Public evidence

engineering.tolerance.worst_case

Machine-checked verification for calculation version 1.3.0 · 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 · 1-D linear magnitude stack Σ|Tᵢ| with RSS comparison; canonical tolerances[] ≥ 0; REST signed-magnitude compatibility warning; O3 mpmath tabulated sum/RSS· 1-D magnitude stack — not a full nominal min/max chain. Canonical Agent/UI magnitudes are non-negative. REST tol[] / tol1… still accept a negative with SIGN_IGNORED_FOR_TOLERANCE_MAGNITUDE. · Protocol · Schema · Production report

Declared partition coverage: PASS · 13/13 declared partitions (single-term, multi-term, all-zero, mixed-magnitude, signed-input-policy, large-N, scale-small, scale-large, canonical-array, legacy-fields, invalid-missing, invalid-numeric, xcal)
Versions: Calculation 1.3.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-16.o3-rss
Verification revision: 2026-09-16.o3-rss · 10/10 property · digest 9146ee258d55

Verification

Legacy regression suite: 27/27 calculation tests · Production surface contract 8/8

Three distinct suites: educational examples on the calculator page, this legacy regression count (27/27 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 1.3.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

Named expert review Not performed

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-09-16.o3-rss. Calculation version 1.3.0. CVP 1.0.0-proposed. 4/4 golden · 11/11 CVP boundary · 9/9 invalid · 10/10 property · 3/3 metamorphic · 8/8 O3 · 5/5 cross-interface · 4/4 cross-calculator · 8/8 CVP contract. digest 9146ee258d55. ≤2 ULP vs O3 applies only to the published tabulated 1-D magnitude vectors (fields, array, signed REST, single, zeros, small, large, 3-4-5). Long equal-term sums such as n=100×0.01 remain Evidence/property and are not an O3 2-ULP claim. It is not a whole-domain guarantee and does not cover GD&T or nominal chains.

Golden (oracle-backed) 4 / 4
CVP boundary 11 / 11
Invalid input 9 / 9
Property 10 / 10
Metamorphic 3 / 3
O3 high-precision 8 / 8
Cross-interface 5 / 5
Cross-calculator 4 / 4
CVP contract 8 / 8
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 2/2 (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 1-D linear magnitude stack Σ|Tᵢ| with RSS comparison; canonical tolerances[] ≥ 0; REST signed-magnitude compatibility warning; O3 mpmath tabulated sum/RSS
Assurance Engineering
Deferred Nominal chains, asymmetric ±Tol, GD&T, geometric stacks, Monte Carlo, and general sensitivity |cᵢ|≠1 are out of this calculator

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 sha256:385eede741ce878fa115231e8c7a6758469899f23e10067431a6df315b7c33ef

Input schema sha256:9aad061f476a351cdcbe3256b8acc8d684a701499f9a3a35e97058aa2e141f80 · Output schema sha256:abd371ac9a76f0e7e9c13648cb220b15a2e9d154c98dd00d109186bda1f48251 · 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: worst-case-analysis
Engine: worst-case-analysis
Engine build: 2026-09-12
Evidence core: 2026-09-12T08:46:25.940Z
Rendered: 2026-09-16T22:03:43.730Z
Last reviewed: 2026-09-12
Model / formula · 2026-08-12 · still current
Interface / input semantics · 2026-09-12

Assumptions

Linear 1-D magnitude stack only
Unit sensitivity |cᵢ|=1
Worst-case assumes every included contributor can reach its declared limit
RSS comparison assumes consistent statistical basis and independence
Canonical/UI magnitudes are non-negative; REST signed values ignore sign

Limitations

1-D linear magnitude stack only — not a full nominal min/max dimensional chain
RSS comparison assumes consistent statistical basis and independence
MCP/agent input schema is canonical (tolerances[] ≥ 0); REST still accepts tol[] / tol1…tol8
Canonical/UI magnitudes must be ≥ 0 (NEGATIVE_TOLERANCE_MAGNITUDE). REST signed values ignore sign (SIGN_IGNORED_FOR_TOLERANCE_MAGNITUDE)
Unit is a shared label; all contributors must already use the same unit — no conversion

Sources

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

NISTIR 6223 — Design for Tolerance of Electromechanical Assemblies — Worst-case tolerance analysis
Supports: Deterministic analysis using component max/min limits for assembly requirements
ASME Y14.5 — Dimensioning and Tolerancing — Dimensional tolerancing / GD&T semantics
Supports: Background language for dimensions and tolerances (not the Σ|t| algorithm itself)

