Vector Operations 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

t2-045

Effect

Computation or source lookup only

Input and validation requirements

The zero vector causes division by zero in normalization, projection, and angle calculations. The instrument must reject such inputs or return an explicit undefined result. A second hazard is convention ambiguity for signed versus unsigned 2D angles.

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": [
      3,
      4,
      0
    ],
    "b": [
      1,
      2,
      2
    ]
  },
  "expected_outputs": {
    "dot": 11,
    "cross": [
      8,
      -6,
      2
    ],
    "magnitude_a": 5,
    "magnitude_b": 3,
    "normalized_a": [
      0.6,
      0.8,
      0
    ],
    "normalized_b": [
      "1/3",
      "2/3",
      "2/3"
    ],
    "projection_a_onto_b": [
      "11/9",
      "22/9",
      "22/9"
    ],
    "angle_radians": "acos(11/15) ≈ 0.7476"
  },
  "working": "dot=3×1+4×2+0×2=3+8+0=11. cross=(4×2−0×2, 0×1−3×2, 3×2−4×1)=(8,−6,2). |a|=sqrt(3²+4²+0²)=sqrt(25)=5. |b|=sqrt(1²+2²+2²)=sqrt(9)=3. normalize(a)=(3/5,4/5,0)=(0.6,0.8,0). normalize(b)=(1/3,2/3,2/3). |b|²=9, so projection coefficient=(a·b)/|b|²=11/9; projection=(11/9)(1,2,2)=(11/9,22/9,22/9). angle=acos(11/(5×3))=acos(11/15)≈0.7476 radians."
}

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-tranche2/tranche2-results.json