Implicit Function Plotter mechanism

Model scope

The core concept is standard, but the supplied formula is incomplete and unsafe as a general implicit-relation plotter. The honest-label warning about resolution is appropriate but insufficient: the product must also disclose missed tangencies, exact-zero behavior, and ambiguous-cell topology. A concrete grid specification, interpolation rule, zero policy, saddle decider, and non-finite-value policy are required before this can pass.

• The stated marching-squares rule of emitting geometry only where sampled corner values change sign can miss valid contours that touch a cell without changing sign, including tangencies and contours passing exactly through grid vertices or edges.
• The specification does not define the edge-intersection interpolation rule; standard marching squares requires linear interpolation t=F_a/(F_a-F_b) along each sign-changing edge, unless a different contouring rule is intended.
• The specification does not define connectivity for ambiguous saddle cases such as marching-squares cases 5 and 10. An asymptotic decider or another explicit tie-breaking rule is required.
• The claim that arbitrary curves are plotted is too broad for a finite sampled grid: narrow features, high-frequency curves, tangencies, discontinuities, and features smaller than the grid spacing can be missed.
• Exact-zero handling, duplicate vertices, contours on grid boundaries, NaN/infinite values, and degenerate cells are unspecified.

Units and conventions

• x and y must use compatible coordinate units within F; quantities added or compared inside F must be dimensionally compatible.
• The domain bounds are assumed to be numeric x_min, x_max, y_min, and y_max values in the same coordinate system used by F.
• F is assumed to return a finite real scalar whose sign is meaningful; no unit is assigned to F itself unless the expression defines one.
• Contour coordinates inherit the coordinate units of x and y; grid resolution is a numerical sampling parameter, not a physical unit.

Inspectable vector

One of 4 source-bound review vectors:

{
  "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)."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

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.

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
• BOUNDARY_HAZARD_CATALOG.json