Source: https://guthlabs.ai/docs/instruments/parametric-curve-plotter/implementation/

instrument implementation / implementation-contract

# Parametric Curve Plotter implementation

A source-bound implementation contract for Parametric Curve Plotter; 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**: t8-026

**Effect**: Computation or source lookup only

## Input and validation requirements

The specification exposes a singular-input failure at t=1, where the curve and arc-length integral are undefined, and it does not specify trigonometric angle units, allowing a 90-versus-pi/2 arc-length discrepancy.

## 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": {
    "x(t)": "2t m",
    "y(t)": "3t m",
    "t_range": "[0,3] s"
  },
  "expected_outputs": {
    "arc_length_exact": "3√13 m",
    "arc_length_numeric_quadrature": "10.81665382639197 m",
    "speed": "√13 m/s",
    "tangent_or_velocity_at_t_1": "(2,3) m/s",
    "curve_endpoints": {
      "at_t_0": "(0,0) m",
      "at_t_3": "(6,9) m"
    },
    "integral_check": {
      "antiderivative_difference": "3√13 m",
      "numeric_quadrature": "10.81665382639197 m"
    }
  },
  "reference_data": {
    "method": "Exact integral and numerical quadrature",
    "derivatives": {
      "x'(t)": "2 m/s",
      "y'(t)": "3 m/s"
    }
  },
  "working": "1. x'(t)=2 and y'(t)=3. 2. Speed=√(2²+3²)=√(4+9)=√13 m/s. 3. Arc length=∫_0^3 √13 dt=√13·(3−0)=3√13 m. 4. Numerically, √13=3.605551275463989, so 3√13=10.81665382639197 m. 5. At t=1, the velocity/tangent vector is (x'(1),y'(1))=(2,3) m/s."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/parametric-curve-plotter/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/parametric-curve-plotter/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/parametric-curve-plotter/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-tranche8/tranche8-results.json`