CVP verified calculation capability
Effective degrees of freedom ν_eff = u_c⁴ / Σ (u_i⁴ / ν_i) (GUM G.4). If uc is omitted, u_c is the uncorrelated RSS of u_i. Not combined RSS as a product page and not expanded U = k·u_c.
Engineering · Uncertainty Capability ID engineering.uncertainty.welch_satterthwaite version 1.0.1 CVP VERIFIED CURRENT Engineering
Effective degrees of freedom
ν_eff = u_c⁴ / Σ (u_i⁴ / ν_i)u_c = √(Σ u_i²)Canonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit | Role |
|---|---|---|---|
u | Standard uncertainty components u_i | — | input / output |
nu | Degrees of freedom ν_i, same length as u | — | input / output |
uc | Optional combined standard uncertainty | — | input / output |
nu_eff | Effective degrees of freedom | — | output |
infinite | — | — | output |
Declared scope for this capability. Do not use it outside this domain.
Assumptions
Not supported
One numerical check. The calculator page holds worked steps and FAQ.
u=[1,1] nu=[8,8] → ν_eff=16
CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · JCGM 100 G.4 ν_eff = u_c⁴ / Σ(u_i⁴/ν_i), including infinite ν_i and an optional supplied u_c, + O3 mpmath tabulated ν_eff.. 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.
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/welch-satterthwaite' \
-H 'Content-Type: application/json' \
-d '{"inputs":{"u":[0.1,0.2],"nu":[10,"inf"]},"calculation_version":"1.0.1"}'{
"inputs": {
"u": [
0.1,
0.2
],
"nu": [
10,
"inf"
]
},
"calculation_version": "1.0.1"
}POST /api/v1/calc/welch-satterthwaite. This is a POST calculate endpoint — do not GET it.
Full REST contract: REST API docs.
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
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.uncertainty.welch_satterthwaite"},"_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.uncertainty.welch_satterthwaite","inputs":{"u":[0.1,0.2],"nu":[10,"inf"]},"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.