Source: https://guthlabs.ai/docs/instruments/set-cardinality-power-set-generator/implementation/

instrument implementation / implementation-contract

# Set Cardinality & Power Set Generator implementation

A source-bound implementation contract for Set Cardinality & Power Set Generator; 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**: 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

[01**Overview**](<https://guthlabs.ai/docs/instruments/set-cardinality-power-set-generator/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/set-cardinality-power-set-generator/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/set-cardinality-power-set-generator/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-tranche4/tranche4-results.json`