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    "result",
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        },
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            "digest_contract": "calculatorx-unit-definition-digests-v2",
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            "definition_lifecycle": "candidate",
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          "exclusiveMinimum": 0
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          "type": "number",
          "exclusiveMinimum": 0
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          "type": "number",
          "exclusiveMinimum": 0
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          "exclusiveMinimum": 0
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          "exclusiveMinimum": 0
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            "regular_polygon",
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            "irregular_polygon"
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          "minItems": 3,
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          "items": {
            "type": "array",
            "minItems": 2,
            "maxItems": 2,
            "items": {
              "type": "number"
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          }
        },
        "square": {
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        "rectangle": {
          "type": "boolean"
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          },
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        },
        {
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        {
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        {
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            "d2",
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        },
        {
          "properties": {
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          },
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        },
        {
          "properties": {
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          },
          "required": [
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        }
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    },
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      "additionalProperties": false,
      "required": [
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        "unit",
        "formatted"
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      "properties": {
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            "path_format": "Paths relative to inputs or result_detail.value; dot separates properties, * denotes array items, $ denotes a scalar result.",
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              },
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                  "registry_status": "preview",
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                0,
                0,
                0,
                0,
                0,
                0
              ],
              "x-unit-policy": "arbitrary_consistent_length",
              "x-uuce-role": "scalar"
            },
            "interior_deg": {
              "type": "number",
              "exclusiveMinimum": 0,
              "x-unit": "deg",
              "x-unit-id": "cx:deg",
              "x-quantity-kind": "plane_angle",
              "x-role": "scalar",
              "x-dimension": [
                0,
                0,
                0,
                0,
                0,
                0,
                0
              ],
              "x-uuce-unit": {
                "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"
              }
            },
            "central_deg": {
              "type": "number",
              "exclusiveMinimum": 0,
              "x-unit": "deg",
              "x-unit-id": "cx:deg",
              "x-quantity-kind": "plane_angle",
              "x-role": "scalar",
              "x-dimension": [
                0,
                0,
                0,
                0,
                0,
                0,
                0
              ],
              "x-uuce-unit": {
                "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"
              }
            },
            "d1": {
              "type": "number",
              "exclusiveMinimum": 0
            },
            "d2": {
              "type": "number",
              "exclusiveMinimum": 0
            },
            "leg": {
              "type": "number",
              "exclusiveMinimum": 0
            },
            "midsegment": {
              "type": "number",
              "exclusiveMinimum": 0
            },
            "outer_circumference": {
              "type": "number",
              "exclusiveMinimum": 0
            },
            "inner_circumference": {
              "type": "number",
              "exclusiveMinimum": 0
            },
            "mode": {
              "enum": [
                "rectangle",
                "square",
                "regular_polygon",
                "annulus",
                "parallelogram",
                "trapezoid",
                "irregular_polygon"
              ]
            },
            "vertices": {
              "type": "array",
              "minItems": 3,
              "maxItems": 8,
              "items": {
                "type": "array",
                "minItems": 2,
                "maxItems": 2,
                "items": {
                  "type": "number"
                }
              }
            },
            "square": {
              "type": "boolean"
            },
            "rectangle": {
              "type": "boolean"
            },
            "isosceles": {
              "type": "boolean"
            },
            "formula": {
              "type": "string"
            },
            "model": {
              "const": "euclidean_plane"
            }
          },
          "oneOf": [
            {
              "properties": {
                "mode": {
                  "const": "rectangle"
                }
              },
              "required": [
                "a",
                "b",
                "diagonal",
                "square"
              ]
            },
            {
              "properties": {
                "mode": {
                  "const": "square"
                }
              },
              "required": [
                "a",
                "b",
                "s",
                "diagonal",
                "square"
              ]
            },
            {
              "properties": {
                "mode": {
                  "const": "regular_polygon"
                }
              },
              "required": [
                "n",
                "s",
                "apothem",
                "circumradius",
                "central_deg",
                "interior_deg"
              ]
            },
            {
              "properties": {
                "mode": {
                  "const": "annulus"
                }
              },
              "required": [
                "R",
                "r",
                "outer_circumference",
                "inner_circumference"
              ]
            },
            {
              "properties": {
                "mode": {
                  "const": "parallelogram"
                }
              },
              "required": [
                "a",
                "b",
                "theta",
                "height",
                "d1",
                "d2",
                "rectangle"
              ]
            },
            {
              "properties": {
                "mode": {
                  "const": "trapezoid"
                }
              },
              "required": [
                "a",
                "b",
                "h",
                "height",
                "leg",
                "midsegment",
                "rectangle",
                "isosceles"
              ]
            },
            {
              "properties": {
                "mode": {
                  "const": "irregular_polygon"
                }
              },
              "required": [
                "n",
                "vertices"
              ]
            }
          ]
        },
        "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"
          ]
        },
        "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": "1.6.0"
    },
    "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.geometry.plane",
    "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": {
      "theta": {
        "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": {
        "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"
        }
      },
      "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"
        }
      }
    },
    "outputs": {
      "theta": {
        "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"
        }
      },
      "interior_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"
        }
      },
      "central_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"
        }
      }
    },
    "quantity_policy": {
      "physical_unit_id": null,
      "input_policy": "Abstract consistent coordinate/length units; no physical unit is selected by this calculator.",
      "derived_policy": "Lengths inherit the input length unit U; areas U^2; volumes U^3. No implicit conversion or fixed metre binding.",
      "coefficient_policy": "Normalized implicit line/equation coefficients have equation-scale conventions, not universal physical unit IDs."
    }
  }
}