Public evidence

engineering.uncertainty.propagate

Machine-checked verification for calculation version 1.9.8 · tier internally_reviewed

Open calculator API Capability Download JSON CVP Manifest Reproduce MCP Review policy

CVP: 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.· All published modes; MC is seeded independent replay plus linear_u_c, not full JCGM 101. O3 covers tabulated linear vectors only. Budget dimensional algebra deferred. · Protocol · Schema · Production report

Declared partition coverage: PASS · 9/9 declared partitions (sum, difference, product, quotient, rss, sensitivity, budget, montecarlo, invalid-domain)
Versions: Calculation 1.9.8 · CVP protocol 1.0.0-proposed · Evidence 2026-09-16.seeded-mc-o3
Verification revision: 2026-09-16.seeded-mc-o3 · 29/29 property · digest 77cad1dafb2f

Verification

Legacy regression suite: 88/88 calculation tests · Production surface contract 8/8

Three distinct suites: educational examples on the calculator page, this legacy regression count (88/88 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 1.9.8 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 2026-09-16.seeded-mc-o3. Calculation version 1.9.8. CVP 1.0.0-proposed. 18/18 golden · 47/47 CVP boundary · 29/29 invalid · 29/29 property · 10/10 O3 · 6/6 cross-interface · 8/8 CVP contract. digest 77cad1dafb2f. Published modes: linear GUM (sum, difference, product, quotient, RSS, sensitivity, budget) and seeded Monte Carlo replay of y_mean/u_c/percentiles. Not a full JCGM 101 validation procedure. RNG: mulberry32; normal sampler: Box-Muller. ≤2 ULP vs O3 applies only to the published tabulated linear GUM vectors (sum, difference, ρ=1 difference, product, quotient, RSS, sensitivity, 3×3 PSD, singular PSD, budget). It is not a whole-domain guarantee and does not cover Monte Carlo.

Golden (oracle-backed) 18 / 18
CVP boundary 47 / 47
Invalid input 29 / 29
Property 29 / 29
O3 high-precision 10 / 10
Cross-interface 6 / 6
CVP contract 8 / 8
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session.
Verified scope 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.
Assurance Engineering
Deferred Adaptive MCM, arbitrary PDFs, and the full JCGM 101 validation procedure. Budget sensitivity-coefficient dimensional algebra is not automatically verified. Correlated non-normal MC remains out of O2. O3 does not cover Monte Carlo.

contract page version PASS
contract capability version PASS
contract input schema version PASS
contract output schema version PASS
evidence version matches manifest PASS
schema valid input executes PASS
engine success output validates schema PASS
schema rejects incomplete input PASS

Fingerprint sha256:d8cfcf55210b3e57585f02738f49bb344b4c1cc9d6597384fadb8f7da98e3fb8

Input schema sha256:263d0ba0dda3ea81aa635bcd61d0eb9e9e9fc347ab4890b6cc20ccacc3a6843f · Output schema sha256:d1d0c1d06cbe6b38725a8566ba4273291b9558081c5786b8e0b65b862a8e66b1 · 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.

Build & scope

Engine identity and declared limitations.

Tool: uncertainty-propagate
Engine: uncertainty-propagate
Engine build: 2026-09-12
Evidence core: 2026-09-12T08:32:37.705Z
Rendered: 2026-09-16T22:03:43.714Z
Last reviewed: 2026-08-10

Assumptions

Default uncorrelated (rho=0); optional correlations when provided.
Linear propagation assumes a local first-order approximation is adequate. For significant model nonlinearity, consider higher-order treatment (JCGM 100:2008/Amd.1:2026) or Monte Carlo propagation (JCGM 101:2008).

