{
  "$schema": "https://json-schema.org/draft/2020-12/schema",
  "$id": "https://www.calculatorx.com/schemas/math.vector.output.json",
  "title": "Vector — success output",
  "type": "object",
  "additionalProperties": false,
  "$defs": {
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      "type": "object",
      "properties": {
        "mode": {
          "const": "magnitude"
        },
        "ux": {
          "type": "number"
        },
        "uy": {
          "type": "number"
        },
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          "type": "number"
        },
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          "type": "number"
        },
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        }
      },
      "required": [
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        "uz",
        "magnitude",
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      ],
      "additionalProperties": false
    },
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      "type": "object",
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        "mode": {
          "const": "normalize"
        },
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          "type": "number"
        },
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          "type": "number"
        },
        "uz": {
          "type": "number"
        },
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          "type": "number",
          "x-unit": "1",
          "x-unit-id": "cx:one",
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            0,
            0,
            0,
            0,
            0,
            0
          ],
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            "quantity_kind": "ratio",
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              0,
              0,
              0,
              0,
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            ],
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            "registry_status": "preview",
            "definition_lifecycle": "candidate",
            "role": "scalar"
          }
        },
        "ny": {
          "type": "number",
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          "x-unit-id": "cx:one",
          "x-quantity-kind": "ratio",
          "x-role": "scalar",
          "x-dimension": [
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            0,
            0,
            0,
            0,
            0,
            0
          ],
          "x-uuce-unit": {
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            "registry_version": "0.3.0-preview.3",
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            "registry_status": "preview",
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          }
        },
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          "type": "number",
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            0,
            0,
            0,
            0,
            0
          ],
          "x-uuce-unit": {
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            "quantity_kind": "ratio",
            "dimension": [
              0,
              0,
              0,
              0,
              0,
              0,
              0
            ],
            "registry_version": "0.3.0-preview.3",
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            "registry_status": "preview",
            "definition_lifecycle": "candidate",
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          }
        },
        "magnitude": {
          "type": "number"
        },
        "formula": {
          "type": "string",
          "minLength": 1
        }
      },
      "required": [
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        "uz",
        "nx",
        "ny",
        "nz",
        "magnitude",
        "formula"
      ],
      "additionalProperties": false
    },
    "resultBranch2Result": {
      "type": "object",
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        "mode": {
          "const": "add"
        },
        "ux": {
          "type": "number"
        },
        "uy": {
          "type": "number"
        },
        "uz": {
          "type": "number"
        },
        "vx": {
          "type": "number"
        },
        "vy": {
          "type": "number"
        },
        "vz": {
          "type": "number"
        },
        "rx": {
          "type": "number"
        },
        "ry": {
          "type": "number"
        },
        "rz": {
          "type": "number"
        },
        "formula": {
          "type": "string",
          "minLength": 1
        }
      },
      "required": [
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        "uy",
        "uz",
        "vx",
        "vy",
        "vz",
        "rx",
        "ry",
        "rz",
        "formula"
      ],
      "additionalProperties": false
    },
    "resultBranch3Result": {
      "type": "object",
      "properties": {
        "mode": {
          "const": "sub"
        },
        "ux": {
          "type": "number"
        },
        "uy": {
          "type": "number"
        },
        "uz": {
          "type": "number"
        },
        "vx": {
          "type": "number"
        },
        "vy": {
          "type": "number"
        },
        "vz": {
          "type": "number"
        },
        "rx": {
          "type": "number"
        },
        "ry": {
          "type": "number"
        },
        "rz": {
          "type": "number"
        },
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        }
      },
      "required": [
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        "vz",
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        "ry",
        "rz",
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      ],
      "additionalProperties": false
    },
    "resultBranch4Result": {
      "type": "object",
      "properties": {
        "mode": {
          "const": "dot"
        },
        "ux": {
          "type": "number"
        },
        "uy": {
          "type": "number"
        },
        "uz": {
          "type": "number"
        },
        "vx": {
          "type": "number"
        },
        "vy": {
          "type": "number"
        },
        "vz": {
          "type": "number"
        },
        "dot": {
