Verified calculation capability

Tolerance stack-up Calculation Capability

1-D RSS or worst-case tolerance stack — Basic tol list or Engineering dimensions (nominal, ±tol, direction). · Engineering · Tolerance

Capability ID engineering.tolerance.stackup · version 1.4.0

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

Model

Worst case (Basic)

Worst case (Basic): stack = Σ|tol_i|
Worst case (Engineering): stack_worst = max(stack_worst_plus, stack_worst_minus)
RSS: stack = √Σ u_i²
Engineering nominal: stack_nom = Σ s_i · nom_i

Solve modes: rss · worst case

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`tol`	Basic mode: tolerance contributions (preferred). Same unit for all entries.	—	input / output
`tol1`	—	—	input
`tol2`	—	—	input
`tol3`	—	—	input
`tol4`	—	—	input
`tol5`	—	—	input
`tol6`	—	—	input
`tol7`	—	—	input
`tol8`	—	—	input
`dimensions`	Engineering mode: named dimensions with nominal, asymmetric ±tol, direction, and statistical_basis (legacy: distribution).	—	input / output
`profile`	—	—	output
`n`	amount of substance	—	output
`stack`	—	—	output
`stack_rss`	—	—	output
`stack_worst`	Scalar worst-case = max(stack_worst_plus, stack_worst_minus). Equals half-range only when tolerances are symmetric about nominal.	—	output
`stack_worst_plus`	stack_max − stack_nom (Engineering); equals stack_worst in Basic	—	output
`stack_worst_minus`	stack_nom − stack_min (Engineering); equals stack_worst in Basic	—	output
`stack_range`	stack_max − stack_min = worst_plus + worst_minus	—	output
`stack_half_range`	stack_range / 2 — not the same as stack_worst when asymmetric	—	output
`stack_nom`	—	—	output
`stack_stat_center`	Engineering: signed stack using uniform midpoints where statistical_basis=uniform; equals stack_nom otherwise. Basic: null	—	output
`stack_center_shift`	stack_stat_center − stack_nom (Engineering); Basic: null	—	output
`stack_min`	—	—	output
`stack_max`	—	—	output
`rss_over_wca`	—	—	output

Assumptions / Validity

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

Assumptions

Linear 1-D stack
All contributors must use the same unit. CalculatorX performs no implicit unit conversion; mixed-unit input is unsupported
Basic mode: signs ignored via |tol|
Engineering: direction + adds / − subtracts; asymmetric ±tol supported
RSS assumes independent contributors
Default statistical_basis=magnitude → u=a with no coverage probability
1sigma → u=a; 3sigma → u=a/3; uniform → u=a/√3
Uniform asymmetric ±tol: statistical center uses interval midpoint; stack_nom stays drawing nominal
Legacy distribution=normal→1sigma, unknown→magnitude, uniform→uniform
stack_half_range ≠ stack_worst when +Tol/−Tol are asymmetric about nominal
When inputs are specification limits rather than σ-based values, prefer magnitude — RSS is an estimate and not a guaranteed assembly limit

Not supported

Geometric GD&T stacks
3-D assembly loops
Monte Carlo (see Monte Carlo Tolerance)

Example

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

Engineering A10+0.05/−0.15 − B5±0.2 + C3±0.1 → nom=8, W−=0.45, W+=0.35, stack_worst=0.45, RSS≈0.245

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Basic RSS/WCA + Engineering dimensions[] + O3 mpmath tabulated RSS/WCA. 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 · Basic RSS/WCA + Engineering dimensions[] + O3 mpmath tabulated RSS/WCA· View Manifest · CVP overview · Specification
Verified scope: Basic RSS/WCA + Engineering dimensions[] + O3 mpmath tabulated RSS/WCA
Assurance: Engineering
Declared partition coverage: PASS · 8/8 declared partitions (basic-rss, basic-wca, engineering-symmetric, engineering-asymmetric, engineering-1sigma, engineering-3sigma, engineering-uniform, invalid-domain)
Deferred: Geometric GD&T, 3-D assembly loops, and Monte Carlo remain out of this calculator (see Monte Carlo Tolerance). O3 does not cover GD&T.
Calculation version: 1.4.0
Verification: 35/35 calculation tests · 4/4 legacy golden · 13/13 legacy boundary · 18/18 legacy property
Production surface contract: 8/8
Versions: Calculation 1.4.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-16.o3-linear
Verification revision: 2026-09-16.o3-linear · 18/18 property · digest 9ae988cdc138
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 Basic RSS/WCA and Engineering dimensions[] vectors (symmetric, asymmetric, 1σ, 3σ, uniform). It is not a whole-domain stack guarantee and does not cover GD&T or 3-D loops.
Interfaces: PASS · UI (SSR) / REST / MCP
ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (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: 10/10 golden · 11/11 CVP boundary · 5/5 invalid · 18/18 property · 10/10 O3 · 6/6 cross-interface · 8/8 CVP contract
Supplemental domain review: Internal · Pass · metrology-engineer
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.4.0 (workspace artifacts agree)
Review-policy tier: Internally reviewed — catalog token internally_reviewed; supplemental; not CVP status

This calculator CURRENT · Public schema 1.4.0 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: tolerance-stackup
Engine: tolerance-stackup
REST: POST /api/v1/calc/tolerance-stackup
MCP: execute_calculation with capability_id: "engineering.tolerance.stackup"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.4.0)
Versioned output schema: Immutable pin (1.4.0)

Operations

Declared calculation modes for this capability.

rss
worst_case

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.stackup"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.4.0) when reproducibility matters. Full protocol notes: MCP docs.