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

instrument implementation / implementation-contract

# Polar Curve Plotter implementation

A source-bound implementation contract for Polar Curve Plotter; deployment and executable qualification remain separate.

Status: **VERIFIED_WITH_ERRATA**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-with-binding-errata

**Evidence ID**: t8-027

**Effect**: Computation or source lookup only

## Input and validation requirements

The singular expression r(theta)=1/(theta-pi/2) produces an undefined plot value and divergent area when the requested range includes theta=pi/2. The degree-versus-radian convention probe also produces materially different numeric output unless units are enforced explicitly.

## Required corrections

````
[
  {
    "vector": 1,
    "field": "enclosed_area_exact / numeric",
    "wrong": "2π ≈ 6.2832",
    "correct": "4π ≈ 12.5664",
    "cause": "area of a circle of radius 2 (r(θ)=2 constant) is π·r²=4π; her own working evaluates 1/2·4·(2π) and writes the intermediate product as \"4π/2\" instead of 4π, dropping a factor of 2 in the polar-area integral ∫½r²dθ"
  }
]
````

## Inspectable interface fixture

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

````
{
  "inputs": {
    "r_theta": "2",
    "theta_range": [
      0,
      "2π"
    ],
    "theta_units": "radians",
    "area_units": "square distance units"
  },
  "expected_outputs": {
    "plot": "Circle centered at the pole with radius 2",
    "enclosed_area_exact": "2π",
    "enclosed_area_numeric": 6.283185307179586,
    "numeric_quadrature_area": 6.283185307179586
  },
  "reference_data": {
    "identity": "A=1/2∫_0^(2π)4 dθ=2π"
  },
  "working": "A=1/2∫_0^(2π)(2)^2 dθ. First, (2)^2=4. Then A=1/2·4·(2π)=4π/2=2π=6.283185307179586."
}
````

## Other records

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

- `tranche errata record`