engineering.uncertainty.welch_satterthwaite

Three distinct suites: educational examples on the calculator page, this legacy regression count (10/10 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.0.1 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-09-23.o2-o3. Calculation version 1.0.1. CVP 1.0.0-proposed. 5/5 golden · 5/5 CVP boundary · 8/8 invalid · 3/3 property · 2/2 metamorphic · 8/8 O3 · 4/4 cross-interface · 6/6 CVP contract. digest 4fa90ba29b01. O2: JCGM 100 G.4 ν_eff = u_c⁴ / Σ(u_i⁴/ν_i) vs separate-module identities (≤2 ULP). Not GUM propagate and not U=k·u_c. ≤2 ULP vs O3 applies only to the published tabulated G.4 vectors (equal Type A, one infinite Type B, supplied u_c, all-infinite, aliases, three components, scale, a zero component). It is not a whole-domain guarantee and does not cover GUM propagate or U=k·u_c.

• Golden (oracle-backed) 5 / 5
• CVP boundary 5 / 5
• Invalid input 8 / 8
• Property 3 / 3
• Metamorphic 2 / 2
• O3 high-precision 8 / 8
• Cross-interface 4 / 4
• CVP contract 6 / 6
• Interfaces PASS · UI (SSR) / REST / MCP
• Interface claim 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.
• Verified scope 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.
• Assurance Engineering
• Deferred Not GUM model combination, not expanded U = k·u_c, and not a t-table lookup of k.

• release artifacts aligned PASS
• schema output required declared PASS
• schema valid input executes PASS
• engine success output validates schema PASS
• schema rejects incomplete input PASS
• rest success payload validates schema PASS

Fingerprint sha256:4d88edabfda1c31c510854b928022b531cd078c3c38bd2c3b726a26e68d0856b

Input schema sha256:69ed3e7bd7690295bcdc384fd8f592f2257a4d676cf6a129e1d2ac2653377127 · Output schema sha256:45740d021dc33caeee449d18a8bc0b5cbc49290f54af70b49443ce930fee34b6 · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Tool

welch-satterthwaite

Engine

welch-satterthwaite

Engine build

2026-09-23

Evidence core

2026-09-23T06:34:01.209Z

Rendered

2026-10-23T01:27:11.170Z

Last reviewed

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Assumptions

• JCGM 100:2008 G.4 Welch–Satterthwaite
• If uc omitted, u_c = RSS of uncorrelated u_i
• Infinite ν_i contribute 0 to the sum
• Not GUM model combination and not expanded U = k·u_c

Limitations

• Does not combine a measurement model (use Uncertainty propagate)
• Does not look up coverage factor k from a t-table
• Does not compute expanded U = k·u_c
• Uncorrelated RSS only when uc is omitted