CVP verified calculation capability

Normalized error En Calculation Capability

Proficiency-testing En = (ylab−xref)/√(Ulab²+Uref²). |En| ≤ 1 is pass (ISO 13528 / ISO/IEC 17043). Ulab and Uref are already expanded. Not zeta, not TUR, and not an ILAC G8 spec decision.

Engineering · Conformity Capability ID engineering.conformity.normalized_error version 1.0.1 CVP VERIFIED CURRENT Engineering

Model

Normalized error

Normalized error: En = (ylab − xref) / √(Ulab² + Uref²)
Decision: |En| ≤ 1 → pass

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`ylab`	Laboratory / participant result	—	input / output
`xref`	Assigned or reference value	—	input / output
`Ulab`	Already-expanded uncertainty of ylab	—	input / output
`Uref`	Already-expanded uncertainty of xref	—	input / output
`En`	—	—	output
`abs_En`	—	—	output
`decision`	—	—	output

Assumptions / Validity

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

Assumptions

ISO 13528 / ISO/IEC 17043 En with already-expanded Ulab and Uref
|En| ≤ 1 is pass; |En| > 1 is fail
Not zeta (standard u), not TUR, and not an ILAC G8 spec decision

Not supported

zeta-score
TUR
ILAC G8 specification decision
U = k·u_c as a product
RSS of a measurement model

Example

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

ylab=2.5 xref=0 Ulab=3 Uref=4 → En=0.5 pass

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Proficiency-testing En from ylab, xref, and already-expanded Ulab and Uref, + O3 mpmath tabulated En.. 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 · Engineering assurance · Proficiency-testing En from ylab, xref, and already-expanded Ulab and Uref, + O3 mpmath tabulated En.· View Manifest · CVP overview · Specification
Verified scope: Proficiency-testing En from ylab, xref, and already-expanded Ulab and Uref, + O3 mpmath tabulated En.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (pass, fail, alias, awkward, invalid-domain)
Deferred: Not zeta (standard uncertainties), not TUR, and not an ILAC G8 specification decision.
Calculation version: 1.0.1
Verification: 9/9 calculation tests · 1/1 legacy golden · 4/4 legacy boundary · 4/4 legacy property
Production surface contract: 6/6
Versions: Calculation 1.0.1 · CVP protocol 1.0.0-proposed · Evidence 2026-09-24.o2-o3
Verification revision: 2026-09-24.o2-o3 · 1/1 property · digest 7b7a4c158ed2
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: proficiency-testing En vs a separate-module hypot identity (≤2 ULP). Not zeta, not TUR, and not an ILAC G8 specification decision. ≤2 ULP vs O3 applies only to the published tabulated En vectors (pass, the |En|=1 boundary, fail, an alias, a negative result, one awkward pair, equal expanded uncertainties, and a close pair). It is not a whole-domain guarantee and does not cover zeta, TUR, or an ILAC G8 specification decision.
Interfaces: PASS · UI (SSR) / REST / MCP
ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
CVP suite: 4/4 golden · 4/4 CVP boundary · 5/5 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 3/3 cross-interface · 6/6 CVP contract
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.1 (workspace artifacts agree)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

This calculator CURRENT · Public schema 1.0.1 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 6/6.

curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/normalized-error' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"ylab":2.5,"xref":0,"Ulab":3,"Uref":4},"calculation_version":"1.0.1"}'

{
  "inputs": {
    "ylab": 2.5,
    "xref": 0,
    "Ulab": 3,
    "Uref": 4
  },
  "calculation_version": "1.0.1"
}

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

Full REST contract: REST API docs.

Tool id: normalized-error
Engine: normalized-error
REST: POST /api/v1/calc/normalized-error
MCP: execute_calculation with capability_id: "engineering.conformity.normalized_error"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.1)
Versioned output schema: Immutable pin (1.0.1)

References

Human-readable sources plus CVP reference evidence classes.

Sources

ISO 13528 — Statistical methods for use in proficiency testing by interlaboratory comparison — Normalized error En using expanded uncertainties
ISO/IEC 17043 — Conformity assessment — General requirements for the competence of proficiency testing providers — Performance evaluation using En

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":"engineering.conformity.normalized_error"},"_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":"engineering.conformity.normalized_error","inputs":{"ylab":2.5,"xref":0,"Ulab":3,"Uref":4},"calculation_version":"1.0.1"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

Pin calculation_version (1.0.1) when the result must stay reproducible.

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