{
  "noncommuting_example": {
    "h": [
      [
        1.0,
        0.0
      ],
      [
        0.0,
        3.0
      ]
    ],
    "k": [
      [
        3.0,
        1.0
      ],
      [
        1.0,
        3.0
      ]
    ],
    "commutator": [
      [
        0.0,
        -2.0
      ],
      [
        2.0,
        0.0
      ]
    ],
    "h_spectrum": [
      1.0,
      3.0
    ],
    "k_spectrum": [
      2.0,
      4.0
    ],
    "low_k_projection_between_2_and_4": [
      [
        0.4999999999999999,
        -0.4999999999999999
      ],
      [
        -0.4999999999999999,
        0.4999999999999999
      ]
    ],
    "squared_distance_e1_to_low_k_range": 0.5,
    "exact_distance": "log(4)",
    "distance_numerical": 1.3862943611198906,
    "upper_bound_scope": "all positive powers, proved by spectral bounds"
  },
  "cauchy_example": {
    "index_start": 1,
    "exact_sum_h": 1,
    "exact_sum_h_odd": "2/3",
    "exact_sum_h_even": "1/3",
    "exact_distance_to_h": "1/m",
    "exact_pair_distance": "abs(1/m-1/l)",
    "density_inverses": "unbounded",
    "identity_evaluation_ratio": "(2*exp(-1/m)+exp(1/m))/3",
    "m1_identity_evaluation_numerical": 1.1513469036006432
  },
  "scalar_entire_example": {
    "ratio": 2,
    "exact_distance": "log(2)",
    "exact_U": "exp(i*z*log(2))",
    "exact_modulus": "exp(-Im(z)*log(2))"
  },
  "font": "Matplotlib-installed DejaVu Sans; no font files copied",
  "outputs": [
    "metric-entire-growth",
    "metric-cauchy-evaluations",
    "metric-noncommuting-log4"
  ],
  "rendered_formats": [
    "png",
    "svg"
  ]
}