Source: https://guthlabs.ai/docs/instruments/friction-wedge-inclined-plane-solver/implementation/

instrument implementation / implementation-contract

# Friction Wedge / Inclined Plane Solver implementation

A source-bound implementation contract for Friction Wedge / Inclined Plane Solver; deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t4-166

**Effect**: Computation or source lookup only

## Input and validation requirements

The generalized formula has a true singularity when cos(phi)-mu*sin(phi)=0, producing an undefined force that must be rejected rather than numerically evaluated. The unspecified sign convention for applied-force angle also changes the computed force from 61.4087 N to 87.1377 N for the same plausible angle input.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "W_N": 1000,
    "theta_deg": 30,
    "mu": 0.5,
    "phi_deg": 0,
    "branch": "impending motion up incline",
    "coefficient_type": "mu_s"
  },
  "expected_outputs": {
    "required_force_N": 933.013,
    "angle_of_repose_deg": 26.565051
  },
  "working": "θ=30°: sinθ=0.5, cosθ=0.8660254. φ=0°: cosφ=1, sinφ=0. Up-incline branch: F=W(sinθ+μcosθ)/(cosφ−μsinφ)=1000(0.5+0.5×0.8660254)/(1−0.5×0)=1000(0.9330127)=933.0127 N≈933.013 N. Angle of repose=atan(0.5)=26.565051°."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/friction-wedge-inclined-plane-solver/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/friction-wedge-inclined-plane-solver/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/friction-wedge-inclined-plane-solver/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche4/tranche4-results.json`