{
  "native_width": 3200,
  "native_height": 2300,
  "scalar_coordinates": "pairs [real,imaginary]",
  "space": "M2 Hilbert--Schmidt, linear-first inner product Tr(Y*X)",
  "corner_rank_in_coefficient_algebra": 1,
  "corner_rank_on_K": 2,
  "whole_complex_dimension": 4,
  "corner_complex_dimension": 2,
  "D": [
    [
      [
        1,
        0
      ],
      [
        0,
        0
      ]
    ],
    [
      [
        0,
        0
      ],
      [
        -1,
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  ],
  "X": [
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      [
        1,
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      ],
      [
        1,
        0
      ]
    ],
    [
      [
        1,
        0
      ],
      [
        -1,
        0
      ]
    ]
  ],
  "WT_X": [
    [
      [
        0,
        1
      ],
      [
        0,
        -1
      ]
    ],
    [
      [
        0,
        1
      ],
      [
        0,
        1
      ]
    ]
  ],
  "S_X": [
    [
      [
        1,
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      [
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        0
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    ],
    [
      [
        -1,
        0
      ],
      [
        -1,
        0
      ]
    ]
  ],
  "u_X": [
    [
      [
        0,
        1
      ],
      [
        0,
        1
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    ],
    [
      [
        0,
        -1
      ],
      [
        0,
        1
      ]
    ]
  ],
  "u": [
    [
      [
        0,
        1
      ],
      [
        0,
        0
      ]
    ],
    [
      [
        0,
        0
      ],
      [
        0,
        -1
      ]
    ]
  ],
  "prescribed_corner": [
    [
      [
        0,
        1
      ],
      [
        0,
        0
      ]
    ],
    [
      [
        0,
        0
      ],
      [
        0,
        0
      ]
    ]
  ],
  "gram_operators": [
    [
      [
        [
          [
            1,
            0
          ],
          [
            0,
            0
          ]
        ],
        [
          [
            0,
            0
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          [
            0,
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      ],
      [
        [
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    [
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          [
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        [
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      ],
      [
        [
          [
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            0,
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        ],
        [
          [
            0,
            0
          ],
          [
            0,
            0
          ]
        ]
      ]
    ]
  ],
  "mixed_basis_checks": [
    {
      "basis_pair": [
        0,
        0
      ],
      "inner_product": 1,
      "image_inner_product": 1
    },
    {
      "basis_pair": [
        0,
        1
      ],
      "inner_product": 0,
      "image_inner_product": 0
    },
    {
      "basis_pair": [
        0,
        2
      ],
      "inner_product": 0,
      "image_inner_product": 0
    },
    {
      "basis_pair": [
        0,
        3
      ],
      "inner_product": 0,
      "image_inner_product": 0
    },
    {
      "basis_pair": [
        1,
        0
      ],
      "inner_product": 0,
      "image_inner_product": 0
    },
    {
      "basis_pair": [
        1,
        1
      ],
      "inner_product": 1,
      "image_inner_product": 1
    },
    {
      "basis_pair": [
        1,
        2
      ],
      "inner_product": 0,
      "image_inner_product": 0
    },
    {
      "basis_pair": [
        1,
        3
      ],
      "inner_product": 0,
      "image_inner_product": 0
    },
    {
      "basis_pair": [
        2,
        0
      ],
      "inner_product": 0,
      "image_inner_product": 0
    },
    {
      "basis_pair": [
        2,
        1
      ],
      "inner_product": 0,
      "image_inner_product": 0
    },
    {
      "basis_pair": [
        2,
        2
      ],
      "inner_product": 1,
      "image_inner_product": 1
    },
    {
      "basis_pair": [
        2,
        3
      ],
      "inner_product": 0,
      "image_inner_product": 0
    },
    {
      "basis_pair": [
        3,
        0
      ],
      "inner_product": 0,
      "image_inner_product": 0
    },
    {
      "basis_pair": [
        3,
        1
      ],
      "inner_product": 0,
      "image_inner_product": 0
    },
    {
      "basis_pair": [
        3,
        2
      ],
      "inner_product": 0,
      "image_inner_product": 0
    },
    {
      "basis_pair": [
        3,
        3
      ],
      "inner_product": 1,
      "image_inner_product": 1
    }
  ],
  "norm_squared": 4,
  "continuous_family": "u_t=diag(exp(it/2),exp(3it/2)); real-line illustrative model, theorem arbitrary nonabelian LCH",
  "proof_links": [
    "L117_RESTORED_PROOF.md#l117-gram",
    "L117_RESTORED_PROOF.md#l117-inner",
    "L117_RESTORED_PROOF.md#l117-model"
  ]
}