Methodology Reference

A single-page consolidation of the JCGM section pointers for every exported symbol of SymbolicUncertainties.jl. Row order matches the EARS specification's exported-API appendix.

The per-function docstrings under src/*.jl are the source of truth for REQ-160 citations; the table below is a navigable consolidation view. Drift between this table and the docstrings is caught by the test/package/test_api_freeze.jl audit (REQ-160 enforcement).

Public surface

Symbol	Description	JCGM / GUM ref
`SymbolicMeasurement`	Estimate + combined standard uncertainty + dof.	§4.1 (estimate), §5.1 (uc), §G.4 (νeff)
`±`	Constructor shorthand `val ± u`.	§6 (notation)
`apply`	Scalar function with optional sensitivity coefficient.	§5.1.3
`propagate`	Multi-variable uncertainty propagation — a convenience over the operators, not a second path.	§5.1.2 eq (10), §5.2.2 eq (13)
`propagate_vector`	Vector-valued measurand propagation.	JCGM 102:2011
`sensitivity_coefficient`	Symbolic `cᵢ = ∂f/∂xᵢ`.	§5.1.3
`uncertainty_contribution`	Symbolic `\|cᵢ\| · uᵢ`.	§5.1.6
`relative_sensitivity`	Fractional variance contribution.	§5.1.6
`dominant_source`	Variable with largest variance contribution.	§5.1.6
`uncertainty_budget`	Full GUM uncertainty budget table, derived from the quantity's own sources.	§5.1.6; EA-4/02 §7.3
`UncertaintyBudget`	The budget value: rows, measurand, `u_c`, and whether correlations are declared.	EA-4/02 §7.3
`BudgetRow`	One budget line.	§5.1.3 eq (11a), (11b)
`expanded_uncertainty`	`U = k · u_c`, returned as an `ExpandedUncertainty`.	§6 (k = 2); §G.1.2 (arbitrary k); Table G.2 (coverage probability)
`ExpandedUncertainty`	`(val, U, k, ν_eff)` — a coverage-interval half-width, deliberately not propagatable.	§6.2
`declare_correlated`	Returns two quantities carrying a declared correlation.	§5.2.2 eq (13)
`covariance`	Covariance of two quantities over their shared sources.	JCGM 102:2011
`correlation`	Correlation coefficient derived from that covariance.	§5.2.2 eq (14)
`welch_satterthwaite`	Effective degrees of freedom.	§G.4
`required_precision`	Symbolic condition on `uᵢ` for target `u_c`.	§5.2 (inverse)
`budget_allocation`	Lagrange allocation of uncertainty budget.	§5.2 (inverse) + Lagrange optimisation
`build_evaluator`	Compile to Julia / C function.	— (code generation)
`Symbolics.substitute`	Numerical substitution — extension method, not a new export.	— (numerical evaluation)
`infer_precision`	Solve for `uᵢ` given observed `u_c`.	— (inverse, see §5.2)
`infer_all_precisions`	Worst-case single-source attribution.	— (inverse, see §5.2)
`latex`	LaTeX string for certificates (requires `Latexify.jl`).	§7 (reporting)
`to_expr`	Extract `(val, err)` tuple of `Num`.	— (export utility)
`propagate_ode`	ODE uncertainty propagation (requires `ModelingToolkit.jl`).	GUM Supplement 3 (anticipated)
`uncertainty_ode`	Augmented `ODESystem` for numerical integration.	GUM Supplement 3 (anticipated)
`check_linearity`	Nonlinearity indicator per input variable.	§5.1.1 (linearity note)
`linearisation_bound`	Rigorous bound on the first-order error over the whole coverage region.	§5.1.1 (linearity note); JCGM 101:2008 (the sampling alternative)
`second_order_correction`	Second-order term on the estimate, returned never applied.	JCGM 100:2008/Amd.1:2026 §4.1.4 NOTE 1; eq (H.10)
`check_units`	Opt-in, non-throwing dimensional report.	§4.3.1 (affine scales); VIM §1.1 (kind)
`UnitReport`	Findings returned by `check_units`.	§4.3.1
`JuliaTarget`	Symbolics code-generation target, re-exported.	— (REQ-132 documented exception)
`CTarget`	Symbolics code-generation target, re-exported.	— (REQ-132 documented exception)

Notes

substitute is accessed as Symbolics.substitute(m, dict) — an extension method on Symbolics.substitute, not a new export from SymbolicUncertainties. The specification captured this decision to avoid the DynamicPolynomials.substitute / ExproniconLite.substitute name clash.
JuliaTarget and CTarget are re-exports from Symbolics.jl — the two documented exceptions to the REQ-132 "no-Symbolics-names-leaked" audit, needed for the build_evaluator(m, variables; target = …) keyword syntax.
propagate_ode and uncertainty_ode are exported stubs in src/mtk_stubs.jl that raise ArgumentError until ModelingToolkit.jl is loaded; the live methods live in ext/SymbolicUncertaintiesModelingToolkitExt.jl.
latex is similarly a stub in src/latex_stub.jl replaced by the SymbolicUncertaintiesLatexifyExt extension when Latexify.jl is loaded.
linearisation_bound and second_order_correction answer two different questions and neither replaces the other: the first bounds the error the first-order law makes in u_c, the second returns the term the 2026 amendment asks for on the estimate y. A product of independent inputs needs the second not at all — its estimate is exact — and the first very much, since all of its nonlinearity sits in the mixed partial.

Cross-reference

Standards-traceability gate: EARS REQ-160 (per-function citation), REQ-161 (per-topic docs page), REQ-162 (six canonical worked examples — see Worked Examples).
Waived requirements: see Limitations for the post-1.0 deferral list.
Citation: CITATION.bib at the repository root.

Re-export docstrings

SymbolicUncertainties.JuliaTarget — Type

JuliaTarget

Re-export of Symbolics.JuliaTarget. Pass to build_evaluator(m, variables; target = JuliaTarget()) to generate a compiled Julia evaluator (the default target). Documented REQ-132 exception — see docs/src/methodology-reference.md.

source

SymbolicUncertainties.CTarget — Type

CTarget

Re-export of Symbolics.CTarget. Pass to build_evaluator(m, variables; target = CTarget()) to generate a C source String callable from C / Fortran / any FFI-compatible host. Documented REQ-132 exception — see docs/src/methodology-reference.md.

source