CVP verified calculation capability

Proficiency-testing z′ Calculation Capability

ISO 13528 z′ = (ylab−xref)/√(σ_pt²+u(x_pt)²). σ_pt and u(x_pt) must both be > 0 so this cannot wrap z-score. |z′| ≤ 2 pass, 2 < |z′| < 3 warning, |z′| ≥ 3 fail. Not z-score, not zeta, and not En.

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

Model

z′

z′: z′ = (ylab − xref) / √(σ_pt² + u(x_pt)²)
Decision: |z′| ≤ 2 → pass; 2 < |z′| < 3 → warning; |z′| ≥ 3 → fail

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`ylab`	Laboratory / participant result	—	input / output
`xref`	Assigned value x_pt	—	input / output
`sigma`	Scheme SDPA σ_pt	—	input / output
`u_xref`	Standard uncertainty of the assigned value u	—	input / output
`z_prime`	—	—	output
`abs_z_prime`	—	—	output
`decision`	—	—	output
`denom`	√	—	output

Assumptions / Validity

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

Assumptions

ISO 13528 z′ = (ylab−xref)/√(σ_pt²+u(x_pt)²)
σ_pt > 0 and u(x_pt) > 0 — u(x_pt)=0 is not a z-score wrap
Not z-score, not zeta, and not En

Not supported

z-score (σ_pt alone)
zeta (ulab+uref)
En (expanded U)
u(x_pt)=0 as a wrap of z
ILAC G8 spec decision

Example

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

ylab=5 xref=0 sigma=3 u_xref=4 → z′=1 pass

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Proficiency-testing z-prime from ylab, xref, σ_pt, and u(x_pt), + O3 mpmath tabulated z-prime.. 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 z-prime from ylab, xref, σ_pt, and u(x_pt), + O3 mpmath tabulated z-prime.· View Manifest · CVP overview · Specification
Verified scope: Proficiency-testing z-prime from ylab, xref, σ_pt, and u(x_pt), + O3 mpmath tabulated z-prime.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (pass, fail, alias, awkward, invalid-domain)
Deferred: Not z-score, not zeta, and not En.
Calculation version: 1.0.1
Verification: 12/12 calculation tests · 1/1 legacy golden · 6/6 legacy boundary · 5/5 legacy property
Production surface contract: 6/6
Versions: Calculation 1.0.1 · CVP protocol 1.0.0-proposed · Evidence 2026-09-25.o2-o3
Verification revision: 2026-09-25.o2-o3 · 1/1 property · digest 7ead485672f6
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: proficiency-testing z-prime vs a separate-module hypot identity (≤2 ULP). Not z-score, not zeta, and not En. ≤2 ULP vs O3 applies only to the published tabulated z-prime vectors. It is not a whole-domain guarantee and does not cover z-score, zeta, or En.
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 · 6/6 CVP boundary · 6/6 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/z-prime' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"ylab":5,"xref":0,"sigma":3,"u_xref":4},"calculation_version":"1.0.1"}'

{
  "inputs": {
    "ylab": 5,
    "xref": 0,
    "sigma": 3,
    "u_xref": 4
  },
  "calculation_version": "1.0.1"
}

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

Full REST contract: REST API docs.

Tool id: z-prime
Engine: z-prime
REST: POST /api/v1/calc/z-prime
MCP: execute_calculation with capability_id: "engineering.conformity.z_prime"
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 — z′ score when the uncertainty of the assigned value is not negligible
ISO/IEC 17043 — Conformity assessment — General requirements for the competence of proficiency testing providers — Performance evaluation using z′

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.z_prime"},"_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.z_prime","inputs":{"ylab":5,"xref":0,"sigma":3,"u_xref":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.