Source: https://guthlabs.ai/docs/instruments/set-operations-visualizer-venn/mechanism/

instrument mechanism / verified-clean

# Set Operations Visualizer (Venn) mechanism

The inspectable method record for Set Operations Visualizer (Venn), kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

No arithmetic or unit conversion is involved. The core operations are standard, but the instrument cannot honestly claim to compute complement without requiring an explicit universal set. Add a documented equality policy, duplicate handling, deterministic display ordering, and a precise three-set symmetric-difference definition before labeling the instrument fully verified.

- The union, intersection, set difference, and symmetric-difference definitions are standard and correct.

- Complement is underspecified: it must be defined relative to an explicit universal set U; without U, complement(A) has no unique result.

- For three sets, symmetric difference should be explicitly defined as elements occurring in an odd number of the sets, equivalently (A Δ B) Δ C.

- The Venn diagram must show a universal-set boundary for complement shading; otherwise the outside region is visually ambiguous.

## Units and conventions

- Set elements are compared by exact JavaScript value/equality semantics; the spec should state whether mixed types such as 1 and "1" are distinct.

- Element order is mathematically irrelevant; displayed results should use a deterministic ordering for reproducibility.

- Duplicate input entries should be deduplicated because the inputs represent sets, not multisets.

- No physical units apply; elements are abstract values.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "sets": {
      "A": [
        1,
        2,
        3,
        5
      ],
      "B": [
        3,
        4,
        5,
        6
      ]
    },
    "operation": "union"
  },
  "expected_outputs": {
    "result": [
      1,
      2,
      3,
      4,
      5,
      6
    ],
    "shaded_regions": [
      "A-only",
      "B-only",
      "A-intersection-B"
    ]
  },
  "working": "Start with A = {1,2,3,5}. Add elements of B = {3,4,5,6}, keeping each element only once: {1,2,3,5} ∪ {3,4,5,6} = {1,2,3,4,5,6}. Region check: A-only = {1,2}, B-only = {4,6}, A∩B = {3,5}; their union is {1,2,3,4,5,6}."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The extreme-integer vector can break the plain-JavaScript implementation: 9007199254740992 and 9007199254740993 are mathematically distinct set elements but can collapse to the same IEEE-754 Number, producing an incorrect union. Complement also requires an explicit universe; without one, the result is undefined.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/set-operations-visualizer-venn/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/set-operations-visualizer-venn/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/set-operations-visualizer-venn/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-tranche6/tranche6-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`