{
  "$schema": "https://json-schema.org/draft/2020-12/schema",
  "title": "Open Prep Question Pack v2",
  "description": "Strict author-facing schema for fixed-numeric, generated-template, exhibit, market-sizing, benchmark, and case-practice packs.",
  "type": "object",
  "unevaluatedProperties": false,
  "required": [
    "format",
    "schemaVersion",
    "kind",
    "id",
    "packVersion",
    "title"
  ],
  "properties": {
    "$schema": {
      "type": "string",
      "format": "uri-reference",
      "pattern": "\\S",
      "maxLength": 500
    },
    "format": {
      "const": "math-drill-question-pack"
    },
    "schemaVersion": {
      "const": 2
    },
    "kind": {
      "description": "Selects the kind-specific content contract; case_practice may bundle any nonempty combination of its six related collections.",
      "enum": ["fixed_numeric", "generated_template", "exhibit", "market_sizing", "benchmark", "case_practice"]
    },
    "id": {
      "$ref": "#/$defs/id"
    },
    "packVersion": {
      "$ref": "#/$defs/nonBlank100"
    },
    "title": {
      "$ref": "#/$defs/nonBlank100"
    },
    "description": {
      "type": "string",
      "pattern": "\\S",
      "maxLength": 500
    },
    "publisher": {
      "$ref": "#/$defs/nonBlank100"
    },
    "license": {
      "$ref": "#/$defs/nonBlank100"
    }
  },
  "oneOf": [
    {
      "title": "Fixed-numeric pack",
      "required": ["kind", "questions"],
      "properties": {
        "kind": {
          "const": "fixed_numeric"
        },
        "questions": {
          "$ref": "#/$defs/fixedNumericQuestionArray"
        }
      }
    },
    {
      "title": "Generated template pack",
      "required": ["kind", "templates"],
      "properties": {
        "kind": {
          "const": "generated_template"
        },
        "templates": {
          "oneOf": [
            {
              "$ref": "#/$defs/nonCaseTemplateArray"
            },
            {
              "$ref": "#/$defs/caseTemplateArray"
            }
          ]
        }
      }
    },
    {
      "title": "Exhibit pack",
      "required": ["kind", "datasets"],
      "properties": {
        "kind": {
          "const": "exhibit"
        },
        "datasets": {
          "$ref": "#/$defs/exhibitDatasetArray"
        }
      }
    },
    {
      "title": "Market-sizing pack",
      "required": ["kind", "templates"],
      "properties": {
        "kind": {
          "const": "market_sizing"
        },
        "templates": {
          "$ref": "#/$defs/marketSizingTemplateArray"
        }
      }
    },
    {
      "title": "Benchmark pack",
      "required": ["kind", "benchmarks"],
      "properties": {
        "kind": {
          "const": "benchmark"
        },
        "benchmarks": {
          "$ref": "#/$defs/benchmarkArray"
        }
      }
    },
    {
      "title": "Case-practice pack",
      "required": ["kind"],
      "properties": {
        "kind": {
          "const": "case_practice"
        },
        "structuringPrompts": {
          "$ref": "#/$defs/caseStructuringPromptArray"
        },
        "brainstormingPrompts": {
          "$ref": "#/$defs/brainstormingPromptArray"
        },
        "synthesisPrompts": {
          "$ref": "#/$defs/synthesisPromptArray"
        },
        "lessons": {
          "$ref": "#/$defs/conceptLessonArray"
        },
        "fitPrompts": {
          "$ref": "#/$defs/fitPracticePromptArray"
        },
        "fullCases": {
          "$ref": "#/$defs/fullCaseSimulationArray"
        }
      },
      "anyOf": [
        {
          "required": ["structuringPrompts"]
        },
        {
          "required": ["brainstormingPrompts"]
        },
        {
          "required": ["synthesisPrompts"]
        },
        {
          "required": ["lessons"]
        },
        {
          "required": ["fitPrompts"]
        },
        {
          "required": ["fullCases"]
        }
      ]
    }
  ],
  "$defs": {
    "id": {
      "type": "string",
      "pattern": "^[a-z0-9][a-z0-9_-]{0,79}$",
      "not": {
        "enum": ["__proto__", "constructor", "prototype"]
      }
    },
    "identifier": {
      "type": "string",
      "pattern": "^[A-Za-z_][A-Za-z0-9_]{0,79}$",
      "not": {
        "enum": ["answer", "__proto__", "constructor", "prototype"]
      }
    },
    "nonBlank100": {
      "type": "string",
      "pattern": "\\S",
      "maxLength": 100
    },
    "nonBlank200": {
