Source: https://guthlabs.ai/docs/instruments/vector-operations-toolkit/implementation/

instrument implementation / implementation-contract

# Vector Operations Toolkit implementation

A source-bound implementation contract for Vector Operations Toolkit; deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## 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

[01**Overview**](<https://guthlabs.ai/docs/instruments/vector-operations-toolkit/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/vector-operations-toolkit/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/vector-operations-toolkit/qualification/>)

## 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`