Verified calculation capability

Type B Uncertainty Calculation Capability

Type B standard uncertainty from a half-width a. Rectangular u_B=a/√3, triangular u_B=a/√6. Not GUM combination and not Monte Carlo. · Engineering · Uncertainty

Capability ID engineering.uncertainty.type_b · version 1.0.0

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

Model

Rectangular

Rectangular: u_B = a / √3
Triangular: u_B = a / √6

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`a`	Half-width of the assumed distribution	—	input / output
`distribution`	Assumed distribution. Default rectangular. uniform is accepted as an alias of rectangular.	—	input / output
`u_B`	—	—	output

Assumptions / Validity

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

Assumptions

Type B: a is the half-width of the assumed distribution
Rectangular (default, including uniform alias) u_B = a/√3; triangular u_B = a/√6
Not GUM combination of several uᵢ
Not Monte Carlo

Not supported

GUM RSS of several uᵢ
Type A from a sample
Monte Carlo
trapezoidal / U-shaped

Example

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

a=3 distribution=rectangular → u_B=3/√3

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Type B u_B from half-width a: rectangular a/√3 (uniform alias) and triangular a/√6 + O3 mpmath tabulated u_B.. 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 · Type B u_B from half-width a: rectangular a/√3 (uniform alias) and triangular a/√6 + O3 mpmath tabulated u_B.· View Manifest · CVP overview · Specification
Verified scope: Type B u_B from half-width a: rectangular a/√3 (uniform alias) and triangular a/√6 + O3 mpmath tabulated u_B.
Assurance: Engineering
Declared partition coverage: PASS · 6/6 declared partitions (rectangular, triangular, uniform-alias, default-dist, half-width-alias, invalid-domain)
Deferred: Not GUM RSS of several uᵢ, not trapezoidal / U-shaped, not Monte Carlo, and not a standalone Combined/Expanded page.
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 47360ca02434
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: u_B = a/√3 (rectangular) or a/√6 (triangular) vs separate-module identities (≤2 ULP). Not GUM combination, not trapezoidal, not Monte Carlo. ≤2 ULP vs O3 applies only to the published tabulated Type B vectors (rectangular, triangular, default, uniform alias, a=1, a=0.5 triangular, scale, half_width). It is not a whole-domain Type B guarantee and does not cover trapezoidal.
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
Engine: type-b
REST: POST /api/v1/calc/type-b
MCP: execute_calculation with capability_id: "engineering.uncertainty.type_b"
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"}}}'

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