          "type": "number"
        },
        "formula": {
          "type": "string",
          "minLength": 1
        }
      },
      "required": [
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        "uy",
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      ],
      "additionalProperties": false
    },
    "resultBranch5Result": {
      "type": "object",
      "properties": {
        "mode": {
          "const": "cross"
        },
        "ux": {
          "type": "number"
        },
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          "type": "number"
        },
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          "type": "number"
        },
        "vx": {
          "type": "number"
        },
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          "type": "number"
        },
        "vz": {
          "type": "number"
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          "type": "number"
        },
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          "type": "number"
        },
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          "type": "number"
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        "formula": {
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      },
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      ],
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    },
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      "type": "object",
      "properties": {
        "mode": {
          "const": "angle"
        },
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          "type": "number"
        },
        "uy": {
          "type": "number"
        },
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          "type": "number"
        },
        "vx": {
          "type": "number"
        },
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          "type": "number"
        },
        "vz": {
          "type": "number"
        },
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          "type": "number",
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          "x-unit-id": "cx:deg",
          "x-quantity-kind": "plane_angle",
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            0,
            0,
            0
          ],
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            "registry_status": "preview",
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          }
        },
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          "type": "number",
          "x-unit": "rad",
          "x-unit-id": "cx:rad",
          "x-quantity-kind": "plane_angle",
          "x-role": "scalar",
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            0,
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            0
          ],
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            ],
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            "registry_status": "preview",
            "definition_lifecycle": "candidate",
            "role": "scalar"
          }
        },
        "cosine": {
          "type": "number",
          "x-unit": "1",
          "x-unit-id": "cx:one",
          "x-quantity-kind": "ratio",
          "x-role": "scalar",
          "x-dimension": [
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            0,
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            0,
            0
          ],
          "x-uuce-unit": {
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            "dependency_digest": "b1c9aa4d586949ee881925298442091ba11dda29f57de0867e43da1cd59e06e5",
            "quantity_kind": "ratio",
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            "registry_version": "0.3.0-preview.3",
            "digest_contract": "calculatorx-unit-definition-digests-v2",
            "registry_status": "preview",
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            "role": "scalar"
          }
        },
        "formula": {
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          "minLength": 1
        }
      },
      "required": [
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        "uy",
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        "vy",
        "vz",
        "angle_deg",
        "angle_rad",
        "cosine",
        "formula"
      ],
      "additionalProperties": false
    },
    "resultBranch7Result": {
      "type": "object",
      "properties": {
        "mode": {
          "const": "projection"
        },
        "ux": {
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        },
        "uy": {
          "type": "number"
        },
        "uz": {
          "type": "number"
        },
        "vx": {
          "type": "number"
        },
        "vy": {
          "type": "number"
        },
        "vz": {
          "type": "number"
        },
        "px": {
          "type": "number"
        },
        "py": {
          "type": "number"
        },
        "pz": {
          "type": "number"
        },
        "scale": {
          "type": "number"
        },
        "formula": {
          "type": "string",
          "minLength": 1
        }
      },
      "required": [
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        "uy",
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        "vx",
        "vy",
        "vz",
        "px",
        "py",
        "pz",
        "scale",
        "formula"
      ],
      "additionalProperties": false
    },
    "resultBranch8Result": {
      "type": "object",
      "properties": {
        "mode": {
          "const": "triple"
        },
        "ux": {
          "type": "number"
        },
        "uy": {
          "type": "number"
        },
        "uz": {
          "type": "number"
        },
        "vx": {
          "type": "number"
        },
        "vy": {
          "type": "number"
        },
        "vz": {
          "type": "number"
        },
        "wx": {
          "type": "number"
        },
        "wy": {
          "type": "number"
        },
        "wz": {
          "type": "number"
        },
        "triple": {
          "type": "number"
        },
        "formula": {
          "type": "string",
          "minLength": 1
        }
      },
      "required": [
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        "ux",
        "uy",
