CVP verified calculation capability

Natural logarithm Calculation Capability

Natural logarithm y = ln(x) = log_e(x) for real x > 0, with exp(result) verification.

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

Model

Definition

Definition: ln(x) = y ⇔ eʸ = x
As log_e: ln(x) = log_e(x)
To common log: log₁₀(x) = ln(x) / ln(10)
Change of base: log_b(x) = ln(x) / ln(b)

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`x`	Argument x > 0	—	input
`xInput`	Share-URL alias for x	—	input
`value`	—	—	output
`y`	—	—	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 ln(x)
`valid_domain`	x > 0
`singularity_policy`	INVALID_INPUT when x ≤ 0
`branch_policy`	real natural log only
`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; argument x > 0. Base is e, not 10.
On many calculators log means log₁₀; in some programming languages log(x) means ln(x).
Published engine is y = ln(x). A legacy y query parameter is ignored and stripped from the address bar. Inverse x = e^y is Antilog with base e.

Example

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

ln(10) ≈ 2.302585092994

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 · 3/3 declared partitions (ln, invalid-domain, xcal)
Calculation version: 1.0.4
Verification: 23/23 calculation tests · 11/11 legacy golden · 12/12 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 eafd28643bc3
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: ≤2 ULP vs O3 applies to the 16 published tabulated natural-log vectors. It is not a guarantee over the whole positive reals or unlisted neighborhoods of 0 and 1.
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 · 12/12 CVP boundary · 12/12 invalid · 2/2 property · 2/2 metamorphic · 3/3 round-trip · 16/16 O3 · 1/1 cross-interface · 12/12 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/ln' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"x":1},"calculation_version":"1.0.4"}'

{
  "inputs": {
    "x": 1
  },
  "calculation_version": "1.0.4"
}

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

Full REST contract: REST API docs.

Tool id: ln
Engine: ln
REST: POST /api/v1/calc/ln
MCP: execute_calculation with capability_id: "math.ln"
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 — Natural logarithm base e; real argument x > 0

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.ln"},"_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.ln","inputs":{"x":1},"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.