Home Developers Capabilities Worst-Case Tolerance Analysis

CVP verified calculation capability

Worst-Case Tolerance Analysis Calculation Capability

1-D linear worst-case tolerance magnitude stack Σ|tol| with RSS comparison (|cᵢ|=1).

Engineering · Tolerance Capability ID engineering.tolerance.worst_case version 1.3.0 CVP VERIFIED CURRENT Engineering

Model

Worst case

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

SymbolQuantityUnitRole
tolerancesCanonical non-negative tolerance magnitudes for Σ|t| worst-case and √Σt² RSS comparisoninput / output
unitOptional shared unit labelinput / output
stackoutput
stack_worstoutput
stack_rssoutput
noutput
toloutput
rss_over_wcaoutput
wc_over_rssoutput

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

Assumptions

Not supported

Example

One numerical check. The calculator page holds worked steps and FAQ.

0.1,0.2,0.1 → total worst-case tolerance ±0.4 · RSS ≈ 0.244949

Open this example in the calculator

Trust

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. 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.

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· View Manifest · CVP overview · Specification
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
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)
Deferred
Nominal chains, asymmetric ±Tol, GD&T, geometric stacks, Monte Carlo, and general sensitivity |cᵢ|≠1 are out of this calculator
Calculation version
1.3.0
Verification
27/27 calculation tests · 7/7 legacy golden · 7/7 legacy boundary · 13/13 legacy property
Production surface contract
10/10
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
Reference
O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope
≤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.
Interfaces
PASS · UI (SSR) / REST / MCP
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.
CVP suite
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
Supplemental domain review
Internal · Pass · tolerance-engineer
  • Model / formula · 2026-08-12 · still current
  • Interface / input semantics · 2026-09-12
Named expert review
Not performed
Version lock
Supported (409 VERSION_MISMATCH)
Artifact consistency
Build verified · 1.3.0 (workspace artifacts agree)
Review-policy tier
Internally reviewed — catalog token internally_reviewed; supplemental; not CVP status
This calculator CURRENT · Public schema 1.3.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

Call this capability

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 10/10.

curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/worst-case-analysis' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"tol1":0.1,"tol2":0.2,"tol3":0.1},"calculation_version":"1.3.0"}'

POST /api/v1/calc/worst-case-analysis. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

Tool id
worst-case-analysis
Engine
worst-case-analysis
REST
POST /api/v1/calc/worst-case-analysis
MCP
execute_calculation with capability_id: "engineering.tolerance.worst_case"
Agent input schema
Canonical (MCP / Agent)
REST input schema
Compatibility (tol[] / tol1…)
Output schema
JSON Schema (latest)
Versioned input schema
Immutable pin (1.3.0)
Versioned output schema
Immutable pin (1.3.0)

References

Human-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

Try with an agent

Inspect, then execute. Same engine as REST and the human calculator.

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.tolerance.worst_case"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

Pin calculation_version (1.3.0) when the result must stay reproducible.

Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.