Verified calculation capability

Type B degrees of freedom Calculation Capability

GUM G.4.2 Type B degrees of freedom: ν = ½(u/σ(u))². σ(u)=0 → ν is infinite. Not Type B u_B from a half-width, not Welch ν_eff, and not U = k·u_c. · Engineering · Uncertainty

Capability ID engineering.uncertainty.type_b_nu · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON CVP Manifest Review policy

Model

Relative uncertainty of u

Relative uncertainty of u: σ(u)/u
Degrees of freedom: ν = ½ (u / σ(u))²

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`u`	Type B standard uncertainty. Aliases: u_i, uB, u_B. Not half-width a.	—	input / output
`sigma_u`	Standard uncertainty of u. Aliases: su, du, delta_u. Zero → infinite ν.	—	input / output
`nu`	Type B ν. null when infinite.	—	output
`rel`	σ(u)/u	—	output
`infinite`	—	—	output

Assumptions / Validity

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

Assumptions

JCGM 100:2008 G.4.2: ν = ½ (u/σ(u))²
σ(u)=0 → ν is infinite (REST returns nu=null, infinite=true)
Not Type B u_B from a half-width, not Welch ν_eff, and not U = k·u_c

Not supported

Type B u_B from half-width a
Welch ν_eff
U = k·u_c
trapezoidal Type B as a new page

Example

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

u=2 sigma_u=0.5 → ν=8 rel=0.25

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · GUM G.4.2 Type B degrees of freedom ν = ½(u/σ(u))², including σ(u)=0 → infinite, + O3 mpmath tabulated ν.. 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 · GUM G.4.2 Type B degrees of freedom ν = ½(u/σ(u))², including σ(u)=0 → infinite, + O3 mpmath tabulated ν.· View Manifest · CVP overview · Specification
Verified scope: GUM G.4.2 Type B degrees of freedom ν = ½(u/σ(u))², including σ(u)=0 → infinite, + O3 mpmath tabulated ν.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (textbook-25, infinite, other-finite, alias, invalid-domain)
Deferred: Not Type B u_B from a half-width, not Welch ν_eff, not U = k·u_c, and not trapezoidal Type B.
Calculation version: 1.0.0
Verification: 8/8 calculation tests · 1/1 legacy golden · 4/4 legacy boundary · 3/3 legacy property
Production surface contract: 4/4
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-16.o2-o3
Verification revision: 2026-09-16.o2-o3 · 3/3 property · digest 083418691428
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: GUM G.4.2 ν = ½(u/σ(u))² vs separate-module identities (≤2 ULP). Not Type B u_B, not Welch ν_eff, not U=k·u_c. ≤2 ULP vs O3 applies only to the published tabulated G.4.2 vectors (GUM 25%, infinite, 10%, aliases, scale, σ(u)/u=0.5). It is not a whole-domain guarantee and does not cover Welch ν_eff or U=k·u_c.
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: 5/5 golden · 4/4 CVP boundary · 7/7 invalid · 3/3 property · 2/2 metamorphic · 8/8 O3 · 4/4 cross-interface · 4/4 CVP contract
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)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

This calculator CURRENT · Public schema 1.0.0 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 4/4.

Tool id: type-b-nu
Engine: type-b-nu
REST: POST /api/v1/calc/type-b-nu
MCP: execute_calculation with capability_id: "engineering.uncertainty.type_b_nu"
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

Reference evidence classes: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior

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.uncertainty.type_b_nu"}}}'

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