Source: https://guthlabs.ai/docs/instruments/slope-field-direction-field-plotter/implementation/

instrument implementation / implementation-contract

# Slope Field / Direction Field Plotter implementation

A source-bound implementation contract for Slope Field / Direction Field 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**: t8-030

**Effect**: Computation or source lookup only

## Input and validation requirements

The input f(x,y)=1/(x-y) with an initial or grid point at (0,0) produces division by zero. The plotter must detect the singularity and reject or omit that point rather than emitting a finite slope or attempting an RK4 step.

## 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",
    "grid_point": {
      "x": 1,
      "y": 2
    },
    "segment_total_length": 0.2,
    "render_mode": "direction_field_only"
  },
  "expected_outputs": {
    "slope": 3,
    "normalized_tangent": {
      "dx": 0.31622776601683794,
      "dy": 0.9486832980505138
    },
    "segment_endpoints": [
      {
        "x": 0.9683772233983162,
        "y": 1.9051316701949486
      },
      {
        "x": 1.0316227766016839,
        "y": 2.094868329805051
      }
    ]
  },
  "reference_data": {
    "segment_rule": "centered endpoints p - 0.1*(1,m)/sqrt(1+m^2) and p + 0.1*(1,m)/sqrt(1+m^2)"
  },
  "working": "At (x,y)=(1,2), m=f(1,2)=1+2=3. Compute sqrt(1+m^2)=sqrt(10)=3.1622776601683793. The unit tangent is (1/sqrt(10),3/sqrt(10))=(0.31622776601683794,0.9486832980505138). Half the segment length is 0.2/2=0.1. The offset is (0.0316227766016838,0.0948683298050514). Subtracting from (1,2) gives (0.9683772233983162,1.9051316701949486); adding gives (1.0316227766016838,2.0948683298050514)."
}
````

## Other records

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