Source: https://guthlabs.ai/docs/instruments/implicit-function-plotter/implementation/

instrument implementation / implementation-contract

# Implicit Function Plotter implementation

A source-bound implementation contract for Implicit Function 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**: t8-028

**Effect**: Computation or source lookup only

## Input and validation requirements

The sign-change-only method can miss an isolated exact-zero contour such as F=x^2+y^2=0, and singular inputs such as F=1/(x-y) can produce undefined samples or false contours if NaN/infinity handling is not explicit. Ambiguous marching-squares saddle cells also require a defined branch rule.

## 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": {
    "F": "x + y - 0.8",
    "domain": {
      "x": [
        0,
        1
      ],
      "y": [
        0,
        1
      ]
    },
    "grid": {
      "nx": 1,
      "ny": 1
    },
    "corner_order": "bottom-left,bottom-right,top-right,top-left"
  },
  "expected_outputs": {
    "contour_segments": [
      [
        {
          "x": 0.8,
          "y": 0
        },
        {
          "x": 0,
          "y": 0.8
        }
      ]
    ],
    "corner_values": {
      "bottom_left": -0.8,
      "bottom_right": 0.2,
      "top_right": 1.2,
      "top_left": 0.2
    }
  },
  "reference_data": {
    "method": "linear interpolation on each sign-changing cell edge",
    "edge_interpolation": "P(t)=(1-t)P_a+tP_b, t=F_a/(F_a-F_b)"
  },
  "working": "Evaluate corners: F(0,0)=-0.8; F(1,0)=0.2; F(1,1)=1.2; F(0,1)=0.2. Bottom edge: t=(-0.8)/(-0.8-0.2)=0.8, so x=0+0.8(1-0)=0.8 and y=0. Left edge: t=(-0.8)/(-0.8-0.2)=0.8, so x=0 and y=0+0.8(1-0)=0.8. The cell has one contour segment joining (0.8,0) to (0,0.8)."
}
````

## Other records

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