      "type": "string",
      "pattern": "\\S",
      "maxLength": 200
    },
    "nonBlank500": {
      "type": "string",
      "pattern": "\\S",
      "maxLength": 500
    },
    "nonBlank1000": {
      "type": "string",
      "pattern": "\\S",
      "maxLength": 1000
    },
    "nonBlank2000": {
      "type": "string",
      "pattern": "\\S",
      "maxLength": 2000
    },
    "category": {
      "enum": [
        "arithmetic",
        "percentages",
        "fractions_decimals_ratios",
        "growth_compounding",
        "weighted_averages",
        "business_math",
        "case_math",
        "market_sizing",
        "exhibit_math"
      ]
    },
    "tag": {
      "enum": [
        "addition",
        "subtraction",
        "multiplication",
        "division",
        "mixed_operations",
        "percentage_of_number",
        "percentage_change",
        "reverse_percentage",
        "percentage_points",
        "margin",
        "fraction_conversion",
        "ratio_conversion",
        "simple_growth",
        "compound_growth",
        "cagr",
        "rule_of_72",
        "weighted_average",
        "revenue",
        "profit",
        "cost",
        "contribution_margin",
        "breakeven",
        "roi",
        "payback",
        "market_share",
        "capacity_utilization",
        "k_m_b_conversion",
        "unit_conversion"
      ]
    },
    "difficulty": {
      "enum": ["beginner", "intermediate", "advanced", "expert"]
    },
    "unit": {
      "description": "percentage values are fractions; percentage_points values are point counts; k, m, and b values are stored in the displayed scaled unit rather than base units.",
      "enum": [
        "none",
        "currency",
        "percentage",
        "percentage_points",
        "units",
        "customers",
        "users",
        "years",
        "months",
        "days",
        "stores",
        "k",
        "m",
        "b"
      ]
    },
    "nonCaseTemplateArray": {
      "type": "array",
      "minItems": 1,
      "maxItems": 500,
      "uniqueItems": true,
      "items": {
        "$ref": "#/$defs/nonCaseTemplate"
      }
    },
    "caseTemplateArray": {
      "type": "array",
      "minItems": 1,
      "maxItems": 500,
      "uniqueItems": true,
      "items": {
        "$ref": "#/$defs/caseTemplate"
      }
    },
    "nonCaseTemplate": {
      "allOf": [
        {
          "$ref": "#/$defs/template"
        },
        {
          "not": {
            "required": ["caseStyle"]
          }
        }
      ]
    },
    "caseTemplate": {
      "allOf": [
        {
          "$ref": "#/$defs/template"
        },
        {
          "required": ["caseStyle"],
          "properties": {
            "category": {
              "const": "case_math"
            }
          }
        }
      ]
    },
    "template": {
      "type": "object",
      "additionalProperties": false,
      "required": [
        "id",
        "category",
        "tags",
        "difficulty",
        "promptTemplate",
        "variables",
        "formula",
        "explanationTemplate"
      ],
      "properties": {
        "id": {
          "$ref": "#/$defs/id"
        },
        "category": {
          "$ref": "#/$defs/category"
        },
        "tags": {
          "type": "array",
          "minItems": 1,
          "maxItems": 10,
          "uniqueItems": true,
          "items": {
            "$ref": "#/$defs/tag"
          }
        },
        "difficulty": {
          "type": "array",
          "minItems": 1,
          "maxItems": 4,
          "uniqueItems": true,
          "items": {
            "$ref": "#/$defs/difficulty"
          }
        },
        "caseStyle": {
          "$ref": "#/$defs/caseStyle"
        },
        "promptTemplate": {
          "type": "string",
          "pattern": "\\S",
          "maxLength": 2000
        },
        "variables": {
          "type": "object",
          "minProperties": 1,
          "maxProperties": 20,
          "propertyNames": {
            "$ref": "#/$defs/identifier"
          },
          "additionalProperties": {
            "$ref": "#/$defs/variableSpec"
          }
        },
        "formula": {
          "$ref": "#/$defs/formula"
        },
        "answerUnit": {
          "$ref": "#/$defs/unit",
          "description": "When caseStyle is present, this must equal interviewMath.expectedUnit; omission is equivalent to none."
