Verified calculation capability

Zeta-score Calculation Capability

Proficiency-testing zeta-score ζ = (ylab−xref)/√(ulab²+uref²). ulab and uref are standard uncertainties (ISO 13528). |ζ| ≤ 2 pass, 2 < |ζ| < 3 warning, |ζ| ≥ 3 fail. Not En, not TUR, and not an ILAC G8 spec decision. · Engineering · Conformity

Capability ID engineering.conformity.zeta_score · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Zeta-score

Zeta-score: ζ = (ylab − xref) / √(ulab² + uref²)
Decision: |ζ| ≤ 2 → pass; 2 < |ζ| < 3 → warning; |ζ| ≥ 3 → fail

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`ylab`	Laboratory / participant result. Aliases: y, x.	—	input / output
`xref`	Assigned or reference value. Aliases: X, ref.	—	input / output
`ulab`	Standard uncertainty of ylab. Aliases: u_lab, u_x. Not expanded U.	—	input / output
`uref`	Standard uncertainty of xref. Aliases: u_ref, u_X. Not expanded U.	—	input / output
`zeta`	—	—	output
`abs_zeta`	—	—	output
`decision`	—	—	output

Assumptions / Validity

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

Assumptions

ISO 13528 zeta-score with standard uncertainties ulab and uref
|ζ| ≤ 2 is pass; 2 < |ζ| < 3 is warning; |ζ| ≥ 3 is fail
Not En (expanded U), not TUR, and not an ILAC G8 spec decision

Not supported

En (expanded U)
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 → ζ=0.5 pass

Open this example in the calculator

Trust

Review-policy: engine tested — automated tests, sources, version lock, and evidence published. Supplemental to CVP; not Domain Expert Review. See CVP and Review policy.

Tier: Engine tested — catalog token engine_tested
Calculation version: 1.0.0
Evidence tests: 11/11 calculation tests · golden 0/0 · boundary 6/6 · property 5/5
Engine tested: Yes
Source checked: Yes
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.0 (workspace artifacts agree)

Production attestation: Embedded snapshot: STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-16T06:44:24.909Z
Semantic contract: PASS
Evidence attested at: 2026-09-16T06:44:24.203Z
Last production check: 2026-09-16T06:44:24.203Z
Public / cache: PASS
Origin: PASS

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 4/4.

Tool id: zeta-score
Engine: zeta-score
REST: POST /api/v1/calc/zeta-score
MCP: execute_calculation with capability_id: "engineering.conformity.zeta_score"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.0)
Versioned output schema: Immutable pin (1.0.0)

References

Human-readable sources plus CVP reference evidence classes.

Sources

ISO 13528 — Statistical methods for use in proficiency testing by interlaboratory comparison — Zeta-score using standard uncertainties
ISO/IEC 17043 — Conformity assessment — General requirements for the competence of proficiency testing providers — Performance evaluation using zeta

Try with an agent

Inspect this capability via same-origin MCP, then call execute_calculation.

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.zeta_score"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.0.0) when reproducibility matters. Full protocol notes: MCP docs.