Source: https://guthlabs.ai/docs/instruments/rotational-kinematics-solver/implementation/

instrument implementation / implementation-contract

# Rotational Kinematics Solver implementation

A source-bound implementation contract for Rotational Kinematics 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**: t4-294

**Effect**: Computation or source lookup only

## Input and validation requirements

The solver has a genuine undefined-result failure when alpha=0 and omega=omega0: time is 0/0 and theta is non-unique. It also has a branch-selection hazard because a valid input set can produce two nonnegative times and two angular velocities.

## 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": {
    "omega0": 2,
    "alpha": 3,
    "t": 4
  },
  "expected_outputs": {
    "omega": 14,
    "theta": 32
  },
  "working": "ω = ω0 + αt = 2 + 3×4 = 14 rad/s. θ = ω0t + ½αt² = 2×4 + ½×3×4² = 8 + 1.5×16 = 8 + 24 = 32 rad. Consistency check: ω² = 14² = 196; ω0² + 2αθ = 2² + 2×3×32 = 4 + 192 = 196."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/rotational-kinematics-solver/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/rotational-kinematics-solver/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/rotational-kinematics-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`