        },
        "tolerance": {
          "description": "Optional comparison policy. When omitted, generated answers accept rounding to two displayed decimal places: absolute tolerance 0.005 for ordinary display values and 0.00005 for canonical percentage fractions (0.005 percentage point).",
          "allOf": [
            {
              "$ref": "#/$defs/tolerance"
            },
            {
              "if": {
                "properties": {
                  "type": {
                    "const": "absolute"
                  }
                },
                "required": ["type"]
              },
              "then": {
                "properties": {
                  "value": {
                    "maximum": 1000000000
                  }
                }
              }
            }
          ]
        },
        "roundingRule": {
          "$ref": "#/$defs/roundingRule",
          "description": "Optional learner-facing rounding instruction. Grading is controlled by tolerance."
        },
        "explanationTemplate": {
          "$ref": "#/$defs/explanationTemplate"
        }
      }
    },
    "variableSpec": {
      "type": "object",
      "description": "Use values or a min/max range. The importer limits a range to 10,001 reachable values.",
      "additionalProperties": false,
      "required": ["type"],
      "properties": {
        "type": {
          "enum": ["integer", "decimal", "percentage", "currency"]
        },
        "values": {
          "type": "array",
          "minItems": 1,
          "maxItems": 100,
          "uniqueItems": true,
          "items": {
            "type": "number"
          }
        },
        "min": {
          "type": "number"
        },
        "max": {
          "type": "number"
        },
        "step": {
          "type": "number",
          "exclusiveMinimum": 0
        },
        "unit": {
          "$ref": "#/$defs/unit"
        }
      },
      "oneOf": [
        {
          "required": ["values"],
          "not": {
            "anyOf": [
              { "required": ["min"] },
              { "required": ["max"] },
              { "required": ["step"] }
            ]
          }
        },
        {
          "required": ["min", "max"],
          "not": {
            "required": ["values"]
          }
        }
      ],
      "allOf": [
        {
          "if": {
            "properties": {
              "type": {
                "const": "integer"
              }
            },
            "required": ["type"]
          },
          "then": {
            "properties": {
              "values": {
                "items": {
                  "type": "integer"
                }
              },
              "min": {
                "type": "integer"
              },
              "max": {
                "type": "integer"
              },
              "step": {
                "type": "integer",
                "minimum": 1
              }
            }
          }
        }
      ]
    },
    "formula": {
      "type": "object",
      "additionalProperties": false,
      "required": ["expression"],
      "properties": {
        "expression": {
          "type": "string",
          "maxLength": 500,
          "allOf": [
            {
              "pattern": "\\S"
            },
            {
              "pattern": "^[A-Za-z0-9_+*/^().\\s-]+$"
            }
          ]
        },
        "outputVariable": {
          "$ref": "#/$defs/identifier"
        }
      }
    },
    "explanationTemplate": {
      "type": "object",
      "additionalProperties": false,
      "required": ["steps"],
      "properties": {
        "steps": {
          "type": "array",
          "minItems": 1,
          "maxItems": 10,
          "items": {
            "type": "string",
            "pattern": "\\S",
            "maxLength": 1000
          }
        },
        "shortcut": {
          "type": "string",
          "pattern": "\\S",
          "maxLength": 1000
        }
      }
    },
    "caseStyle": {
      "type": "object",
      "additionalProperties": false,
      "required": ["calculationStepCount", "industry", "interviewMath"],
      "properties": {
        "calculationStepCount": {
          "enum": [2, 3, 4, 5, 6]
        },
        "industry": {
          "enum": [
            "airlines",
            "banking",
            "consumer_goods",
            "healthcare",
            "insurance",
            "manufacturing",
            "marketplaces",
            "retail",
            "saas",
            "telecom"
          ]
        },
        "interviewMath": {
          "$ref": "#/$defs/interviewMath"
        }
      }
    },
    "interviewMath": {
      "type": "object",
      "additionalProperties": false,
      "required": ["expectedUnit", "equationOptions", "interpretationOptions"],
      "properties": {
        "expectedUnit": {
          "$ref": "#/$defs/unit",
          "description": "Must equal the template answerUnit, or none when answerUnit is omitted."
