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              "properties": {
                "mode": {
                  "const": "chol"
                },
                "A": {
                  "type": "array",
                  "minItems": 2,
                  "maxItems": 4,
                  "items": {
                    "type": "array",
                    "minItems": 2,
                    "maxItems": 4,
                    "items": {
                      "type": "number"
                    }
                  }
                },
                "L": {
                  "type": "array",
                  "minItems": 2,
                  "maxItems": 4,
                  "items": {
                    "type": "array",
                    "minItems": 2,
                    "maxItems": 4,
                    "items": {
                      "type": "number"
                    }
                  }
                },
                "effective_A": {
                  "type": "array",
                  "minItems": 2,
                  "maxItems": 4,
                  "items": {
                    "type": "array",
                    "minItems": 2,
                    "maxItems": 4,
                    "items": {
                      "type": "number"
                    }
                  }
                }
              },
              "required": [
                "mode",
                "order",
                "A",
                "L",
                "effective_A",
                "symmetry_error",
                "symmetry_tolerance",
                "symmetry_policy",
                "relative_reconstruction_residual",
                "reconstruction_tolerance"
              ],
              "allOf": [
                {
                  "if": {
                    "properties": {
                      "order": {
                        "const": 2
                      }
                    }
                  },
                  "then": {
                    "properties": {
                      "A": {
                        "minItems": 2,
                        "maxItems": 2,
                        "items": {
                          "minItems": 2,
                          "maxItems": 2
                        }
                      },
                      "L": {
                        "minItems": 2,
                        "maxItems": 2,
                        "items": {
                          "minItems": 2,
                          "maxItems": 2
                        }
                      },
                      "effective_A": {
                        "minItems": 2,
                        "maxItems": 2,
                        "items": {
                          "minItems": 2,
                          "maxItems": 2
                        }
                      }
                    }
                  }
                },
                {
                  "if": {
                    "properties": {
                      "order": {
                        "const": 3
                      }
                    }
                  },
                  "then": {
                    "properties": {
                      "A": {
                        "minItems": 3,
                        "maxItems": 3,
                        "items": {
                          "minItems": 3,
                          "maxItems": 3
                        }
                      },
                      "L": {
                        "minItems": 3,
                        "maxItems": 3,
                        "items": {
                          "minItems": 3,
                          "maxItems": 3
                        }
                      },
                      "effective_A": {
                        "minItems": 3,
                        "maxItems": 3,
                        "items": {
                          "minItems": 3,
                          "maxItems": 3
                        }
                      }
                    }
                  }
                },
                {
                  "if": {
                    "properties": {
                      "order": {
                        "const": 4
                      }
                    }
                  },
                  "then": {
                    "properties": {
                      "A": {
                        "minItems": 4,
                        "maxItems": 4,
                        "items": {
                          "minItems": 4,
                          "maxItems": 4
                        }
                      },
                      "L": {
                        "minItems": 4,
                        "maxItems": 4,
                        "items": {
                          "minItems": 4,
                          "maxItems": 4
                        }
                      },
                      "effective_A": {
                        "minItems": 4,
                        "maxItems": 4,
                        "items": {
                          "minItems": 4,
                          "maxItems": 4
                        }
                      }
                    }
                  }
                }
              ]
            },
            {
              "properties": {
                "mode": {
                  "const": "qr"
                }
              },
              "required": [
                "mode",
                "order",
                "A",
                "Q",
                "R"
              ]
            },
            {
              "properties": {
                "mode": {
                  "const": "svd"
                }
              },
              "required": [
                "mode",
                "order",
                "A",
                "U",
                "S",
                "VT",
                "singular_values"
              ]
            },
            {
              "properties": {
                "mode": {
                  "const": "lstsq"
                }
              },
              "required": [
                "mode",
                "order",
                "A",
                "vector",
                "residual_2"
              ]
            },
            {
              "properties": {
                "mode": {
                  "const": "rref"
                }
              },
              "required": [
                "mode",
                "order",
                "A",
                "rref",
                "rank"
              ]
            },
            {
              "properties": {
                "mode": {
                  "const": "condition"
                }
              },
              "required": [
                "mode",
                "order",
                "A",
                "condition_number",
                "infinite"
              ]
            },
            {
              "properties": {
                "mode": {
                  "const": "nullspace"
                }
              },
              "required": [
                "mode",
                "order",
                "A",
                "basis",
                "dimension"
              ]
            },
            {
              "properties": {
                "mode": {
                  "const": "columnspace"
                }
              },
              "required": [
                "mode",
                "order",
                "A",
                "basis",
                "dimension"
              ]
            },
            {
              "properties": {
                "mode": {
                  "const": "rowspace"
                }
              },
              "required": [
                "mode",
                "order",
                "A",
                "basis",
                "dimension"
              ]
            },
            {
              "properties": {
                "mode": {
                  "const": "leftnullspace"
                }
              },
              "required": [
                "mode",
                "order",
                "A",
                "basis",
                "dimension"
              ]
            },
            {
              "properties": {
                "mode": {
                  "const": "eigen"
                }
              },
              "required": [
                "mode",
                "order",
                "A",
                "eigenvalues",
                "solver",
                "eigenvectors"
              ]
            }
          ]
        },
        "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": "1.14.16"
    },
    "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"
        }
      }
    }
  }
}