3D Surface Plotter

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Mathematics — arithmetic through advanced (algebra, matrices, calculus, sequences/series, number theory, combinatorics, graphing, complex numbers, geometry, logic, sets)

Tranche

tranche-8

Evidence ID

t8-029

Ledger rows

1

No ledger note is attached.

Review findings

The stated grid-sampling approach is mathematically appropriate for approximate surface visualization. Verdict is NEEDS_REVIEW because sampling resolution, contour extraction, gradient-shading behavior, coordinate/trigonometric units, singularity handling, and the required honest approximation label are unspecified.

Formula and scope findings

• Grid sampling of f(x,y) is a standard numerical plotting method, but the specification does not define grid resolution, spacing, interpolation, or adaptive refinement; undersampling can miss narrow features, discontinuities, and extrema.
• Contour projection is claimed but no contour-extraction method, interpolation rule, or contour-level input is specified. A standard implementation would use marching squares or an equivalent method on sampled cells.
• Optional gradient shading is underspecified. For z=f(x,y), the standard upward surface normal is n=(-f_x,-f_y,1), normalized as n/||n||; numerical gradients require a finite-difference scheme and boundary handling.
• The empty honest_label is inadequate for a numerically sampled plotter: it should disclose that surfaces and contours are approximate and may be unreliable near discontinuities, singularities, or undersampled features.

Unit assumptions

• x and y are numerical coordinate values with user-defined units; no physical unit metadata is specified.
• z inherits the units implied by f(x,y). For mixed or dimensional expressions, the expression parser must enforce dimensionally valid operations.
• Trigonometric arguments are assumed to be in radians unless the instrument explicitly documents degree input.
• The contour level z=c must use the same z units as the function output.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

The specification does not define handling for singular expression samples. For f(x,y)=1/(x-y), a normal grid containing x=y produces 1/0. If the plotter forwards Infinity or NaN to the rendering pipeline instead of rejecting the sample and splitting the surface, mesh generation, contouring, shading, or camera bounds can fail.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "inputs": {
    "expression": "f(x,y)=x^2+y^2",
    "x_domain": [
      -1,
      1
    ],
    "y_domain": [
      -1,
      1
    ],
    "sample_x": [
      -1,
      0,
      1
    ],
    "sample_y": [
      -1,
      0,
      1
    ],
    "contour_level": 1
  },
  "expected_outputs": {
    "sampled_z_rows_by_y": [
      [
        2,
        1,
        2
      ],
      [
        1,
        0,
        1
      ],
      [
        2,
        1,
        2
      ]
    ],
    "contour_level_1_reference_points": [
      [
        -1,
        0
      ],
      [
        0,
        -1
      ],
      [
        0,
        1
      ],
      [
        1,
        0
      ]
    ],
    "gradient_at": {
      "x": 1,
      "y": 0,
      "gradient": [
        2,
        0
      ],
      "upward_unit_normal": [
        "-2/sqrt(5)",
        "0",
        "1/sqrt(5)"
      ]
    }
  },
  "reference_data": {
    "surface": "Paraboloid z=x^2+y^2",
    "contour_equation": "x^2+y^2=1",
    "gradient_formula": "(f_x,f_y)=(2x,2y)",
    "normal_formula": "n=(-f_x,-f_y,1)/sqrt(f_x^2+f_y^2+1)"
  },
  "working": "Evaluate each grid point: f(-1,-1)=(-1)^2+(-1)^2=1+1=2; f(0,-1)=0^2+(-1)^2=0+1=1; f(1,-1)=1+1=2. For y=0: f(-1,0)=1+0=1; f(0,0)=0+0=0; f(1,0)=1+0=1. For y=1 the row is again [2,1,2]. The level-1 contour satisfies x^2+y^2=1, whose axis intersections are (-1,0),(0,-1),(0,1),(1,0). At (1,0), (f_x,f_y)=(2,0), so n=(-2,0,1), ||n||=sqrt(4+1)=sqrt(5), giving the stated unit normal."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json · VERIFIED_CLEAN
• evidence-tranche8/tranche8-results.json
• BOUNDARY_HAZARD_CATALOG.json