        },
        "equationOptions": {
          "type": "array",
          "minItems": 2,
          "maxItems": 10,
          "uniqueItems": true,
          "items": {
            "$ref": "#/$defs/equationOption"
          },
          "contains": {
            "type": "object",
            "required": ["setupCorrect"],
            "properties": {
              "setupCorrect": {
                "const": true
              }
            }
          },
          "minContains": 1,
          "maxContains": 1
        },
        "interpretationOptions": {
          "type": "array",
          "minItems": 2,
          "maxItems": 10,
          "uniqueItems": true,
          "items": {
            "$ref": "#/$defs/interpretationOption"
          },
          "contains": {
            "type": "object",
            "required": ["isCorrect"],
            "properties": {
              "isCorrect": {
                "const": true
              }
            }
          },
          "minContains": 1,
          "maxContains": 1
        }
      }
    },
    "equationOption": {
      "type": "object",
      "additionalProperties": false,
      "required": ["id", "label", "formulaCorrect", "setupCorrect"],
      "properties": {
        "id": {
          "$ref": "#/$defs/id"
        },
        "label": {
          "type": "string",
          "pattern": "\\S",
          "maxLength": 1000
        },
        "formulaCorrect": {
          "type": "boolean"
        },
        "setupCorrect": {
          "type": "boolean"
        }
      },
      "allOf": [
        {
          "if": {
            "properties": {
              "setupCorrect": {
                "const": true
              }
            },
            "required": ["setupCorrect"]
          },
          "then": {
            "properties": {
              "formulaCorrect": {
                "const": true
              }
            }
          }
        }
      ]
    },
    "interpretationOption": {
      "type": "object",
      "additionalProperties": false,
      "required": ["id", "label", "isCorrect"],
      "properties": {
        "id": {
          "$ref": "#/$defs/id"
        },
        "label": {
          "type": "string",
          "pattern": "\\S",
          "maxLength": 1000
        },
        "isCorrect": {
          "type": "boolean"
        }
      }
    },
    "roundingRule": {
      "enum": ["exact", "nearest_whole", "nearest_0_1", "nearest_1k", "nearest_1m"]
    },
    "tolerance": {
      "oneOf": [
        {
          "type": "object",
          "additionalProperties": false,
          "required": ["type", "value"],
          "properties": {
            "type": {
              "const": "absolute"
            },
            "value": {
              "type": "number",
              "minimum": 0,
              "maximum": 1000000000
            }
          }
        },
        {
          "type": "object",
          "additionalProperties": false,
          "required": ["type", "value"],
          "properties": {
            "type": {
              "const": "percentage"
            },
            "value": {
              "type": "number",
              "minimum": 0,
              "maximum": 1
            }
          }
        },
        {
          "type": "object",
          "additionalProperties": false,
          "required": ["type", "min", "max"],
          "properties": {
            "type": {
              "const": "range"
            },
            "min": {
              "type": "number"
            },
            "max": {
              "type": "number"
            }
          }
        }
      ]
    },
    "answerErrorChecks": {
      "type": "object",
      "additionalProperties": false,
      "minProperties": 1,
      "properties": {
        "percentagePointValue": {
          "type": "number"
        },
        "roundingTolerance": {
          "$ref": "#/$defs/tolerance"
        }
      }
    },
    "answer": {
      "type": "object",
      "additionalProperties": false,
      "required": ["value", "unit"],
      "properties": {
        "value": {
          "type": "number"
        },
        "unit": {
          "$ref": "#/$defs/unit"
        },
        "tolerance": {
          "$ref": "#/$defs/tolerance"
        },
        "errorChecks": {
          "$ref": "#/$defs/answerErrorChecks"
        },
        "roundingRule": {
          "$ref": "#/$defs/roundingRule"
        }
      }
    },
    "explanation": {
      "type": "object",
      "additionalProperties": false,
      "required": ["short", "steps"],
      "properties": {
        "short": {
          "type": "string",
          "pattern": "\\S",
          "maxLength": 1000
        },
        "steps": {
          "type": "array",
          "minItems": 1,
          "maxItems": 10,
          "items": {
            "type": "string",
            "pattern": "\\S",
            "maxLength": 1000
          }
        },
        "shortcut": {
          "type": "string",
          "pattern": "\\S",
          "maxLength": 1000
        }
      }
    },
    "questionTags": {
      "type": "array",
      "minItems": 1,
      "maxItems": 10,
      "uniqueItems": true,
      "items": {
        "$ref": "#/$defs/tag"
      }
    },
    "exhibitDatasetArray": {
      "type": "array",
      "minItems": 1,
