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

Open calculator REST API MCP Evidence Evidence JSON CVP Manifest Review policy

Model

Worst case

Worst case: T_WC = Σ |T_i|
Unit sensitivity: T_Y = Σ |c_i| T_i (|c_i|=1)
RSS (compare): T_RSS = √Σ T_i²

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`tolerances`	Canonical non-negative tolerance magnitudes for Σ\|t\| worst-case and √Σt² RSS comparison.	—	input / output
`unit`	Optional shared unit label (echoed in result).	—	input / output
`stack`	—	—	output
`stack_worst`	—	—	output
`stack_rss`	—	—	output
`n`	amount of substance	—	output
`tol`	—	—	output
`rss_over_wca`	—	—	output
`wc_over_rss`	—	—	output

Assumptions / Validity

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

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

Not supported

Nominal chains
asymmetric +Tol/−Tol
GD&T
geometric stacks
Monte Carlo
general sensitivity |cᵢ|≠1

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: 8/8
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 8/8.

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 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.tolerance.worst_case"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.3.0) when reproducibility matters. Full protocol notes: MCP docs.