{
  "schema": "groups.qft.org/operator-inventory-examples/1",
  "versions": {
    "schema": "2.0.0",
    "dataset": "2026.11-workbench.4",
    "application": "6.0.0",
    "algorithm": "groups-workbench-4.0.0",
    "released": "2026-11-08"
  },
  "scope": "Six complete bounded field inventories with explicit conjugates, selected canonical dimensions, and optional charge rules. Every result is recomputed locally on import.",
  "setupSchema": "groups.qft.org/operator-enumeration/1",
  "calculationSchema": "groups.qft.org/operator-enumeration-calculation/1",
  "jsonSchema": "/data/operator-enumeration.schema.json",
  "examples": [
    {
      "id": "sm-1",
      "title": "Standard Model · one generation",
      "summary": "Enumerate the complete scalar/Weyl polynomial sectors through dimension six, with explicit conjugate fields. Derivatives and field strengths are excluded.",
      "expected": {
        "sectorCount": 46,
        "invariantCount": "55",
        "byDimension": {
          "2": "1",
          "4": "7",
          "5": "2",
          "6": "45"
        }
      },
      "guide": "/physics/standard-model-operator-sectors/",
      "route": "/tools/operator-enumeration/?example=sm-1",
      "inventory": "/data/operator-inventories/sm-1.json",
      "calculation": "/data/operator-enumerations/sm-1.json"
    },
    {
      "id": "sm-3",
      "title": "Standard Model · three generations",
      "summary": "Keep all flavor components. Distinct conjugate sectors are counted separately; flavor-basis rotations and Hermiticity are not imposed.",
      "expected": {
        "sectorCount": 46,
        "invariantCount": "2874",
        "byDimension": {
          "2": "1",
          "4": "55",
          "5": "12",
          "6": "2806"
        }
      },
      "guide": "/physics/standard-model-operator-sectors/",
      "route": "/tools/operator-enumeration/?example=sm-3",
      "inventory": "/data/operator-inventories/sm-3.json",
      "calculation": "/data/operator-enumerations/sm-3.json"
    },
    {
      "id": "sm-3-bl",
      "title": "Standard Model · conserve B and L",
      "summary": "Impose zero total integer 3B and lepton number L. This removes the Weinberg and baryon-number-violating sectors from the three-generation inventory.",
      "expected": {
        "sectorCount": 36,
        "invariantCount": "2316",
        "byDimension": {
          "2": "1",
          "4": "55",
          "6": "2260"
        }
      },
      "guide": "/physics/standard-model-operator-sectors/",
      "route": "/tools/operator-enumeration/?example=sm-3-bl",
      "inventory": "/data/operator-inventories/sm-3-bl.json",
      "calculation": "/data/operator-enumerations/sm-3-bl.json"
    },
    {
      "id": "higgs",
      "title": "One Higgs doublet",
      "summary": "H and H† produce one invariant each at dimensions two, four, and six: the first three positive powers of H†H.",
      "expected": {
        "sectorCount": 3,
        "invariantCount": "3",
        "byDimension": {
          "2": "1",
          "4": "1",
          "6": "1"
        }
      },
      "guide": "/learn/from-fields-to-interactions/",
      "route": "/tools/operator-enumeration/?example=higgs",
      "inventory": "/data/operator-inventories/higgs.json",
      "calculation": "/data/operator-enumerations/higgs.json"
    },
    {
      "id": "sterile-3",
      "title": "Sterile Weyl fields · three flavors",
      "summary": "A gauge-singlet left Weyl field and its explicit right-handed conjugate. Count their mass and four-fermion polynomial sectors.",
      "expected": {
        "sectorCount": 5,
        "invariantCount": "60",
        "byDimension": {
          "3": "12",
          "6": "48"
        }
      },
      "guide": "/learn/from-fields-to-interactions/",
      "route": "/tools/operator-enumeration/?example=sterile-3",
      "inventory": "/data/operator-inventories/sterile-3.json",
      "calculation": "/data/operator-enumerations/sterile-3.json"
    },
    {
      "id": "scalar-z2",
      "title": "A scalar with Z₂ selection",
      "summary": "One neutral scalar generator odd under Z₂. The selected zero-charge sector keeps only even powers; it does not impose a reality condition on the scalar.",
      "expected": {
        "sectorCount": 3,
        "invariantCount": "3",
        "byDimension": {
          "2": "1",
          "4": "1",
          "6": "1"
        }
      },
      "guide": "/learn/from-fields-to-interactions/",
      "route": "/tools/operator-enumeration/?example=scalar-z2",
      "inventory": "/data/operator-inventories/scalar-z2.json",
      "calculation": "/data/operator-enumerations/scalar-z2.json"
    }
  ]
}