Set Cardinality & Power Set Generator mechanism

Model scope

No incorrect arithmetic formula was found, but the specification is incomplete for implementation verification. Define finite-set normalization, element equality, subset/superset semantics, Cartesian-product arity, output ordering, and one exact element cap before labeling the instrument fully verified.

• |P(S)|=2^|S| is correct only for finite sets whose elements are distinct; the finite-set constraint is not stated explicitly.
• Cartesian product enumeration is named but no formal definition, operand arity, or cardinality formula is provided. For finite A and B, the standard definition is A×B={(a,b):a∈A,b∈B} and |A×B|=|A|×|B|.
• Subset and superset checks have no stated formulas or equality semantics. They should define X⊆Y as every element of X being in Y, and X⊇Y as Y⊆X.
• The specification does not say whether duplicate input values are normalized as sets or treated as separate list entries.
• The power-set formula determines cardinality but not the ordering of the enumerated power-set list.

Units and conventions

• Set elements are mathematical values with exact equality; there are no physical units and no unit conversion.
• Inputs are finite sets represented as arrays, with duplicates removed before cardinality, subset, superset, or power-set operations.
• For the expected enumerated lists below, subsets and Cartesian-product pairs are ordered deterministically using the input-array order and increasing bit-mask order.
• The subset check is X⊆Y, and the superset check is Y⊇X.
• The Cartesian-product tests use two operands, A and B; an empty operand produces an empty Cartesian product.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "S": [],
    "A": [],
    "B": [
      "x"
    ],
    "subset_check": {
      "X": [],
      "Y": [
        "x"
      ]
    }
  },
  "expected_outputs": {
    "cardinality": 0,
    "power_set": [
      []
    ],
    "cartesian_product": [],
    "cartesian_product_cardinality": 0,
    "subset": true,
    "superset": true
  },
  "working": "|S|=0. Therefore |P(S)|=2^0=1, and the only subset is the empty set: P(S)=[∅]. For the product, |A×B|=|A|×|B|=0×1=0, so A×B=∅. Every element of X=∅ is in Y={x}, so X⊆Y is true; equivalently Y⊇X is true."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The instrument has a documented practical break above approximately 12 elements: a 13-element set mathematically requires 8192 power-set entries and should be rejected, while an unguarded extreme input with 1024 elements causes direct JavaScript Number evaluation of 2^1024 to become Infinity.

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-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json