Source: https://guthlabs.ai/docs/instruments/coordinate-geometry-toolkit/implementation/

instrument implementation / implementation-contract

# Coordinate Geometry Toolkit implementation

A source-bound implementation contract for Coordinate Geometry Toolkit; 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**: t4-189

**Effect**: Computation or source lookup only

## Input and validation requirements

- Slope division by zero when x2=x1; vertical lines need a separate representation.

- Line equation is undefined or non-unique when the two input points coincide, and vertical lines cannot be represented safely as y=mx+b.

- Point-line distance divides by zero when a=0 and b=0; this input must be rejected.

- A unique circle does not exist for three collinear points, and coincident or insufficiently distinct points create degeneracies.

- Mixed coordinate units, such as one point in meters and another in centimeters, produce incorrect distances unless converted first.

- Finite-precision arithmetic can cause near-collinear three-point circle inputs to be unstable.

- The spec does not define output formats for vertical lines, undefined slopes, degenerate circles, or invalid inputs.

## 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": {
    "operation": "distance_and_midpoint",
    "point1": {
      "x": 1,
      "y": 2
    },
    "point2": {
      "x": 4,
      "y": 6
    },
    "unit": "m"
  },
  "expected_outputs": {
    "distance": 5,
    "midpoint": {
      "x": 2.5,
      "y": 4
    },
    "distance_unit": "m"
  },
  "working": "dx = x2 - x1 = 4 - 1 = 3. dy = y2 - y1 = 6 - 2 = 4. distance = sqrt(dx^2 + dy^2) = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5 m. midpoint = ((x1+x2)/2, (y1+y2)/2) = ((1+4)/2, (2+6)/2) = (5/2, 8/2) = (2.5, 4)."
}
````

## Other records

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