{
  "capability_id": "math.scientific_notation",
  "tool_id": "scientific-notation",
  "engine": "scientific-notation",
  "calculation_version": "1.1.1",
  "generated_at": "2026-09-16T22:03:43.784Z",
  "engine_build": "2026-09-16",
  "test_count": 6,
  "passed": 6,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 4,
      "passed": 4
    },
    "boundary": {
      "total": 2,
      "passed": 2
    },
    "property": {
      "total": 0,
      "passed": 0
    }
  },
  "engine_tested": true,
  "expert_reviewed": false,
  "internally_reviewed": false,
  "review_kind": null,
  "source_checked": true,
  "reviewed_by": null,
  "reviewer_role": null,
  "last_reviewed": null,
  "expert_review": {
    "status": "optional_not_performed",
    "reviewer": null,
    "scope": [
      "formula",
      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
    ],
    "note": "Domain expert review is optional under CVP (CVP-EXP-01). Absence does not block CVP Verified. See Review policy for supplemental domain assurance."
  },
  "internal_review": {
    "status": "not_applicable",
    "reviewer": null
  },
  "page": "https://www.calculatorx.com/calc/math/scientific-notation",
  "api": "https://www.calculatorx.com/api/v1/calc/scientific-notation",
  "schema_input": "https://www.calculatorx.com/schemas/math.scientific_notation.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/math.scientific_notation.output.json",
  "assumptions": [
    "Finite IEEE-754 binary64 values. Inputs outside the supported floating-point range are rejected or reported as overflow/underflow. Very large/small in-range values use exponential display.",
    "UI, share URLs, REST, and validation cases all call this same engine."
  ],
  "limitations": [
    "Missing/invalid numbers → INVALID_NUMBER / MISSING_REQUIRED_INPUT",
    "Division by zero in operate → DIVISION_BY_ZERO"
  ],
  "boundary_conditions": [
    "Division by zero rejected (DIVISION_BY_ZERO)",
    "Empty or unparsable input rejected (MISSING_REQUIRED_INPUT / INVALID_NUMBER)",
    "Inputs outside the IEEE-754 binary64 range rejected (RESULT_OVERFLOW / RESULT_UNDERFLOW)",
    "Zero is returned as 0, not A × 10ⁿ with 1 ≤ |A| < 10"
  ],
  "sources": [
    {
      "title": "OpenStax Elementary Algebra 2e — Scientific Notation",
      "section": "5.2 An application of exponents: scientific notation",
      "url": "https://openstax.org/books/elementary-algebra-2e/pages/5-2-an-application-of-exponents-scientific-notation",
      "supports": "A number in scientific notation is written A × 10ⁿ with 1 ≤ |A| < 10 and integer n; 0 is the exception",
      "kind": "reference",
      "accessed": "2026-08-30"
    },
    {
      "title": "BIPM SI Brochure (9th edition)",
      "section": "Table 8 — SI prefixes (powers of 10³)",
      "url": "https://www.bipm.org/en/publications/si-brochure",
      "supports": "Engineering notation uses exponents that are multiples of 3 so values line up with SI prefixes",
      "kind": "standard",
      "accessed": "2026-08-30"
    },
    {
      "title": "NIST SI prefixes",
      "section": "SI prefixes from 10⁻³⁰ to 10³⁰",
      "url": "https://www.nist.gov/pml/owm/metric-si-prefixes",
      "supports": "Prefix names (milli, micro, kilo, mega, …) attached to engineering exponents",
      "kind": "standard",
      "accessed": "2026-08-30"
    }
  ],
  "methods": [
    "IEEE-754 binary64 parse of decimal / E-notation / A×10ⁿ",
    "Normalize via Number#toExponential; engineering exponent ≡ 0 (mod 3)",
    "Test suites are not interchangeable: 20 published examples on this page · 124 automated engine checks (IUT) · CVP verification suite on Evidence (Manifest is the verification source of truth)"
  ],
  "fingerprint": "sha256:9a238f0352b1ee8fac2433daff2b1604ed630fa6ba1278faa001a1756432dc31",
  "tests": [
    {
      "id": "dec-sci-12300",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "dec-sci",
        "value": 12300
      },
      "expect": {
        "coef": 1.23,
        "exp": 4
      },
      "expectWarning": null,
      "actual": {
        "coef": 1.23,
        "exp": 4
      },
      "tol": 1e-12
    },
    {
      "id": "dec-sci-1",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "dec-sci",
        "value": 1
      },
      "expect": {
        "coef": 1,
        "exp": 0
      },
      "expectWarning": null,
      "actual": {
        "coef": 1,
        "exp": 0
      },
      "tol": 0
    },
    {
      "id": "dec-sci-zero",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "dec-sci",
        "value": 0
      },
      "expect": {
        "coef": 0,
        "exp": 0
      },
      "expectWarning": null,
      "actual": {
        "coef": 0,
        "exp": 0
      },
      "tol": 0
    },
    {
      "id": "sci-dec-basic",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "mode": "sci-dec",
        "coef": 3.5,
        "exp": 2
      },
      "expect": 350,
      "expectWarning": null,
      "actual": 350,
      "tol": 0
    },
    {
      "id": "bad-mode",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "nope",
        "value": 1
      },
      "expectError": "INVALID_MODE",
      "code": "INVALID_MODE",
      "error": "scientificNotation unknown mode: nope"
    },
    {
      "id": "missing-value",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "mode": "dec-sci"
      },
      "expectError": "INVALID_NUMBER",
      "code": "INVALID_NUMBER",
      "error": "invalid decimal: undefined"
    }
  ],
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 6,
      "total": 6,
      "golden": 4,
      "boundary": 2,
      "property": 0
    },
    "contract_checks": {
      "passed": 3,
      "total": 3
    }
  },
  "evidence_core_generated_at": "2026-09-16T06:41:00.884Z",
  "rendered_at": "2026-09-16T22:03:43.784Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "1.1.1",
    "artifacts": {
      "engine": "1.1.1",
      "page": "1.1.1",
      "capability": "1.1.1",
      "evidence": "1.1.1",
      "input_schema": "1.1.1",
      "output_schema": "1.1.1",
      "mcp_contract": "1.1.1"
    },
    "digests": {
      "input_schema_sha256": "8401fb09da01304188d42eb3b98befb8fc6556ac1c214494cb4e66659e678866",
      "output_schema_sha256": "c78ddeb1a0b3992927c92f7b3768727bce008e6543747be1b605dc2625f6772f",
      "evidence_sha256": "f8ddc450cf499d7311cc29afa5cf7deebc14a243b17fd3d9b3bdff0b394b1e28",
      "evidence_core_sha256": "f8ddc450cf499d7311cc29afa5cf7deebc14a243b17fd3d9b3bdff0b394b1e28",
      "capability_sha256": "eafa3545ec9a0b4cdc7e3e6e7c09bf45d67b89572f13ff62879a9d06bc0edb49",
      "engine_sha256": "c8d4ccdbfeaf61d7b024d4e1babb0c2ba3b324c1b37bd0cb456a526d8d2b1bd1",
      "mcp_contract_sha256": "863098b311a7b17dc4b229a6302b90b3545b175f716e5d84772c7be8e9716b86"
    },
    "contract_checks": {
      "total": 3,
      "passed": 3,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.1.1"
        },
        {
          "id": "schema-valid-input-executes",
          "status": "pass"
        },
        {
          "id": "engine-success-output-validates-schema",
          "status": "pass"
        }
      ]
    },
    "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json"
  }
}
