Public evidence

math.exponent

Machine-checked verification for calculation version 1.0.4 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest Reproduce MCP Review policy

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance· Real forward power; inverse via solve_for · Protocol · Schema · Production report

Declared partition coverage: PASS · 5/5 declared partitions (forward, solve-base, solve-exp, invalid-domain, xcal)
Versions: Calculation 1.0.4 · CVP protocol 1.0.0-proposed · Evidence 2026-09-08.xcal
Verification revision: 2026-09-08.xcal · 2/2 property · digest e5bdc1674386

Verification

Legacy regression suite: 38/38 calculation tests · Production surface contract 3/3

Three distinct suites: educational examples on the calculator page, this legacy regression count (38/38 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.0.4 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-09-08.xcal. Calculation version 1.0.4. CVP 1.0.0-proposed. 3/3 golden · 22/22 CVP boundary · 21/21 invalid · 2/2 property · 2/2 metamorphic · 3/3 round-trip · 6/6 O3 · 1/1 cross-interface · 11/11 cross-calculator · 4/4 URL→result→graph · 1/1 CVP contract. digest e5bdc1674386. ≤2 ULP vs O3 applies to the 6 published tabulated vectors ((2,10), (10,2), (5,0), (9,0.5), (2,−3), (e,1)). It is not a guarantee over all real bases and exponents.

Golden (oracle-backed) 3 / 3
CVP boundary 22 / 22
Invalid input 21 / 21
Property 2 / 2
Metamorphic 2 / 2
Round-trip 3 / 3
O3 high-precision 6 / 6
Cross-interface 1 / 1
Cross-calculator 11 / 11
URL → result → graph 4 / 4
CVP contract 1 / 1
Interfaces PASS · UI (SSR) / REST / MCP / URL→result→graph
Interface claim Success 1/1. Integration: URL → SSR result → Live graph current point (4/4). Hydration/slider/history are URL-canonical contracts, not a live browser session.
Assurance Core

release artifacts aligned PASS
schema valid input executes PASS
engine success output validates schema PASS

Fingerprint sha256:706200fba755b76ba5f07e0f52328bb7dc198c70a2633895f579bcb11ff1445d

Input schema sha256:ce9f339fda5323c16b5118ed74d125a73b9d09a65acd73fc515078d08c8d06c4 · Output schema sha256:bc3ef2f7394c1739149d1c1e3751fe91fa1e793ef15fc5f1621834eebad02c63 · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Build & scope

Engine identity and declared limitations.

Tool: exponent
Engine: exponent
Engine build: 2026-09-10
Evidence core: 2026-09-10T22:48:17.762Z
Rendered: 2026-09-16T22:03:43.778Z
Last reviewed: —

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

0⁰ and 0^(negative) → UNDEFINED_POWER
Negative base with non-integer exponent → NOT_REAL
Forward solve_for=y returns a scalar; inverse returns a structured object

Sources

Standards and references supporting this tool specification. Methods are listed separately — they are algorithms, not bibliographic sources.

NIST Digital Library of Mathematical Functions, Chapter 4 — Logarithm, Exponential, Powers
Supports: Real powers a^n, including negative exponents as reciprocals and fractional exponents as roots when the result is real
NIST DLMF §4.2 — Logarithm and the exponential as inverse operations
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
CalculatorX mathematical conventions — 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.

Legacy published checks

Golden and boundary cases from the legacy Evidence JSON. CVP property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the Manifest — including SKIP when a suite has no vectors.

ID	Kind	Status	Detail
`two-to-ten`	golden	pass	Expected 1024 · Actual 1024
`five-neg-two`	golden	pass	Expected 0.04 · Actual 0.04
`sqrt-nine`	golden	pass	Expected 3 · Actual 3
`seven-to-zero`	golden	pass	Expected 1 · Actual 1
`neg-base-odd`	golden	pass	Expected -8 · Actual -8
`e-to-one`	golden	pass	Expected 2.718281828459045 · Actual 2.718281828459045
`zero-to-five`	golden	pass	Expected 0 · Actual 0
`half-squared`	golden	pass	Expected 0.25 · Actual 0.25
`zero-to-zero`	boundary	pass	Expected UNDEFINED_POWER · Actual UNDEFINED_POWER
`zero-neg`	boundary	pass	Expected UNDEFINED_POWER · Actual UNDEFINED_POWER
`neg-sqrt`	boundary	pass	Expected NOT_REAL · Actual NOT_REAL
`overflow`	boundary	pass	Expected RESULT_OVERFLOW · Actual RESULT_OVERFLOW
`underflow`	boundary	pass	Expected RESULT_UNDERFLOW · Actual RESULT_UNDERFLOW
`empty-a`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`cube-root-two`	golden	pass	Expected 1.2599210498948732 · Actual 1.2599210498948732
`e-to-three`	golden	pass	Expected 20.085536923187668 · Actual 20.085536923187668
`two-neg-ten`	golden	pass	Expected 0.0009765625 · Actual 0.0009765625
`neg-base-zero`	golden	pass	Expected 1 · Actual 1
`ten-308`	golden	pass	Expected 1e+308 · Actual 1e+308
`empty-n`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`empty-both`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`a-object`	boundary	pass	Expected INVALID_NUMBER · Actual INVALID_NUMBER
`n-array`	boundary	pass	Expected INVALID_NUMBER · Actual INVALID_NUMBER
`n-boolean`	boundary	pass	Expected INVALID_NUMBER · Actual INVALID_NUMBER
`a-infinity`	boundary	pass	Expected INVALID_NUMBER · Actual INVALID_NUMBER
`n-nan`	boundary	pass	Expected INVALID_NUMBER · Actual INVALID_NUMBER
`a-abc`	boundary	pass	Expected INVALID_NUMBER · Actual INVALID_NUMBER
`solve-base-even-two-reals`	boundary	pass	warning TWO_REAL_SOLUTIONS
`solve-base-odd-neg`	golden	pass	Expected -2 · Actual n=3 · value=-2 · solve_for=a · a=-2 · y=-8
`solve-base-even-neg`	boundary	pass	Expected NOT_REAL · Actual NOT_REAL
`solve-base-n-zero-y-one`	boundary	pass	Expected INFINITELY_MANY · Actual INFINITELY_MANY
`solve-base-n-zero-y-two`	boundary	pass	Expected NO_REAL_SOLUTION · Actual NO_REAL_SOLUTION
`solve-exp-1024`	golden	pass	Expected 10 · Actual n=10 · value=10 · solve_for=n · a=2 · y=1024
`solve-exp-one-one`	boundary	pass	Expected INFINITELY_MANY · Actual INFINITELY_MANY
`solve-exp-one-two`	boundary	pass	Expected NO_REAL_SOLUTION · Actual NO_REAL_SOLUTION
`solve-exp-zero-zero`	boundary	pass	Expected INFINITELY_MANY · Actual INFINITELY_MANY
`solve-exp-neg-base-integer`	golden	pass	Expected 3 · Actual n=3 · value=3 · solve_for=n · a=-2 · y=-8
`invalid-solve-for`	boundary	pass	Expected INVALID_SOLVE_FOR · Actual INVALID_SOLVE_FOR