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
`wca`	golden	pass	Expected stack=0.4 · stack_rss=0.2449489742783178 · wc_over_rss=1.632993161855452 · Actual n=3 · mode=worst_case · stack=0.4 · stack_worst=0.4 · stack_rss=0.24494897427831783 · rss_over_wca=0.6123724356957946 · wc_over_rss=1.632993161855452
`empty`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`two`	golden	pass	Expected stack=1 · stack_rss=0.7071067811865476 · Actual n=2 · mode=worst_case · stack=1 · stack_worst=1 · stack_rss=0.7071067811865476 · rss_over_wca=0.7071067811865476 · wc_over_rss=1.414213562373095
`one`	golden	pass	Expected n=1 · stack=0.2 · stack_rss=0.2 · Actual n=1 · mode=worst_case · stack=0.2 · stack_worst=0.2 · stack_rss=0.2 · rss_over_wca=1 · wc_over_rss=1
`zeros`	golden	pass	Expected n=3 · stack=0 · stack_rss=0 · Actual n=3 · mode=worst_case · stack=0 · stack_worst=0 · stack_rss=0
`signed`	golden	pass	Expected stack=0.6 · stack_rss=0.37416573867739417 · Actual n=3 · mode=worst_case · stack=0.6000000000000001 · stack_worst=0.6000000000000001 · stack_rss=0.37416573867739417 · rss_over_wca=0.6236095644623235 · wc_over_rss=1.6035674514745464
`canonical`	golden	pass	Expected n=3 · stack=0.4 · unit=mm · Actual n=3 · mode=worst_case · unit=mm · stack=0.4 · stack_worst=0.4 · stack_rss=0.24494897427831783 · rss_over_wca=0.6123724356957946 · wc_over_rss=1.632993161855452
`tol-array`	golden	pass	Expected stack=0.4 · Actual n=3 · mode=worst_case · stack=0.4 · stack_worst=0.4 · stack_rss=0.24494897427831783 · rss_over_wca=0.6123724356957946 · wc_over_rss=1.632993161855452
`boundary-wca-zeros`	boundary	pass	Expected stack=0 · stack_rss=0 · Actual n=3 · mode=worst_case · stack=0 · stack_worst=0 · stack_rss=0
`boundary-wca-signed`	boundary	pass	Expected stack=0.6 · Actual n=3 · mode=worst_case · stack=0.6000000000000001 · stack_worst=0.6000000000000001 · stack_rss=0.37416573867739417 · rss_over_wca=0.6236095644623235 · wc_over_rss=1.6035674514745464
`boundary-wca-canonical`	boundary	pass	Expected stack=0.4 · unit=mm · Actual n=3 · mode=worst_case · unit=mm · stack=0.4 · stack_worst=0.4 · stack_rss=0.24494897427831783 · rss_over_wca=0.6123724356957946 · wc_over_rss=1.632993161855452
`boundary-wca-many`	boundary	pass	Expected n=100 · stack=1 · Actual n=100 · mode=worst_case · stack=1.0000000000000007 · stack_worst=1.0000000000000007 · stack_rss=0.09999999999999998 · rss_over_wca=0.09999999999999991 · wc_over_rss=10.000000000000009
`boundary-wca-overflow`	boundary	pass	Expected RESULT_OVERFLOW · Actual RESULT_OVERFLOW
`boundary-wca-canonical-negative`	boundary	pass	Expected NEGATIVE_TOLERANCE_MAGNITUDE · Actual NEGATIVE_TOLERANCE_MAGNITUDE
`property-wca`	property	pass	0.4
`property-permutation`	property	pass	order-invariant
`property-sign-invariance`	property	pass	sign-invariant
`property-sign-ignored-warning`	property	pass	sign-ignored-warning
`property-scale`	property	pass	WC(k·t)=\|k\|WC(t)
`property-monotonic`	property	pass	add \|t\| ≥
`property-wc-ge-rss`	property	pass	Σ\|t\| ≥ √Σt²
`property-one`	property	pass	single
`property-zeros`	property	pass	all-zero
`property-canonical`	property	pass	tolerances[]
`property-scale-n`	property	pass	n=1000
`property-warnings`	property	pass	structured warnings
`property-wc-over-rss`	property	pass	WC/RSS