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        "vx",
        "vy",
        "vz",
        "wx",
        "wy",
        "wz",
        "triple",
        "formula"
      ],
      "additionalProperties": false
    },
    "calcResult": {
      "oneOf": [
        {
          "$ref": "#/$defs/resultBranch0Result"
        },
        {
          "$ref": "#/$defs/resultBranch1Result"
        },
        {
          "$ref": "#/$defs/resultBranch2Result"
        },
        {
          "$ref": "#/$defs/resultBranch3Result"
        },
        {
          "$ref": "#/$defs/resultBranch4Result"
        },
        {
          "$ref": "#/$defs/resultBranch5Result"
        },
        {
          "$ref": "#/$defs/resultBranch6Result"
        },
        {
          "$ref": "#/$defs/resultBranch7Result"
        },
        {
          "$ref": "#/$defs/resultBranch8Result"
        }
      ]
    }
  },
  "required": [
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    "capability_id",
    "engine",
    "inputs",
    "result",
    "result_detail",
    "calculation_version",
    "verification"
  ],
  "properties": {
    "id": {
      "type": "string",
      "description": "Requested tool id"
    },
    "status": {
      "const": "success"
    },
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      "const": "math.vector"
    },
    "tool": {
      "type": "string",
      "description": "Requested tool id"
    },
    "engine": {
      "type": "string"
    },
    "inputs": {
      "type": "object",
      "description": "Normalized calculation inputs (aliases resolved)"
    },
    "result": {
      "$ref": "#/$defs/calcResult"
    },
    "result_detail": {
      "type": "object",
      "additionalProperties": false,
      "required": [
        "value",
        "unit",
        "formatted"
      ],
      "properties": {
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          "type": "object",
          "const": {
            "protocol": "calculatorx-field-unit-contract-v1",
            "capability_id": "math.vector",
            "registry_version": "0.3.0-preview.3",
            "declaration_scope": "Field/branch declarations only; inactive fields are not asserted to exist. No conversion-engine migration or new numerical certification.",
            "path_format": "Paths relative to inputs or result_detail.value; dot separates properties, * denotes array items, $ denotes a scalar result.",
            "inputs": {},
            "outputs": {
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                "reference": {
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                  "revision": "1.0.0",
                  "content_digest": "ebb31e3abee53f3bf57339c87949e1018d141739fba8a07f54c42ebfd219262b",
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                  "registry_status": "preview",
                  "definition_lifecycle": "candidate",
                  "role": "scalar"
                }
              },
              "angle_rad": {
                "unit": "rad",
                "reference": {
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                  "revision": "1.0.0",
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                  "registry_status": "preview",
                  "definition_lifecycle": "candidate",
                  "role": "scalar"
                }
              },
              "cosine": {
                "unit": "1",
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                  "registry_status": "preview",
                  "definition_lifecycle": "candidate",
                  "role": "scalar"
                }
              },
              "nx": {
                "unit": "1",
                "reference": {
                  "unit_id": "cx:one",
                  "revision": "1.0.0",
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                  "role": "scalar"
                }
              },
              "ny": {
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                  "revision": "1.0.0",
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                  "digest_contract": "calculatorx-unit-definition-digests-v2",
                  "registry_status": "preview",
                  "definition_lifecycle": "candidate",
                  "role": "scalar"
                }
              },
              "nz": {
                "unit": "1",
                "reference": {
                  "unit_id": "cx:one",
                  "revision": "1.0.0",
                  "content_digest": "98cc3ffc58d8733c483b60c4d7e238fe8ad43a6aadcced9496b74f33a01ef599",
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                  "registry_status": "preview",
                  "definition_lifecycle": "candidate",
                  "role": "scalar"
                }
              }
            },
            "quantity_policy": {
              "physical_unit_id": null,
              "input_policy": "Components within each vector use a consistent arbitrary operand unit.",
              "derived_policy": "Magnitude inherits its operand unit; dot/cross products combine operand units, triple products combine three. Normalized direction components and cosine are ratios."
            }
          }
        },
        "value": {
          "$ref": "#/$defs/calcResult"
        },
        "unit": {
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          ]
        },
        "formatted": {
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            "null"
          ]
        }
      }
    },
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        },
        {
          "type": "string"
        },
        {
          "type": "object",
          "additionalProperties": false,
          "properties": {
            "id": {
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            },
            "expression": {
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          }
        }
      ]
    },
    "assumptions": {
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    },
    "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"
          ]
        },
        "citation_kind": {
          "type": "string"
        },
        "expert_review": {
          "type": "string"
        },
        "domain_review": {
          "type": "string"
        },
        "calculation_version": {
