CVP verified calculation capability

Slip or tip Calculation Capability

Whether a block on a level surface slips or tips under a horizontal force. Slip uses the friction engine. Tip is the moment of the weight about the leading edge. Not an incline, and not a wedge.

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

Model

Slip

Slip: P_slip = μ W
Tip: P_tip = W b / (2 d)

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`W`	Weight, in newtons	—	input / output
`mu`	Friction coefficient at impending slip	—	input / output
`b`	Width of the base in the direction of the force	—	input / output
`d`	Height of the horizontal force above the surface	—	input / output
`N`	—	—	output
`P_slip`	—	—	output
`P_tip`	—	—	output
`P`	—	—	output
`model`	—	—	output
`solver`	—	—	output

Assumptions / Validity

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

Assumptions

The surface is level and the force is horizontal
The weight acts through the center of a base of width b
mode is slip, tip, or either
Not an incline, a wedge, a screw, or a belt

Example

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

W=100 mu=0.25 b=2 d=2 → slip, P=25

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Level surface: P_slip = μW and P_tip = W b/(2 d); P is the smaller. + O3 mpmath tabulated P.. 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 · Level surface: P_slip = μW and P_tip = W b/(2 d); P is the smaller. + O3 mpmath tabulated P.· View Manifest · CVP overview · Specification
Verified scope: Level surface: P_slip = μW and P_tip = W b/(2 d); P is the smaller. + O3 mpmath tabulated P.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (slip, tip, alias, awkward, invalid-domain)
Deferred: Not an incline, not wedges, not screws, and not belts.
Calculation version: 1.0.0
Verification: 7/7 calculation tests · 3/3 legacy golden · 4/4 legacy boundary
Production surface contract: 6/6
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-27.o2-o3
Verification revision: 2026-09-27.o2-o3 · 1/1 property · digest fcf2cdd2fb94
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: P vs a separate-module identity (≤2 ULP). Not an incline, not wedges, not screws, and not belts. ≤2 ULP vs O3 applies only to the published tabulated slip-or-tip vectors.
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: 4/4 golden · 4/4 CVP boundary · 6/6 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 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/slip-or-tip' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"W":100,"mu":0.25,"b":2,"d":2},"calculation_version":"1.0.0"}'

{
  "inputs": {
    "W": 100,
    "mu": 0.25,
    "b": 2,
    "d": 2
  },
  "calculation_version": "1.0.0"
}

POST /api/v1/calc/slip-or-tip. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

Tool id: slip-or-tip
Engine: slip-or-tip
REST: POST /api/v1/calc/slip-or-tip
MCP: execute_calculation with capability_id: "mechanical.statics.slip_or_tip"
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 — Dry friction — tipping or slipping
Beer, Johnston, and Mazurek, Vector Mechanics for Engineers: Statics — Dry friction — tipping or slipping

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":"mechanical.statics.slip_or_tip"},"_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.slip_or_tip","inputs":{"W":100,"mu":0.25,"b":2,"d":2},"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.