{
  "group": "Z/3Z",
  "measure": "counting Haar",
  "inner_product": "linear in first variable",
  "vectors": {
    "u": [
      "1",
      "0",
      "0"
    ],
    "v": [
      "3/5",
      "4/5",
      "0"
    ],
    "w": [
      "4/5",
      "0",
      "3/5"
    ],
    "z": [
      "0",
      "1",
      "0"
    ]
  },
  "overlap": "12/25",
  "matrix_interpretation": "Images under Phi in B(L2G); regular operators have the additional identity factor.",
  "matrices": {
    "E_uv": [
      [
        "3/5",
        "4/5",
        "0"
      ],
      [
        "0",
        "0",
        "0"
      ],
      [
        "0",
        "0",
        "0"
      ]
    ],
    "E_wz": [
      [
        "0",
        "4/5",
        "0"
      ],
      [
        "0",
        "0",
        "0"
      ],
      [
        "0",
        "3/5",
        "0"
      ]
    ],
    "product": [
      [
        "0",
        "12/25",
        "0"
      ],
      [
        "0",
        "0",
        "0"
      ],
      [
        "0",
        "0",
        "0"
      ]
    ],
    "right_shift_R": [
      [
        "0",
        "1",
        "0"
      ],
      [
        "0",
        "0",
        "1"
      ],
      [
        "1",
        "0",
        "0"
      ]
    ],
    "conjugated_E": [
      [
        "0",
        "0",
        "0"
      ],
      [
        "0",
        "0",
        "0"
      ],
      [
        "4/5",
        "0",
        "3/5"
      ]
    ]
  },
  "identities_exact": true,
  "proof_locators": [
    "IS41",
    "IS43",
    "IS44",
    "IS45",
    "IS46",
    "IS47"
  ],
  "limits": "Finite example checks the algebraic identities. Full-support and arbitrary-coefficient statements are proved in the lesson, not inferred numerically.",
  "licence": "CC0-1.0 to the extent of rights held"
}