CVP verified calculation capability

Proficiency-testing z-score Calculation Capability

ISO 13528 z-score z = (ylab−xref)/σ_pt. σ_pt is the scheme standard deviation for proficiency assessment (SDPA), not laboratory u and not expanded U. |z| ≤ 2 pass, 2 < |z| < 3 warning, |z| ≥ 3 fail. Not zeta, not En, and not an ILAC G8 spec decision.

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

Model

z-score

z-score: z = (ylab − xref) / σ_pt
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 or reference value	—	input / output
`sigma`	Standard deviation for proficiency assessment σ_pt	—	input / output
`z`	—	—	output
`abs_z`	—	—	output
`decision`	—	—	output

Assumptions / Validity

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

Assumptions

ISO 13528 z-score with scheme SDPA σ_pt
|z| ≤ 2 is pass; 2 < |z| < 3 is warning; |z| ≥ 3 is fail
Not zeta (lab u), not En (expanded U), not TUR, and not an ILAC G8 spec decision

Not supported

zeta (lab u)
En (expanded U)
TUR
ILAC G8 spec decision
computing σ_pt from a PT dataset

Example

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

ylab=2.5 xref=0 sigma=5 → z=0.5 pass

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Proficiency-testing z-score from ylab, xref, and a scheme σ_pt, + O3 mpmath tabulated z-score.. 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-score from ylab, xref, and a scheme σ_pt, + O3 mpmath tabulated z-score.· View Manifest · CVP overview · Specification
Verified scope: Proficiency-testing z-score from ylab, xref, and a scheme σ_pt, + O3 mpmath tabulated z-score.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (pass, fail, alias, awkward, invalid-domain)
Deferred: Not zeta (laboratory u), not En (expanded U), and not an ILAC G8 specification decision.
Calculation version: 1.0.1
Verification: 13/13 calculation tests · 1/1 legacy golden · 6/6 legacy boundary · 6/6 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 e0f1dac3e62d
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: proficiency-testing z-score vs a separate-module division identity (≤2 ULP). Not zeta, not En, and not an ILAC G8 specification decision. ≤2 ULP vs O3 applies only to the published tabulated z-score vectors (pass, the |z|=2 boundary, warning, fail, an alias, a negative result, one awkward pair, and another |z|=2 pair). It is not a whole-domain guarantee and does not cover zeta, En, 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 · 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-score' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"ylab":2.5,"xref":0,"sigma":5},"calculation_version":"1.0.1"}'

{
  "inputs": {
    "ylab": 2.5,
    "xref": 0,
    "sigma": 5
  },
  "calculation_version": "1.0.1"
}

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

Full REST contract: REST API docs.

Tool id: z-score
Engine: z-score
REST: POST /api/v1/calc/z-score
MCP: execute_calculation with capability_id: "engineering.conformity.z_score"
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 z = (x − X) / σ_pt
ISO/IEC 17043 — Conformity assessment — General requirements for the competence of proficiency testing providers — Performance statistics in proficiency testing

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_score"},"_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_score","inputs":{"ylab":2.5,"xref":0,"sigma":5},"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.