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  "capability_id": "math.factorial",
  "tool_id": "factorial",
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  "page": "https://www.calculatorx.com/calc/math/factorial",
  "api": "https://www.calculatorx.com/api/v1/calc/factorial",
  "schema_input": "https://www.calculatorx.com/schemas/math.factorial.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/math.factorial.output.json",
  "assumptions": [
    "n is an integer satisfying 0 ≤ n ≤ 5000.",
    "Ordinary (single) factorial only — not multifactorial and not the real Gamma function for non-integers."
  ],
  "limitations": [
    "Ordinary (single) factorial only — not multifactorial and not Γ(n+1) for non-integers",
    "Domain is 0 ≤ n ≤ 5000 (product/resource bound, not a mathematical bound)",
    "Missing n → MISSING_REQUIRED_INPUT",
    "Non-numeric or non-integer n → INVALID_NUMBER",
    "n < 0 → VALUE_MUST_BE_NON_NEGATIVE",
    "n > 5000 → VALUE_ABOVE_MAX",
    "Digits-only strings: trimmed length≤64; matching n/nInput aliases; string scientific notation rejected. JSON numeric finite rounding is permitted; raw nonzero underflow rejected.",
    "Scientific display uses the first12 digits without rounding; exact contains every digit.",
    "Unknown fields → UNKNOWN_INPUT; aliases disagree → INPUT_ALIAS_CONFLICT; excessive text → INPUT_TOO_LARGE"
  ],
  "boundary_conditions": [
    "Missing n → MISSING_REQUIRED_INPUT",
    "Non-numeric n → INVALID_NUMBER",
    "Non-integer n (for example 5.5) → INVALID_NUMBER",
    "n < 0 → VALUE_MUST_BE_NON_NEGATIVE",
    "n > 5000 → VALUE_ABOVE_MAX"
  ],
  "sources": [
    {
      "title": "NIST Digital Library of Mathematical Functions, Chapter 5",
      "section": "Gamma Function",
      "url": "https://dlmf.nist.gov/5",
      "supports": "Ordinary factorial of a nonnegative integer; n! = Γ(n+1)",
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      "section": "Special values and extrema",
      "url": "https://dlmf.nist.gov/5.4",
      "supports": "n! = Γ(n+1), including 0! = 1. This calculator publishes ordinary factorial only; non-integer Gamma values are out of scope.",
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      "publisher": "National Institute of Standards and Technology"
    },
    {
      "title": "CalculatorX mathematical conventions",
      "section": "Domain 0 ≤ n ≤ 5000; exact BigInt n!",
      "supports": "Matches the on-page contract. Permutation count P(n,n)=n! is an interpretation, not a second engine.",
      "kind": "definition"
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