
              "type": "string"
            },
            "verified_scope": {
              "type": "string"
            },
            "verification_revision": {
              "type": [
                "string",
                "null"
              ]
            },
            "evidence_digest": {
              "type": [
                "string",
                "null"
              ]
            },
            "production": {
              "type": [
                "string",
                "null"
              ],
              "description": "Production freshness, e.g. CURRENT"
            },
            "evidence": {
              "type": "string",
              "format": "uri"
            }
          }
        }
      }
    },
    "review": {
      "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": [
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            ]
          },
          "then": {
            "properties": {
              "engine_tested": {
                "const": true
              }
            }
          }
        }
      ]
    },
    "calculation_version": {
      "type": "string",
      "const": "1.0.1"
    },
    "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"
        }
      }
    }
  }
}