      "maxItems": 100,
      "uniqueItems": true,
      "items": {
        "$ref": "#/$defs/exhibitDataset"
      }
    },
    "exhibitDataset": {
      "type": "object",
      "additionalProperties": false,
      "required": [
        "id",
        "title",
        "description",
        "unit",
        "columns",
        "rows",
        "visualization",
        "questions"
      ],
      "properties": {
        "id": {
          "$ref": "#/$defs/id"
        },
        "title": {
          "$ref": "#/$defs/nonBlank100"
        },
        "description": {
          "type": "string",
          "pattern": "\\S",
          "maxLength": 500
        },
        "sourceNote": {
          "type": "string",
          "pattern": "\\S",
          "maxLength": 500
        },
        "unit": {
          "$ref": "#/$defs/unit"
        },
        "columns": {
          "type": "array",
          "minItems": 2,
          "maxItems": 20,
          "uniqueItems": true,
          "items": {
            "$ref": "#/$defs/exhibitColumn"
          }
        },
        "rows": {
          "type": "array",
          "minItems": 1,
          "maxItems": 500,
          "uniqueItems": true,
          "items": {
            "$ref": "#/$defs/exhibitRow"
          }
        },
        "visualization": {
          "$ref": "#/$defs/exhibitVisualization"
        },
        "questions": {
          "type": "array",
          "minItems": 1,
          "maxItems": 50,
          "uniqueItems": true,
          "items": {
            "$ref": "#/$defs/exhibitQuestion"
          }
        }
      }
    },
    "exhibitColumn": {
      "type": "object",
      "additionalProperties": false,
      "required": ["id", "label", "role", "valueType"],
      "properties": {
        "id": {
          "$ref": "#/$defs/id"
        },
        "label": {
          "$ref": "#/$defs/nonBlank100"
        },
        "description": {
          "type": "string",
          "pattern": "\\S",
          "maxLength": 500
        },
        "role": {
          "enum": ["dimension", "metric"]
        },
        "valueType": {
          "enum": ["currency", "number", "percentage", "text", "year"]
        },
        "unit": {
          "$ref": "#/$defs/unit"
        }
      },
      "allOf": [
        {
          "if": {
            "properties": {
              "role": {
                "const": "dimension"
              }
            },
            "required": ["role"]
          },
          "then": {
            "properties": {
              "valueType": {
                "enum": ["text", "year"]
              }
            }
          }
        },
        {
          "if": {
            "properties": {
              "role": {
                "const": "metric"
              }
            },
            "required": ["role"]
          },
          "then": {
            "properties": {
              "valueType": {
                "enum": ["currency", "number", "percentage"]
              }
            }
          }
        }
      ]
    },
    "exhibitRow": {
      "type": "object",
      "additionalProperties": false,
      "required": ["id", "cells"],
      "properties": {
        "id": {
          "$ref": "#/$defs/id"
        },
        "label": {
          "$ref": "#/$defs/nonBlank100"
        },
        "cells": {
          "type": "object",
          "minProperties": 2,
          "maxProperties": 20,
          "propertyNames": {
            "$ref": "#/$defs/id"
          },
          "additionalProperties": {
            "oneOf": [
              {
                "type": "number"
              },
              {
                "type": "string",
                "pattern": "\\S",
                "maxLength": 500
              }
            ]
          }
        }
      }
    },
    "columnIdArray": {
      "type": "array",
      "minItems": 1,
      "maxItems": 8,
      "uniqueItems": true,
      "items": {
        "$ref": "#/$defs/id"
      }
    },
    "exhibitVisualization": {
      "oneOf": [
        {
          "$ref": "#/$defs/tableVisualization"
        },
        {
          "$ref": "#/$defs/pieVisualization"
        },
        {
          "$ref": "#/$defs/scatterVisualization"
        },
        {
          "$ref": "#/$defs/seriesVisualization"
        },
        {
          "$ref": "#/$defs/waterfallVisualization"
        }
      ]
    },
    "tableVisualization": {
      "type": "object",
      "additionalProperties": false,
      "required": ["type"],
      "properties": {
        "type": {
          "const": "table"
        },
        "title": {
          "$ref": "#/$defs/nonBlank100"
        },
        "selectedColumnIds": {
          "type": "array",
          "minItems": 1,
          "maxItems": 20,
          "uniqueItems": true,
          "items": {
            "$ref": "#/$defs/id"
          }
        }
      }
    },
    "pieVisualization": {
      "type": "object",
      "additionalProperties": false,
      "required": ["type", "categoryColumnId", "valueColumnId"],
      "properties": {
        "type": {
          "const": "pie_chart"
        },
        "title": {
          "$ref": "#/$defs/nonBlank100"
        },
        "categoryColumnId": {
          "$ref": "#/$defs/id"
        },
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