CVP verified calculation capability

Linear Thermal Expansion Calculation Capability

Constant-coefficient free linear expansion: delta_length = alpha * initial_length * delta_temperature.

Materials · Thermal Capability ID materials.thermal.linear_expansion version 1.0.0 CVP VERIFIED CURRENT Engineering

Model

Length change

Length change: ΔL = α L₀ ΔT
Final length: Lf = L₀(1 + αΔT)
Mean coefficient: α = ΔL / (L₀ ΔT)

Modes: delta length · final length · coefficient · temperature change

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`length`	Initial length in metres	m	input / output
`alpha_per`	User-supplied mean linear expansion coefficient in inverse kelvin	K	input / output
`delta_temperature`	Signed temperature difference in kelvin	K	input / output
`delta_length`	Signed length change in metres	m	input / output
`model`	—	—	output
`thermal_strain`	—	—	output
`final_length`	—	m	output

Assumptions / Validity

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

Assumptions

Constant mean linear expansion coefficient over the entered temperature interval
Free, unconstrained expansion
One-dimensional isotropic response along the measured direction
No material-property database or automatic coefficient selection
Not thermal stress, volumetric expansion, phase transformation, creep, or temperature-dependent integration

Not supported

named-material lookup
constrained thermal stress
anisotropic tensors
phase changes
creep
volumetric expansion
or integrating α(T)

Example

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

length_m=2, alpha_per_K=12e-6, delta_temperature_K=50 → delta_length_m=0.0012

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 · 5/5 declared partitions (forward, final-length, coefficient, temperature, invalid-domain)
Calculation version: 1.0.0
Verification: 7/7 calculation tests · 4/4 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 3511c5999fb0
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. 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: 5/5 golden · 2/2 CVP boundary · 7/7 invalid · 2/2 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/linear-thermal-expansion' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"mode":"delta_length","length_m":2,"alpha_per_K":0.000012,"delta_temperature_K":50},"calculation_version":"1.0.0"}'

{
  "inputs": {
    "mode": "delta_length",
    "length_m": 2,
    "alpha_per_K": 0.000012,
    "delta_temperature_K": 50
  },
  "calculation_version": "1.0.0"
}

POST /api/v1/calc/linear-thermal-expansion. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

Tool id: linear-thermal-expansion
Engine: linear-thermal-expansion
REST: POST /api/v1/calc/linear-thermal-expansion
MCP: execute_calculation with capability_id: "materials.thermal.linear_expansion"
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

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":"materials.thermal.linear_expansion"},"_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":"materials.thermal.linear_expansion","inputs":{"mode":"delta_length","length_m":2,"alpha_per_K":0.000012,"delta_temperature_K":50},"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.