{
  "capability_id": "math.log",
  "tool_id": "log",
  "engine": "log",
  "calculation_version": "1.1.6",
  "generated_at": "2026-10-28T03:01:57.866Z",
  "engine_build": "2026-10-27",
  "test_count": 45,
  "passed": 45,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "passed": 22,
      "total": 22
    },
    "boundary": {
      "passed": 23,
      "total": 23
    },
    "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/log",
  "api": "https://www.calculatorx.com/api/v1/calc/log",
  "schema_input": "https://www.calculatorx.com/schemas/math.log.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/math.log.output.json",
  "assumptions": [
    "Real arithmetic; argument x > 0; base b > 0 and b ≠ 1.",
    "Unspecified log is common (base 10). ln is the dedicated natural-log page; this engine also accepts base e.",
    "UI, SSR share URLs, REST, and validation cases all call this same three-mode engine.",
    "When b, x, and y are all present with no explicit solve_for, the engine computes y and ignores the extra y (legacy share URLs)."
  ],
  "limitations": [
    "Solve y=log_b(x), x=b^y or b=x^(1/y). Positive finite x and base b>0,b≠1; y finite. Omitted base defaults10 only for forward/argument solve.",
    "Strict decimal/scientific text up to512 characters or e; matching known-input aliases; unknown keys, nonfinite types and nonzero text rounded to zero reject. Legacy all-three selects y; requested output fields are ignored.",
    "No numerical snapping near1/2/e/10. Symbolic base e uses Math.log/exp; numeric bases preserve binary64 values. Base1 rounding rejects RESULT_ROUNDED_TO_ONE, distinct from no mathematical solution.",
    "Independent Decimal200 fixed complete-pack vectors:4ULP for logarithm/argument and128ULP for solved base; known fields exact binary64.16 existing common-log O3 vectors retain2ULP. Neither is a whole-domain guarantee.",
    "Display normally12 significant digits, preserving extra digits near1; complete native exports retain raw inputs. Conditioning grows near base1 and y=0 for base solve. Local typing; URL/REST/MCP send inputs and may enter logs."
  ],
  "boundary_conditions": [
    "Invalid given base (≤ 0 or 1) returns INVALID_BASE.",
    "x ≤ 0 returns INVALID_ARGUMENT (real log is undefined).",
    "0 < b < 1 is valid (for example log_{0.5}(0.25) = 2 and inverse x = 0.5² = 0.25).",
    "x = 1 returns y = 0 for every valid base; x = b returns y = 1.",
    "Solving for b with x = 1 and y = 0 returns NON_UNIQUE_BASE (any valid base satisfies b⁰ = 1).",
    "Solving for b with x ≠ 1 and y = 0 returns NO_REAL_SOLUTION.",
    "Solving for b when the only real candidate is b = 1 (x = 1, y ≠ 0) returns NO_REAL_SOLUTION.",
    "Extreme inputs that overflow or underflow IEEE-754 return RESULT_OVERFLOW / RESULT_UNDERFLOW, not Infinity or 0.",
    "Invalid solve_for returns INVALID_SOLVE_FOR.",
    "Missing both x and y returns MISSING_REQUIRED_INPUT."
  ],
  "sources": [
    {
      "title": "NIST Digital Library of Mathematical Functions, Chapter 4",
      "section": "Logarithm, Exponential, Powers",
      "url": "https://dlmf.nist.gov/4",
      "supports": "Logarithm as the inverse of the exponential; log_b(x)=y ⇔ b^y=x",
      "kind": "reference"
    },
    {
      "title": "NIST DLMF §4.2",
      "section": "Logarithm: definitions and inverse of the exponential",
      "url": "https://dlmf.nist.gov/4.2",
      "supports": "b^(log_b x) = x and log_b(b^y) = y for valid real b and x > 0",
      "kind": "reference",
      "publisher": "National Institute of Standards and Technology"
    },
    {
      "title": "CalculatorX mathematical conventions",
      "section": "Common (base 10), natural (base e), and real bases b > 0, b ≠ 1",
      "supports": "Unspecified log is common (base 10); custom bases may be in (0, 1); real log requires x > 0",
      "kind": "definition"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:36ea10b0e2113c1354027bdab7d5812f7c7426207fc2a5df8dac68d7430801ab",
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 45,
      "total": 45,
      "golden": 22,
      "boundary": 23,
      "property": 0
    },
    "contract_checks": {
      "passed": 6,
      "total": 6
    }
  },
  "evidence_core_generated_at": "2026-10-27T02:30:37.745Z",
  "rendered_at": "2026-10-28T03:01:57.866Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "1.1.6",
    "artifacts": {
      "engine": "1.1.6",
      "page": "1.1.6",
      "capability": "1.1.6",
      "evidence": "1.1.6",
      "input_schema": "1.1.6",
      "output_schema": "1.1.6",
      "mcp_contract": "1.1.6"
    },
    "digests": {
      "input_schema_sha256": "a1a6766ec07f567848082fb89fb3c34dce8aaa0b252f8702931fc74fe395bf24",
      "output_schema_sha256": "b069e80c0bb536f1b63e7806faa1ab2dd1aea918a5d35c5abaf997f5df7e611a",
      "evidence_sha256": "1b64590f3d2035278452f01abf959cd24b989622fd3faa96d2d720f4a638565f",
      "evidence_core_sha256": "1b64590f3d2035278452f01abf959cd24b989622fd3faa96d2d720f4a638565f",
      "capability_sha256": "54a73aec78c88867ae755ed5b5f1c959941b4e8e8b2ad8db34039fb2fc806e40",
      "engine_sha256": "c6ebd8436f08b413e1ac6317b2d48550f2e6639a90dff254244e3aa562158b8d",
      "mcp_contract_sha256": "5898d9426fe62990b5c5eed0b7ac18076acb83b29b083b5b4dd52f28efe79ae5"
    },
    "contract_checks": {
      "total": 6,
      "passed": 6,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.1.6"
        },
        {
          "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"
  }
}