CVP verified calculation capability

Rectangular section Calculation Capability

Centroidal area moments and elastic section moduli of a rectangle from its width and height. Composite sections stay on the area-moment page.

Mechanical · Statics Capability ID mechanical.statics.rectangular_section version 1.0.0 CVP VERIFIED CURRENT Engineering

Model

About the centroid

About the centroid: Ix = b h³/12, Iy = h b³/12
Elastic section modulus: Sx = b h²/6, Sy = h b²/6

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`b`	Width, parallel to x	—	input / output
`h`	Height, parallel to y	—	input / output
`area`	—	—	output
`Ix`	—	—	output
`Iy`	—	—	output
`kx`	—	—	output
`ky`	—	—	output
`Sx`	—	—	output
`Sy`	—	—	output
`model`	—	—	output
`solver`	—	—	output

Assumptions / Validity

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

Assumptions

Centroidal axes parallel to the sides
Ix = b h³/12 and Iy = h b³/12
Sx = b h²/6 and Sy = h b²/6
Not a composite section, a circle, bending stress, or a plastic modulus

Example

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

b=2 h=6 → area=12, Ix=36, Iy=4, Sx=12, Sy=4

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance. 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· View Manifest · CVP overview · Specification
Assurance: Engineering
Declared partition coverage: PASS · 2/2 declared partitions (domain, invalid-domain)
Calculation version: 1.0.0
Verification: 6/6 calculation tests · 3/3 legacy golden · 3/3 legacy boundary
Production surface contract: 6/6
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed
CVP identity: 0/0 property · digest d5f0ecab3894
Reference: O1 model · O2 expected_values · O2 numerical_behavior
Interfaces: PASS · UI (SSR) / REST / MCP
ui-ssr is query-result HTML, not a live browser session.
CVP suite: 1/1 golden · 3/3 CVP boundary · 3/3 invalid · 1/1 cross-interface · 6/6 CVP contract
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.0 (workspace artifacts agree)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

This calculator CURRENT · Public schema 1.0.0 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 6/6.

curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/rectangular-section' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"b":2,"h":6},"calculation_version":"1.0.0"}'

{
  "inputs": {
    "b": 2,
    "h": 6
  },
  "calculation_version": "1.0.0"
}

POST /api/v1/calc/rectangular-section. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

Tool id: rectangular-section
Engine: rectangular-section
REST: POST /api/v1/calc/rectangular-section
MCP: execute_calculation with capability_id: "mechanical.statics.rectangular_section"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.0)
Versioned output schema: Immutable pin (1.0.0)

References

Human-readable sources plus CVP reference evidence classes.

Sources

Hibbeler, Engineering Mechanics: Statics — Moments of inertia — rectangular area
Gere and Goodno, Mechanics of Materials — Moments of inertia — rectangular area

Reference evidence classes: O1 model · 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":"mechanical.statics.rectangular_section"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

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: execute_calculation' \
  -d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"execute_calculation","arguments":{"capability_id":"mechanical.statics.rectangular_section","inputs":{"b":2,"h":6},"calculation_version":"1.0.0"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

Pin calculation_version (1.0.0) when the result must stay reproducible.

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