Limitations

Linear GUM (binary/sensitivity/RSS/budget) or Monte Carlo (JCGM 101) with normal/rectangular draws; not adaptive/MCMC
MC: N in 100…100000 (default 10000), deterministic Mulberry32 seed; confidence → empirical percentiles; k → U=k·u_c
budget/sensitivity Type A/B + distributions are metadata (except MC uses distribution for draws); u is standard uncertainty
contributions are diagonal (c·u)² fractions for linear modes; with correlations percents may not sum to 100%
Product/quotient use absolute first-order forms in linear mode; MC quotient rejects >5% near-zero denominator draws (MONTECARLO_UNSTABLE)
n×n correlation matrix not positive semidefinite → CORRELATION_MATRIX_NOT_PSD (singular PSD allowed); duplicate unordered pair → DUPLICATE_CORRELATION; conflicting ρ for the same pair → CONFLICTING_CORRELATION
Optional Quantity Engine v1.1: SI-prefix conversion + electrical derived rewrites (1000 mV + 2 V → 3 V; V/A → Ω; A·Ω → V; V×A → VA); different additive dimensions → UNIT_MISMATCH; not full SI algebra
Unknown mode → INVALID_MODE; k and confidence together → INVALID_INPUT
confidence with nonzero ρ/correlations → CORRELATED_DOF_NOT_SUPPORTED (use fixed k)
MC rectangular + correlation → CORRELATED_NON_NORMAL_MC_NOT_SUPPORTED (normal marginals only)
Public Agent schema uses canonical field names only (components.u/c/x; correlations i/j as index or name). Runtime still accepts legacy aliases (ua/uncertainty/sensitivity/value) for compatibility.

Sources

Standards and references supporting this tool specification. Methods are listed separately — they are algorithms, not bibliographic sources.

JCGM 100:2008 — Evaluation of measurement data (GUM) — Law of propagation of uncertainty
Supports: u_c² = Σ (∂f/∂xᵢ)² u²(xᵢ) for uncorrelated inputs
JCGM 100:2008/Amd.1:2026 — Nonlinearity in measurement models — Amendment 1
Supports: First-order linear propagation may be inadequate when the measurement model is significantly nonlinear
JCGM GUM-6:2020 — Developing and using measurement models — Measurement modelling
Supports: Guidance on constructing measurement models for uncertainty evaluation
JCGM 101:2008 — Propagation of distributions using a Monte Carlo method — GUM Supplement 1
Supports: Methodological reference for the implemented Monte Carlo subset (normal/rectangular, seeded sampling, percentile intervals); not adaptive MCM, arbitrary PDFs, or full JCGM 101 validation procedure
NIST Technical Note 1297 — Guidelines for evaluating and expressing uncertainty
Supports: Combined standard uncertainty practice; reporting of u_c
NIST Guide to the SI (SP 811) — Expression of uncertainty with SI quantities
Supports: Unit-consistent reporting of results and uncertainties

Legacy published checks

Golden and boundary cases from the legacy Evidence JSON. CVP property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the Manifest — including SKIP when a suite has no vectors.

