Verified calculation capability
Propagate standard uncertainties: GUM linear (binary/sensitivity/RSS/budget) or Monte Carlo (JCGM 101); optional correlations, contributions, νeff, Student-t/percentile coverage → U. · Engineering · Uncertainty
Capability ID engineering.uncertainty.propagate · version 1.9.8
Sum
u_c(a+b) = √(u_a² + u_b² + 2ρ u_a u_b)u_c(a−b) = √(u_a² + u_b² − 2ρ u_a u_b)u_c = √((b·u_a)² + (a·u_b)² + 2ρ a b u_a u_b)u_c = √((u_a/b)² + (a·u_b/b²)² + 2ρ (1/b)(−a/b²) u_a u_b)u_c = √[Σ(c_i u_i)² + 2 Σ_{i<j} c_i c_j u_i u_j ρ_ij]u_c = √Σ u_i²U = k · u_cνeff = u_c⁴ / Σ ((cᵢ uᵢ)⁴ / νᵢ)k = t_{(1+p)/2, νeff}; U = k·u_cCanonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit | Role |
|---|---|---|---|
y | Combined value (binary) or optional y (machine precision) | — | output |
u_c | Combined standard uncertainty (machine / raw precision) | — | output |
u_rel | |u_c/y| when y ≠ 0 | — | output |
reported | Human-facing rounded values (2 significant digits on u_c; y aligned to same decimal place). formatted_* strings keep trailing zeros JSON numbers cannot. | — | output |
a | acceleration | — | output |
b | — | — | output |
ua | — | — | output |
ub | — | — | output |
terms | Number of uncertainty terms (sensitivity/rss) | — | output |
unit | Resolved output unit for y and u_c (Quantity Engine v1.1: SI-prefix + derived rewrites; not full SI algebra) | — | output |
unit_a | — | — | output |
unit_b | — | — | output |
quantity | Present when SI-prefix conversion scaled inputs into the output unit | — | output |
rho | Correlation used (binary; default 0) | — | output |
correlations | Normalized correlation pairs applied (sensitivity) | — | output |
k | Coverage factor when provided | — | output |
U | Expanded uncertainty k·u_c when k provided | — | output |
contributions | Diagonal variance contributions (% of u_c²) | — | output |
largest | — | — | output |
covariance_contributions | Off-diagonal 2ρ c_i c_j u_i u_j shares of u_c² | — | output |
nu_eff | Welch–Satterthwaite νeff when dof provided; Infinity when all ν→∞ | — | output |
nua | — | — | output |
nub | — | — | output |
nu_eff_infinite | True when νeff → ∞ (JSON-safe; nu_eff is then null) | — | output |
k_source | How k was obtained | — | output |
confidence | Coverage probability when Student-t auto-k used | — | output |
components | Echo of budget components (normalized) | — | output |
y_mean | — | — | output |
y_median | — | — | output |
y_p025 | — | — | output |
y_p975 | — | — | output |
y_low | — | — | output |
y_high | — | — | output |
linear_u_c | First-order GUM u_c for comparison | — | output |
N | — | — | output |
seed | — | — | output |
model | — | — | output |
n_valid | Monte Carlo samples used for mean/std after singularity filtering | — | output |
invalid_samples | — | — | output |
near_singularity_samples | — | — | output |
invalid_fraction | — | — | output |
Declared scope for this capability. Do not use it outside this domain.
Assumptions
One numerical check. The calculator page holds worked steps and FAQ.
sum, a=100±0.1, b=50±0.2 → y=150, u_c≈0.2236 (reported u_c=0.22)
CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Linear GUM: sum, difference, product, quotient, RSS, sensitivity, budget. Correlation matrices must be PSD (singular PSD allowed). O3 mpmath (80 dps) tabulated linear u_c. Monte Carlo: O2-B seeded mulberry32+Box-Muller replay of y_mean/u_c/percentiles (≤2 ULP) for sum, difference, product, quotient, correlated normal, and budget/rectangular; linear_u_c vs first-order GUM.. 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 8/8.
Declared calculation modes for this capability.
sumdifferenceproductquotientsensitivityrssbudgetmontecarloHuman-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 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.propagate"}}}'
Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.9.8) when reproducibility matters. Full protocol notes: MCP docs.