Set Cardinality & Power Set Generator 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

t4-201

Effect

Computation or source lookup only

Input and validation requirements

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.

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": {
    "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."
}

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