ID	Kind	Status	Detail
`sum-default`	golden	pass	Expected y=150 · u_c=0.22360679774997896 · Actual mode=sum · y=150 · u_c=0.223606797749979 · u_rel=0.00149071198499986 · a=100 · b=50 · ua=0.1 · ub=0.2
`product-default`	golden	pass	Expected y=50 · u_c=0.7071067811865476 · Actual mode=product · y=50 · u_c=0.7071067811865476 · u_rel=0.01414213562373095 · a=10 · b=5 · ua=0.1 · ub=0.05
`sensitivity`	golden	pass	Expected u_c=0.6324555320336759 · u_rel=0.06324555320336758 · Actual mode=sensitivity · u_c=0.632455532033676 · u_rel=0.0632455532033676 · y=10 · terms=2 · nu_eff_infinite=false
`rss`	golden	pass	Expected u_c=0.5 · Actual mode=rss · u_c=0.5 · terms=2 · nu_eff_infinite=false
`product-a-zero`	golden	pass	Expected y=0 · u_c=0.5 · Actual mode=product · y=0 · u_c=0.5 · a=0 · b=5 · ua=0.1 · ub=0.05 · rho=0
`quotient-b-zero`	boundary	pass	Expected DIVISION_BY_ZERO · Actual DIVISION_BY_ZERO
`missing-ua`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`invalid-mode`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`rho-sum`	golden	pass	Expected y=150 · u_c=0.3 · rho=1 · Actual mode=sum · y=150 · u_c=0.30000000000000004 · u_rel=0.0020000000000000005 · a=100 · b=50 · ua=0.1 · ub=0.2
`k-expanded`	golden	pass	Expected U=0.4472135954999579 · k=2 · Actual mode=sum · y=150 · u_c=0.223606797749979 · u_rel=0.00149071198499986 · a=100 · b=50 · ua=0.1 · ub=0.2
`nueff-binary`	golden	pass	Expected nu_eff=225 · Actual mode=sum · y=150 · u_c=0.223606797749979 · u_rel=0.00149071198499986 · a=100 · b=50 · ua=0.1 · ub=0.2
`student-t-k`	golden	pass	Expected nu_eff=9 · k=2.26215716274 · Actual mode=sum · y=1 · u_c=0.1 · u_rel=0.1 · a=1 · b=0 · ua=0.1 · ub=0
`budget-basic`	golden	pass	Expected y=5 · u_c=0.00223606797749979 · Actual mode=budget · u_c=0.0022360679774997894 · u_rel=0.0004472135954999579 · y=5 · terms=2 · nu_eff_infinite=false
`mc-sum`	golden	pass	Expected linear_u_c=0.22360679774997896 · Actual mode=montecarlo · model=sum · a=100 · b=50 · ua=0.1 · ub=0.2 · rho=0 · terms=2
`boundary-product-b-zero`	boundary	pass	Expected y=0 · u_c=0.25 · Actual mode=product · y=0 · u_c=0.25 · a=5 · b=0 · ua=0.1 · ub=0.05 · rho=0
`boundary-quotient-a-zero`	boundary	pass	Expected y=0 · u_c=0.02 · Actual mode=quotient · y=0 · u_c=0.020000000000000004 · a=0 · b=5 · ua=0.1 · ub=0.05 · rho=0
`boundary-all-zero-u`	boundary	pass	Expected y=2 · u_c=0 · Actual mode=sum · y=2 · u_c=0 · u_rel=0 · a=1 · b=1 · ua=0 · ub=0
`boundary-coeffs-length`	boundary	pass	Expected INVALID_INPUT · Actual INVALID_INPUT
`boundary-empty-uncertainties`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`boundary-neg-ua`	boundary	pass	Expected VALUE_MUST_BE_NON_NEGATIVE · Actual VALUE_MUST_BE_NON_NEGATIVE
`boundary-unit-mismatch`	boundary	pass	Expected UNIT_MISMATCH · Actual UNIT_MISMATCH
`boundary-unit-sum`	boundary	pass	Expected y=150 · u_c=0.22360679774997896 · unit=V · Actual mode=sum · y=150 · u_c=0.223606797749979 · u_rel=0.00149071198499986 · a=100 · b=50 · ua=0.1 · ub=0.2
`boundary-unit-si-sum`	boundary	pass	Expected y=3 · u_c=0.010049875621120889 · unit=V · Actual mode=sum · y=3 · u_c=0.01004987562112089 · u_rel=0.00334995854037363 · a=1000 · b=2 · ua=1 · ub=0.01
`boundary-unit-product`	boundary	pass	Expected y=2760 · unit=VA · Actual mode=product · y=2760 · u_c=25.942243542145693 · u_rel=0.0093993636022267 · a=230 · b=12 · ua=1 · ub=0.1
