{
  "norm_model": {
    "algebra": "ell-infinity(N), N={1,2,...}",
    "trace": "sum a_n",
    "density": "h_n=exp(n)",
    "weight": "sum exp(n)*a_n",
    "cocycle": "u(t)_n=exp(i*n*t)"
  },
  "witness": {
    "t_k": "pi/k",
    "coordinate": "n=k",
    "phase_exact": "-1",
    "norm_distance_exact": 2
  },
  "seminorm": {
    "weights": "w_n=2^(-n)",
    "square_exact": "12*(1-cos(t))/(5-4*cos(t))",
    "all_positive_l1_functionals_required_for_continuity": true
  },
  "plot_samples": [
    {
      "k": 1,
      "time_exact": "pi/1",
      "norm_exact": 2,
      "seminorm_numeric": 1.632993161855452
    },
    {
      "k": 2,
      "time_exact": "pi/2",
      "norm_exact": 2,
      "seminorm_numeric": 1.5491933384829666
    },
    {
      "k": 4,
      "time_exact": "pi/4",
      "norm_exact": 2,
      "seminorm_numeric": 1.2722078683685727
    },
    {
      "k": 8,
      "time_exact": "pi/8",
      "norm_exact": 2,
      "seminorm_numeric": 0.8368012546193234
    },
    {
      "k": 16,
      "time_exact": "pi/16",
      "norm_exact": 2,
      "seminorm_numeric": 0.462730634176261
    },
    {
      "k": 32,
      "time_exact": "pi/32",
      "norm_exact": 2,
      "seminorm_numeric": 0.2380994386639882
    },
    {
      "k": 64,
      "time_exact": "pi/64",
      "norm_exact": 2,
      "seminorm_numeric": 0.11993838022842988
    }
  ],
  "matrix_model": {
    "D": [
      [
        4,
        0
      ],
      [
        0,
        1
      ]
    ],
    "s0": "pi/(2*log(4))",
    "sigma_s0_e21": [
      [
        "0",
        "0"
      ],
      [
        "-i",
        "0"
      ]
    ],
    "product_coefficient": [
      [
        "-i",
        "0"
      ],
      [
        "0",
        "0"
      ]
    ],
    "product_degree": "2*s0",
    "adjoint_coefficient": [
      [
        "0",
        "0"
      ],
      [
        "i",
        "0"
      ]
    ],
    "adjoint_degree": "-s0",
    "a_star_a": [
      [
        0,
        0
      ],
      [
        0,
        1
      ]
    ],
    "a_a_star": [
      [
        1,
        0
      ],
      [
        0,
        0
      ]
    ]
  },
  "scalar_direction": {
    "from_weight": 1,
    "to_weight": 4,
    "time": "pi/(2*log(4))",
    "coefficient_factor": "-i"
  },
  "proof_locators": [
    "GRD.7.c",
    "GRD.7.d",
    "GRD.7.e",
    "GRD.7.j",
    "GRD.7.k",
    "GRD.7.l",
    "GRD.7.m"
  ],
  "matrix_checks": "passed using exact integer and imaginary-unit entries",
  "plotted_lines_only_connect_finite_samples": true
}