{ "capability_id": "math.exponent", "tool_id": "exponent", "engine": "exponent", "calculation_version": "1.0.5", "generated_at": "2026-10-28T03:01:57.876Z", "engine_build": "2026-10-26", "test_count": 38, "passed": 38, "failed": 0, "tests_summary": { "golden": { "passed": 16, "total": 16 }, "boundary": { "passed": 22, "total": 22 }, "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/exponent", "api": "https://www.calculatorx.com/api/v1/calc/exponent", "schema_input": "https://www.calculatorx.com/schemas/math.exponent.input.json", "schema_output": "https://www.calculatorx.com/schemas/math.exponent.output.json", "assumptions": [ "Real arithmetic only. Complex values are not returned.", "0⁰ is undefined. 0 raised to a negative power is undefined.", "Negative bases are allowed only with an integer exponent. Non-integer exponents of a negative base are NOT_REAL (this engine does not special-case odd roots).", "Token e as base uses Math.exp(n), not (Math.E)**n.", "Solve exponent uses n = log(y)/log(a) only when a > 0, a ≠ 1, y > 0. 1ⁿ = 1 is INFINITELY_MANY; 1ⁿ = 2 is NO_REAL_SOLUTION; 0ⁿ = 0 (n > 0) is INFINITELY_MANY.", "Solve base: odd integer n → unique real a = sign(y)·|y|^(1/n). Even integer n and y > 0 → two reals ± with warning TWO_REAL_SOLUTIONS (principal value is non-negative). Even n and y < 0 → NOT_REAL. n = 0 and y = 1 → INFINITELY_MANY." ], "limitations": [ "Real power equation y=a^n. solve_for y/a/n; omit the unknown and provide exactly the two known fields. Omitted mode inferred from the two fields. Matching aliases only, unknown keys reject.", "Strict decimal/scientific tokens up to512 characters; null/blank/nonfinite/hex/boolean reject; nonzero text rounded to zero rejects NUMERIC_UNDERFLOW. Raw JSON numeric underflow rejects before parse loss. Integer exponent must be an exact safe integer. Semantic constraints follow shape validation.", "Only symbolic e uses exp/log; numeric approximations retain their own value. Negative-base forward domain requires integer n; inverse n for negative bases requires an integer reproducing signed y. Base -1 gives infinitely many integer exponents for y=±1. Inverse even integer powers preserve both signs.", "Binary64, not exact decimal. Independent fixed review vectors allow16 ULP forward/log-ratio and128 ULP inverse-base reciprocal powers; legacy O3 six vectors retain2 ULP. Not a whole-domain guarantee. Forward relative sensitivity |n| in a; inverse exponent ill-conditioned near a=1. Subnormal results have low relative accuracy. Overflow/nonzero-to-zero results reject.", "12 significant digit display, full typed outputs/raw inputs/version in exports. Negative-base graphs do not draw a continuous real curve. Typing local; shared URLs/REST/MCP send inputs and may enter logs; links run current version." ], "boundary_conditions": [ "Missing required inputs for the selected solve_for returns MISSING_REQUIRED_INPUT. Invalid solve_for returns INVALID_SOLVE_FOR.", "Non-numeric, object, array, boolean, NaN, or Infinity inputs return INVALID_NUMBER.", "0⁰ and 0^(n<0) return UNDEFINED_POWER.", "Negative a with non-integer n returns NOT_REAL.", "IEEE-754 overflow returns RESULT_OVERFLOW, not Infinity. Underflow to 0 for nonzero a returns RESULT_UNDERFLOW.", "Identity cases 1ⁿ = 1 and a⁰ = 1 (a ≠ 0) return INFINITELY_MANY. Impossible identities return NO_REAL_SOLUTION." ], "sources": [ { "title": "NIST Digital Library of Mathematical Functions, Chapter 4", "section": "Logarithm, Exponential, Powers", "url": "https://dlmf.nist.gov/4", "supports": "Real powers a^n, including negative exponents as reciprocals and fractional exponents as roots when the result is real", "kind": "reference" }, { "title": "NIST DLMF §4.2", "section": "Logarithm and the exponential as inverse operations", "url": "https://dlmf.nist.gov/4.2", "supports": "a^n = exp(n ln a) for a > 0; this engine uses that identity via IEEE-754 a**n / Math.exp, not a table", "kind": "reference", "publisher": "National Institute of Standards and Technology" }, { "title": "CalculatorX mathematical conventions", "section": "0^0 undefined; negative base only with integer exponent", "supports": "Matches the on-page real-arithmetic contract. solve_for=y is the scalar forward engine; a and n are published inverses of aⁿ = y with explicit multiplicity.", "kind": "definition" } ], "methods": [], "fingerprint": "sha256:d4013bacbd388a47625fb668af202302ed27ce38f01bcbb9c5dc42b40ba89765", "tier": "engine_tested", "verification": { "tests": { "passed": 38, "total": 38, "golden": 16, "boundary": 22, "property": 0 }, "contract_checks": { "passed": 6, "total": 6 } }, "evidence_core_generated_at": "2026-10-26T10:51:29.010Z", "rendered_at": "2026-10-28T03:01:57.876Z", "release_integrity": { "status": "verified", "scope": "workspace", "production_attestation_required": true, "calculation_version": "1.0.5", "artifacts": { "engine": "1.0.5", "page": "1.0.5", "capability": "1.0.5", "evidence": "1.0.5", "input_schema": "1.0.5", "output_schema": "1.0.5", "mcp_contract": "1.0.5" }, "digests": { "input_schema_sha256": "3fd911557db6d76fa297415bd3213a3035cdee322d6ddd6924c90747c8ebf0d9", "output_schema_sha256": "f6e814508aeb4a4b236f001a6be51ffdb55e48e84c48560170944c80a373f757", "evidence_sha256": "7f4ca4e6c7dc0f8d7e3ca170e2635d1c02014a7c4816d52c0d39d87070496274", "evidence_core_sha256": "7f4ca4e6c7dc0f8d7e3ca170e2635d1c02014a7c4816d52c0d39d87070496274", "capability_sha256": "2bb3a4099907f72f3201eb731124492da38696aa4dc7541b7b9f8656964c71b4", "engine_sha256": "c6ebd8436f08b413e1ac6317b2d48550f2e6639a90dff254244e3aa562158b8d", "mcp_contract_sha256": "5898d9426fe62990b5c5eed0b7ac18076acb83b29b083b5b4dd52f28efe79ae5" }, "contract_checks": { "total": 6, "passed": 6, "failed": 0, "items": [ { "id": "release-artifacts-aligned", "status": "pass", "detail": "1.0.5" }, { "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" } }