{
  "capability_id": "math.scientific_notation",
  "tool_id": "scientific-notation",
  "engine": "scientific-notation",
  "calculation_version": "2.0.1",
  "generated_at": "2026-10-22T08:54:35.135Z",
  "engine_build": "2026-10-21",
  "test_count": 9,
  "passed": 9,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "passed": 4,
      "total": 4
    },
    "boundary": {
      "passed": 5,
      "total": 5
    },
    "property": {
      "passed": 0,
      "total": 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": [
    "Canonical Agent modes are convert / engineering / normalize / operate. dec-sci, sci-dec, numInput, coefInput, expInput, aInput, bInput are URL/engine adapter aliases, not the Agent contract.",
    "Missing/invalid numbers → INVALID_NUMBER / MISSING_REQUIRED_INPUT",
    "Division by zero in operate → DIVISION_BY_ZERO",
    "Each numeric text token is at most512 characters. Normalize exponent is an integer within±10000. Decimal exponents in A×10^n are combined before one binary64 conversion; finite nonzero subnormals accepted; nonzero values rounded to zero are rejected.",
    "Matching adapter aliases only; inactive/unknown fields and invalid mode/op are rejected. Shortest binary64 decimal display does not preserve significant figures. Shared URLs reach the server."
  ],
  "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": "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"
    },
    {
      "title": "UC Berkeley CS61C Course Notes — Normalized Numbers",
      "section": "§2.1 Scientific Notation (Base-10)",
      "url": "https://notes.cs61c.org/content/floating-point/fp-floating-point/",
      "supports": "Decimal scientific notation as a coefficient times a power of ten, normalization, and the distinction from binary floating-point representation. CalculatorX states its sign, zero and exponent policies separately. Mathematical representation reference only; not implementation validation or endorsement.",
      "kind": "reference",
      "publisher": "UC Berkeley CS61C course staff"
    }
  ],
  "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": "sha256:18ec84e2612d3f9fcba0e9b4508b97d3ac41997c24d0605abaeb38abc1d3a900",
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 9,
      "total": 9,
      "golden": 4,
      "boundary": 5,
      "property": 0
    },
    "contract_checks": {
      "passed": 6,
      "total": 6
    }
  },
  "evidence_core_generated_at": "2026-10-21T06:25:13.024Z",
  "rendered_at": "2026-10-22T08:54:35.135Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "2.0.1",
    "artifacts": {
      "engine": "2.0.1",
      "page": "2.0.1",
      "capability": "2.0.1",
      "evidence": "2.0.1",
      "input_schema": "2.0.1",
      "output_schema": "2.0.1",
      "mcp_contract": "2.0.1"
    },
    "digests": {
      "input_schema_sha256": "4756bfd7d99f3e794b01565b1a471e36291ed736a53492e8510ea70bd8afe8d7",
      "output_schema_sha256": "aa2cb423283955ce4ae093b9eaa7fa8f69d4d5137340ab83fe5392d68026733e",
      "evidence_sha256": "73abb82b9900c7ad3aa465b0214b7d118a6cb17c60f0639403d8e19223a3354f",
      "evidence_core_sha256": "73abb82b9900c7ad3aa465b0214b7d118a6cb17c60f0639403d8e19223a3354f",
      "capability_sha256": "104dbeea4fbe576f54d49e875e76cd158929089790a697cbd11ee870605669c2",
      "engine_sha256": "a664ae25cd2134de7de43a99352933043215473589aec38c9416508150cb1008",
      "mcp_contract_sha256": "a1a8617719bef45391ee6917dc1783a01de2eedf297e7596b3cb5017cd0e1560"
    },
    "contract_checks": {
      "total": 6,
      "passed": 6,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "2.0.1"
        },
        {
          "id": "schema-output-required-declared",
          "status": "pass"
        },
        {
          "id": "schema-valid-input-executes",
          "status": "pass"
        },
        {
          "id": "engine-success-output-validates-schema",
          "status": "pass"
        },
        {
          "id": "schema-rejects-incomplete-input",
          "status": "pass"
        },
        {
          "id": "rest-success-payload-validates-schema",
          "status": "pass"
        }
      ]
    },
    "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json"
  },
  "tests": [],
  "disclosure": {
    "policy": "calculatorx-public-evidence-v1",
    "full_validation": "private",
    "representation": "summary"
  }
}