`boundary-unit-si-quotient`	boundary	pass	Expected y=0.5 · unit=1 · Actual mode=quotient · y=0.5 · u_c=0.0025495097567963926 · u_rel=0.005099019513592785 · a=1000 · b=2 · ua=1 · ub=0.01
`boundary-unit-ohm`	boundary	pass	Expected y=5 · unit=Ω · Actual mode=quotient · y=5 · u_c=0.05590169943749475 · u_rel=0.01118033988749895 · a=10 · b=2 · ua=0.1 · ub=0.01
`boundary-unit-mv-ma`	boundary	pass	Expected y=500 · unit=Ω · Actual mode=quotient · y=500 · u_c=2.5495097567963922 · u_rel=0.005099019513592784 · a=1000 · b=2 · ua=1 · ub=0.01
`boundary-unit-a-ohm`	boundary	pass	Expected y=10 · unit=V · Actual mode=product · y=10 · u_c=0.20615528128088306 · u_rel=0.020615528128088305 · a=2 · b=5 · ua=0.01 · ub=0.1
`boundary-nua-null-infinite`	boundary	pass	Expected y=150 · nu_eff_infinite=true · Actual mode=sum · y=150 · u_c=0.223606797749979 · u_rel=0.00149071198499986 · a=100 · b=50 · ua=0.1 · ub=0.2
`boundary-mc-sum`	boundary	pass	Expected linear_u_c=0.22360679774997896 · Actual mode=montecarlo · model=sum · a=100 · b=50 · ua=0.1 · ub=0.2 · rho=0 · terms=2
`boundary-mc-N`	boundary	pass	Expected VALUE_OUT_OF_RANGE · Actual VALUE_OUT_OF_RANGE
`boundary-mc-budget`	boundary	pass	Expected linear_u_c=0.22360679774997896 · Actual mode=montecarlo · model=linear · terms=2 · y=2.9979412161635093 · u_c=0.22221998921316938 · u_rel=0.07412419830484407 · y_mean=2.9979412161635093 · y_median=2.999790879812373
`boundary-rho-diff`	boundary	pass	Expected y=50 · u_c=0.1 · rho=1 · Actual mode=difference · y=50 · u_c=0.1 · u_rel=0.002 · a=100 · b=50 · ua=0.1 · ub=0.2
`boundary-rho-out`	boundary	pass	Expected VALUE_OUT_OF_RANGE · Actual VALUE_OUT_OF_RANGE
`boundary-k-invalid`	boundary	pass	Expected VALUE_MUST_BE_POSITIVE · Actual VALUE_MUST_BE_POSITIVE
`boundary-sens-corr`	boundary	pass	Expected u_c=0.3 · Actual mode=sensitivity · u_c=0.30000000000000004 · terms=2 · nu_eff_infinite=false
`boundary-rss-corr-reject`	boundary	pass	Expected INVALID_INPUT · Actual INVALID_INPUT
`boundary-contrib-sum`	boundary	pass	Expected u_c=0.22360679774997896 · Actual mode=sum · y=150 · u_c=0.223606797749979 · u_rel=0.00149071198499986 · a=100 · b=50 · ua=0.1 · ub=0.2
`boundary-nueff-sens`	boundary	pass	Expected nu_eff=32 · Actual mode=sensitivity · u_c=0.28284271247461906 · terms=2 · nu_eff=32.000000000000014 · nu_eff_infinite=false
`boundary-dof-length`	boundary	pass	Expected INVALID_INPUT · Actual INVALID_INPUT
`boundary-nua-alone`	boundary	pass	Expected INVALID_INPUT · Actual INVALID_INPUT
`boundary-student-t`	boundary	pass	Expected nu_eff=9 · k=2.26215716274 · Actual mode=rss · u_c=0.1 · terms=1 · nu_eff=9 · nu_eff_infinite=false · k=2.2621571627981485 · U=0.22621571627981485 · k_source=student_t
`boundary-student-normal`	boundary	pass	Expected k=1.95996398454 · Actual mode=sum · y=150 · u_c=0.223606797749979 · u_rel=0.00149071198499986 · a=100 · b=50 · ua=0.1 · ub=0.2
`boundary-k-and-confidence`	boundary	pass	Expected INVALID_INPUT · Actual INVALID_INPUT
`boundary-confidence-range`	boundary	pass	Expected VALUE_OUT_OF_RANGE · Actual VALUE_OUT_OF_RANGE
`boundary-corr-confidence`	boundary	pass	Expected CORRELATED_DOF_NOT_SUPPORTED · Actual CORRELATED_DOF_NOT_SUPPORTED
`boundary-corr-confidence-sens`	boundary	pass	Expected CORRELATED_DOF_NOT_SUPPORTED · Actual CORRELATED_DOF_NOT_SUPPORTED
