Coordinate Geometry Toolkit implementation

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

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