          "type": "string"
        },
        "calc_tests": {
          "type": [
            "string",
            "null"
          ]
        },
        "tests_passed": {
          "type": [
            "integer",
            "null"
          ]
        },
        "tests_total": {
          "type": [
            "integer",
            "null"
          ]
        },
        "artifact_contract": {
          "type": [
            "string",
            "null"
          ]
        },
        "trust_peek": {
          "type": [
            "string",
            "null"
          ]
        },
        "verification_revision": {
          "type": "string"
        },
        "verified_scope": {
          "type": "string"
        },
        "evidence_digest": {
          "type": "string",
          "pattern": "^[a-f0-9]{64}$"
        }
      },
      "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": "1.8.0"
    },
    "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"
        }
      }
    }
  },
  "x-unit-contract": {
    "protocol": "calculatorx-field-unit-contract-v1",
    "capability_id": "math.vector",
    "registry_version": "0.3.0-preview.3",
    "declaration_scope": "Field/branch declarations only; inactive fields are not asserted to exist. No conversion-engine migration or new numerical certification.",
    "path_format": "Paths relative to inputs or result_detail.value; dot separates properties, * denotes array items, $ denotes a scalar result.",
    "inputs": {},
    "outputs": {
      "angle_deg": {
        "unit": "deg",
        "reference": {
          "unit_id": "cx:deg",
          "revision": "1.0.0",
          "content_digest": "ebb31e3abee53f3bf57339c87949e1018d141739fba8a07f54c42ebfd219262b",
          "dependency_digest": "eef386126ec6524884c84bab06f2a96996df913376c0ce5ccdaca0e7faf7b9c3",
          "quantity_kind": "plane_angle",
          "dimension": [
            0,
            0,
            0,
            0,
            0,
            0,
            0
          ],
          "registry_version": "0.3.0-preview.3",
          "digest_contract": "calculatorx-unit-definition-digests-v2",
          "registry_status": "preview",
          "definition_lifecycle": "candidate",
          "role": "scalar"
        }
      },
      "angle_rad": {
        "unit": "rad",
        "reference": {
          "unit_id": "cx:rad",
          "revision": "1.0.0",
          "content_digest": "842467a958d28ac79bf34e796043449f6af24819d77b2b67f540dbabdecc8e3e",
          "dependency_digest": "9c07023393c6212aab52719f503df1bdc9456559b5c4719ff1fec47d0623e0ad",
          "quantity_kind": "plane_angle",
          "dimension": [
            0,
            0,
            0,
            0,
            0,
            0,
            0
          ],
          "registry_version": "0.3.0-preview.3",
          "digest_contract": "calculatorx-unit-definition-digests-v2",
          "registry_status": "preview",
          "definition_lifecycle": "candidate",
          "role": "scalar"
        }
      },
      "cosine": {
        "unit": "1",
        "reference": {
          "unit_id": "cx:one",
          "revision": "1.0.0",
          "content_digest": "98cc3ffc58d8733c483b60c4d7e238fe8ad43a6aadcced9496b74f33a01ef599",
          "dependency_digest": "b1c9aa4d586949ee881925298442091ba11dda29f57de0867e43da1cd59e06e5",
          "quantity_kind": "ratio",
          "dimension": [
            0,
            0,
            0,
            0,
            0,
            0,
            0
          ],
          "registry_version": "0.3.0-preview.3",
          "digest_contract": "calculatorx-unit-definition-digests-v2",
          "registry_status": "preview",
          "definition_lifecycle": "candidate",
          "role": "scalar"
        }
      },
      "nx": {
        "unit": "1",
        "reference": {
          "unit_id": "cx:one",
          "revision": "1.0.0",
          "content_digest": "98cc3ffc58d8733c483b60c4d7e238fe8ad43a6aadcced9496b74f33a01ef599",
          "dependency_digest": "b1c9aa4d586949ee881925298442091ba11dda29f57de0867e43da1cd59e06e5",
          "quantity_kind": "ratio",
          "dimension": [
            0,
            0,
            0,
            0,
            0,
            0,
            0
          ],
          "registry_version": "0.3.0-preview.3",
          "digest_contract": "calculatorx-unit-definition-digests-v2",
          "registry_status": "preview",
          "definition_lifecycle": "candidate",
          "role": "scalar"
        }
      },
      "ny": {
        "unit": "1",
        "reference": {
          "unit_id": "cx:one",
          "revision": "1.0.0",
          "content_digest": "98cc3ffc58d8733c483b60c4d7e238fe8ad43a6aadcced9496b74f33a01ef599",
          "dependency_digest": "b1c9aa4d586949ee881925298442091ba11dda29f57de0867e43da1cd59e06e5",
          "quantity_kind": "ratio",
          "dimension": [
            0,
            0,
            0,
            0,
            0,
            0,
            0
          ],
          "registry_version": "0.3.0-preview.3",
          "digest_contract": "calculatorx-unit-definition-digests-v2",
          "registry_status": "preview",
          "definition_lifecycle": "candidate",
          "role": "scalar"
        }
      },
      "nz": {
        "unit": "1",
        "reference": {
          "unit_id": "cx:one",
          "revision": "1.0.0",
          "content_digest": "98cc3ffc58d8733c483b60c4d7e238fe8ad43a6aadcced9496b74f33a01ef599",
          "dependency_digest": "b1c9aa4d586949ee881925298442091ba11dda29f57de0867e43da1cd59e06e5",
          "quantity_kind": "ratio",
          "dimension": [
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            0,
            0,
            0,
            0,
            0,
            0
          ],
          "registry_version": "0.3.0-preview.3",
          "digest_contract": "calculatorx-unit-definition-digests-v2",
          "registry_status": "preview",
          "definition_lifecycle": "candidate",
          "role": "scalar"
        }
      }
    },
    "quantity_policy": {
      "physical_unit_id": null,
      "input_policy": "Components within each vector use a consistent arbitrary operand unit.",
      "derived_policy": "Magnitude inherits its operand unit; dot/cross products combine operand units, triple products combine three. Normalized direction components and cosine are ratios."
    }
  }
}