`boundary-mc-rect-corr`	boundary	pass	Expected CORRELATED_NON_NORMAL_MC_NOT_SUPPORTED · Actual CORRELATED_NON_NORMAL_MC_NOT_SUPPORTED
`boundary-mc-quotient-unstable`	boundary	pass	Expected MONTECARLO_UNSTABLE · Actual MONTECARLO_UNSTABLE
`boundary-cov-contrib`	boundary	pass	Expected u_c=0.3 · Actual mode=sum · y=150 · u_c=0.30000000000000004 · u_rel=0.0020000000000000005 · a=100 · b=50 · ua=0.1 · ub=0.2
`boundary-budget`	boundary	pass	Expected y=5 · u_c=0.0022360679774997894 · Actual mode=budget · u_c=0.0022360679774997894 · u_rel=0.0004472135954999579 · y=5 · terms=2 · nu_eff_infinite=false
`boundary-budget-named-corr`	boundary	pass	Expected u_c=0.3 · Actual mode=budget · u_c=0.30000000000000004 · terms=2 · nu_eff_infinite=false
`boundary-budget-empty`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`boundary-budget-partial-x`	boundary	pass	Expected INVALID_INPUT · Actual INVALID_INPUT
`boundary-corr-psd-3x3`	boundary	pass	Expected u_c=0.20493901531919195 · Actual mode=sensitivity · u_c=0.20493901531919198 · terms=3 · nu_eff_infinite=false
`boundary-corr-singular-psd`	boundary	pass	Expected u_c=0.3 · Actual mode=sensitivity · u_c=0.30000000000000004 · terms=3 · nu_eff_infinite=false
`boundary-corr-not-psd`	boundary	pass	Expected CORRELATION_MATRIX_NOT_PSD · Actual CORRELATION_MATRIX_NOT_PSD
`boundary-corr-duplicate`	boundary	pass	Expected DUPLICATE_CORRELATION · Actual DUPLICATE_CORRELATION
`boundary-corr-conflict`	boundary	pass	Expected CONFLICTING_CORRELATION · Actual CONFLICTING_CORRELATION
`property-sum-y`	property	pass	y=a+b
`property-sum-u`	property	pass	u=√(ua²+ub²)
`property-diff-u`	property	pass	diff shares RSS u
`property-product`	property	pass	product absolute first-order
`property-product-a-zero`	property	pass	product a=0 → y=0, u_c=\|b\|ua, u_rel null
`property-quotient-a-zero`	property	pass	quotient a=0 → u_c=\|ua/b\|, u_rel null
`property-quotient-b-zero`	property	pass	quotient b=0 → DIVISION_BY_ZERO
`property-sens`	property	pass	√Σ(c·u)²
`property-rss`	property	pass	3-4-5 RSS
`property-zero-u`	property	pass	all ua=0 → u_c=0
`property-reported`	property	pass	reported u_c=0.22 (2 sig) with formatted_y=150.00; raw retained
`property-unit-match`	property	pass	matching units → V
`property-unit-mismatch`	property	pass	V+A → UNIT_MISMATCH
`property-unit-si-prefix`	property	pass	1000 mV + 2 V → 3 V
`property-unit-product`	property	pass	product units → VA
`property-unit-ohm`	property	pass	V/A → Ω
`property-unit-mv-ma`	property	pass	mV/mA → Ω after SI convert
`property-rho-perfect`	property	pass	sum ρ=1 → ua+ub
`property-rho-anti`	property	pass	sum ρ=−1 → \|ua−ub\|
`property-expanded-U`	property	pass	U=k·u_c with reported.U
`property-sens-rho0`	property	pass	sensitivity ρ=0 matches uncorrelated
`property-contrib`	property	pass	ub dominates → 80%
`property-nueff`	property	pass	WS νeff with νb→∞
`property-types`	property	pass	Type A/B + labels pass-through
`property-student-t`	property	pass	Student-t k(ν=9, p=0.95)
`property-budget`	property	pass	budget y=Σx, Vref largest
`property-mc-sum`	property	pass	MC sum ≈ linear u_c within 3%
`property-corr-singular-psd`	property	pass	all ρ=1 3×3 → u_c=0.3
`property-corr-not-psd`	property	pass	pairwise \|ρ\|≤1 but non-PSD 3×3 → CORRELATION_MATRIX_NOT_PSD