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    "Integers only; negatives treated by absolute value",
    "Each integer ≤ 48 decimal digits (product bound, not a mathematical bound)",
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    "Need at least two numbers → NEED_TWO_NUMBERS",
    "Non-integers → INVALID_NUMBER",
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    "At most32 integers; list text≤4096 characters, individual array strings≤128 characters",
    "Aliases values/numbers/numsInput must normalize to the same ordered list; unknown fields rejected",
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    "Missing list → MISSING_REQUIRED_INPUT",
    "Non-integers rejected → INVALID_NUMBER",
    "More than 48 digits → VALUE_ABOVE_MAX",
    "All zeros → UNDEFINED"
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    {
      "title": "Encyclopedia of Mathematics — Greatest common divisor",
      "section": "Definition; pairwise fold; prime-factor form",
      "url": "https://encyclopediaofmath.org/wiki/Greatest_common_divisor",
      "supports": "GCF of n integers exists when not all are zero; (a₁,…,aₙ,aₙ₊₁)=((a₁,…,aₙ),aₙ₊₁); shared-prime min exponents",
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      "section": "Remainder recurrence GCF(a,b)=GCF(b, a mod b)",
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      "supports": "Binary Euclidean primitive used inside the pairwise fold",
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      "supports": "Negatives by |n|; ignore zeros unless the whole set is 0; exact BigInt with a product digit cap",
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    {
      "title": "MIT Mathematics for Computer Science — Chapter 8: Number Theory",
      "section": "Chapter 8, including sections 8.2–8.9 and problem 8.24",
      "url": "https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-spring-2015/mit6_042js15_textbook.pdf",
      "supports": "Divisibility, prime factorization, gcd and the Euclidean algorithm, lcm via prime exponents, division with remainder, modular congruence and multiplicative inverses. CalculatorX’s signed-remainder and zero-input policies are stated separately on the page. Mathematical reference only; not validation or endorsement of this implementation.",
      "kind": "reference",
      "publisher": "Massachusetts Institute of Technology"
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    "Prime-factor GCF (cross-check when every |n| ≤ 1,000,000)",
    "Factor-list GCF (cross-check when every |n| ≤ 10,000)"
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