Set Operations Visualizer (Venn) mechanism

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

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