Conic Section Identifier & Plotter 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

t8-033

Effect

Computation or source lookup only

Input and validation requirements

The all-zero coefficient input produces discriminant zero but is not a conic and causes zero-denominator or undefined-parameter calculations. The instrument must reject it instead of classifying it as a parabola. Rotated-conic outputs also require an explicit rotation convention because equivalent angle choices can swap axis labels and signs.

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": {
    "A": 1,
    "B": 0,
    "C": 1,
    "D": -4,
    "E": 6,
    "F": -3
  },
  "expected_outputs": {
    "conic_type": "circle",
    "standard_form": "(x-2)^2+(y+3)^2=16",
    "center": [
      "2",
      "-3"
    ],
    "radius": "4",
    "eccentricity": "0",
    "foci": [
      [
        "2",
        "-3"
      ]
    ],
    "vertices": [
      [
        "6",
        "-3"
      ],
      [
        "-2",
        "-3"
      ],
      [
        "2",
        "1"
      ],
      [
        "2",
        "-7"
      ]
    ],
    "directrices": "undefined for a circle under the standard focus/directrix definition",
    "plot_locus": "circle centered at (2,-3) with radius 4"
  },
  "reference_data": {
    "classification_discriminant": "B²-4AC",
    "standard_circle_form": "(x-h)²+(y-k)²=r²"
  },
  "working": "Discriminant: B²-4AC = 0²-4(1)(1) = -4 < 0, so the nondegenerate conic is ellipse-type; equal positive quadratic coefficients identify a circle. Complete squares: x²-4x=(x-2)²-4 and y²+6y=(y+3)²-9. Therefore (x-2)²-4+(y+3)²-9-3=0, so (x-2)²+(y+3)²=16. Center=(2,-3), radius=sqrt(16)=4, eccentricity=0. The four axis vertices are (2±4,-3) and (2,-3±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-tranche8/tranche8-results.json