CVP verified calculation capability

Exponentiation Calculation Capability

Real power y = aⁿ with solve_for y (default scalar), a, or n.

Math Capability ID math.exponent version 1.0.4 CVP VERIFIED CURRENT Core

Model

Positive integer exponent

Positive integer exponent: aⁿ = a × a × … × a (n ∈ ℤ>0)
General real exponent, a > 0: aⁿ = exp(n ln a)
Negative integer exponent: a⁻ⁿ = 1 / aⁿ
Solve exponent (a > 0, a ≠ 1, y > 0): n = log(y) / log(a)
Solve base, odd integer n: a = ⁿ√y (unique real)
Solve base, even integer n and y > 0: a = ± ⁿ√y

Solve: solve_for = y | a | n

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`a`	Base a	—	input
`base`	Alias for a	—	input
`aInput`	Share-URL alias for a	—	input
`n`	Exponent	—	input
`nInput`	Share-URL alias for n	—	input
`y`	Power when solving for a or n	—	input
`api_version`	—	—	output
`api_contract_version`	—	—	output
`spec_version`	—	—	output
`page`	Canonical calculator page URL	—	output
`links`	—	—	output

Trusted Math contract

Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.

Field	Declaration
`numeric_domain`	real
`exactness`	float64
`algorithm`	float64 pow; algebraic snap for textbook integer cases
`valid_domain`	real base/exponent in the published IEEE domain
`singularity_policy`	UNDEFINED_POWER for 0^0 and 0^(negative); NOT_REAL for negative^non-integer
`branch_policy`	real only — negative^non-integer is NOT_REAL, not a complex branch
`tolerance`	not applicable — closed form; capability Evidence owns comparison, no global default
`convergence`	not applicable — non-iterative
`conditioning`	not applicable — not a matrix κ product
`rounding`	ieee754_round_ties_to_even
`overflow`	ieee754_nonfinite_or_coded_error
`reproducibility`	deterministic algorithm + Capability@Version
`independent_oracle`	Evidence published cases
`golden_vectors`	Evidence golden + boundary + property (and published_reference_case when listed)

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

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.

Example

One numerical check. The calculator page holds worked steps and FAQ.

2¹⁰ = 1024; a² = 4 → a = ±2; 2ⁿ = 1024 → n = 10

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance. Computational verification is defined by CVP. Supplemental domain review (internal) and named expert review are defined by the Review policy and do not by themselves determine CVP conformance.

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance· View Manifest · CVP overview · Specification
Assurance: Core
Declared partition coverage: PASS · 5/5 declared partitions (forward, solve-base, solve-exp, invalid-domain, xcal)
Calculation version: 1.0.4
Verification: 38/38 calculation tests · 16/16 legacy golden · 22/22 legacy boundary
Production surface contract: 5/5
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
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: ≤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.
Interfaces: PASS · UI (SSR) / REST / MCP / URL→result→graph
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.
CVP suite: 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
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.4 (workspace artifacts agree)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

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

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 5/5.

curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/exponent' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"a":2,"n":10},"calculation_version":"1.0.4"}'

{
  "inputs": {
    "a": 2,
    "n": 10
  },
  "calculation_version": "1.0.4"
}

POST /api/v1/calc/exponent. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

Tool id: exponent
Engine: exponent
REST: POST /api/v1/calc/exponent
MCP: execute_calculation with capability_id: "math.exponent"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.4)
Versioned output schema: Immutable pin (1.0.4)

References

Human-readable sources plus CVP reference evidence classes.

Sources

Derived identities

CalculatorX mathematical conventions — 0^0 undefined; negative base only with integer exponent

Reference evidence classes: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior

Try with an agent

Inspect, then execute. Same engine as REST and the human calculator.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"math.exponent"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: execute_calculation' \
  -d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"execute_calculation","arguments":{"capability_id":"math.exponent","inputs":{"a":2,"n":10},"calculation_version":"1.0.4"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

Pin calculation_version (1.0.4) when the result must stay reproducible.

Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.