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      "passed": 2
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    "property": {
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  "expert_reviewed": false,
  "internally_reviewed": false,
  "review_kind": null,
  "source_checked": true,
  "reviewed_by": null,
  "reviewer_role": null,
  "last_reviewed": null,
  "expert_review": {
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    "reviewer": null,
    "scope": [
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      "assumptions",
      "limitations",
      "sources",
      "tests"
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    "note": "Domain expert review is optional under CVP (CVP-EXP-01). Absence does not block CVP Verified. See Review policy for supplemental domain assurance."
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  "api": "https://www.calculatorx.com/api/v1/calc/modulo",
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  "schema_output": "https://www.calculatorx.com/schemas/math.modulo.output.json",
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    "Integers only"
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  "limitations": [
    "Euclidean remainder, not truncated or floored remainder toward −∞ of the quotient only",
    "Not IEEE remainder or floating-point fmod",
    "modulus = 0 → DIVISION_BY_ZERO",
    "Share URLs use modulus, not m (m is reserved elsewhere)"
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  "boundary_conditions": [
    "missing a or modulus → MISSING_REQUIRED_INPUT",
    "modulus = 0 → DIVISION_BY_ZERO"
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  "sources": [
    "ISO 80000-2:2019 Quantities and units — Mathematics (integer division / remainder)",
    "Knuth, The Art of Computer Programming, Euclidean division (remainder ≥ 0)"
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  "methods": [],
  "fingerprint": "sha256:5ba3a81dd04037965fc6b23d197c431682f90dc6c960dd3d5db6d516b6d5828f",
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        "modulus": 5
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        "quotient": 3
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      "expectWarning": null,
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        "remainder": 2,
        "quotient": 3,
        "identity": "17 = (3)·(5) + 2",
        "convention": "euclidean"
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      "tol": null
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      "expectWarning": null,
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        "quotient": -4,
        "identity": "-17 = (-4)·(5) + 3",
        "convention": "euclidean"
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      "kind": "boundary",
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        "modulus": 0
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      "code": "DIVISION_BY_ZERO",
      "error": "modulus must be non-zero."
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    {
      "id": "boundary-mod-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
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      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "Enter an integer modulus."
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      "id": "property-mod-neg",
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      "expect": true,
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      "actual": -17
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      "ok": true,
      "kind": "property",
      "detail": "r still in [0,|m|)",
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      "boundary": 2,
      "property": 5
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