{
  "licence": "CC0-1.0; font components retain their terms",
  "coordinate": "r=t/(2*pi)",
  "plot_grid": {
    "r_min": -1,
    "r_max": 1,
    "points": 1201
  },
  "dispersion": "d_n(t)=1-|sum_j p_nj exp(i t log p_nj)|^2",
  "repeated_state": {
    "c": 1,
    "p": "1/(1+exp(-1))",
    "q": "exp(-1)/(1+exp(-1))",
    "partial_sum": "N*4*p*q*sin(t/2)^2",
    "N": [
      4,
      16,
      64
    ],
    "inner_times": "2*pi*Z"
  },
  "nearly_tracial": {
    "n_starts_at": 1,
    "epsilon": "1/(n+2)",
    "p": "(1+epsilon)/2",
    "q": "(1-epsilon)/2",
    "N": [
      4,
      16,
      64,
      256
    ],
    "tail_upper_bound": "(9/4)*t^2/(N+2)",
    "inner_times": "R",
    "exact_state_periods": "{0}"
  },
  "sample_r": [
    -1.0,
    -0.75,
    -0.5,
    -0.25,
    0.0,
    0.25,
    0.5,
    0.75,
    1.0
  ],
  "nearly_tracial_partial_sums": {
    "4": [
      3.15147561153783,
      2.8354455600333512,
      1.7693202734186146,
      0.5418358479492531,
      0.0,
      0.5418358479492531,
      1.7693202734186146,
      2.8354455600333512,
      3.15147561153783
    ],
    "16": [
      6.509876049693881,
      4.855093456440983,
      2.710874975837843,
      0.7840748603242544,
      0.0,
      0.7840748603242544,
      2.710874975837843,
      4.855093456440983,
      6.509876049693881
    ],
    "64": [
      8.02251140170847,
      5.712434730290231,
      3.093988503453762,
      0.8801656529415084,
      0.0,
      0.8801656529415084,
      3.093988503453762,
      5.712434730290231,
      8.02251140170847
    ],
    "256": [
      8.462846633585684,
      5.960265574587455,
      3.204180737054624,
      0.9077204925554802,
      0.0,
      0.9077204925554802,
      3.204180737054624,
      5.960265574587455,
      8.462846633585684
    ]
  },
  "proof_locators": [
    "MIV8.d",
    "MIV9.a",
    "MIV9.b",
    "MIV10.a",
    "MIV10.f",
    "MIV10.g"
  ],
  "limits": "Finite numerical samples illustrate the exact formulas; they do not prove convergence or classify the factor.",
  "programme_inputs": [
    "OA-APPROX/infinite-tensor-products.html#theorem-6-1",
    "OA-APPROX/infinite-tensor-products.html#theorem-7-2"
  ],
  "human_background": "H. Araki and E. J. Woods, A Classification of Factors, https://ems.press/journals/prims/articles/2441"
}