{
  "proof_locators": [
    "OA-FLOW.CR.5",
    "OA-FLOW.CR.7"
  ],
  "licence": "CC0-1.0 to the extent of rights held",
  "interpretation": "Finite scalar checks and plotted samples; not a proof of the operator limit.",
  "filters": "f_n(lambda)=sech(2*n*asinh(abs(lambda)/(8*n)))",
  "limit": "sech(lambda/4)",
  "checks": [
    {
      "n": 1,
      "epsilon": 0.25,
      "maximum_scalar_recurrence_residual": 5.551115123125783e-17,
      "maximum_surviving_paths_length_2n": 0,
      "path_bound": 3,
      "maximum_sampled_filter_error": 0.08249279160053476
    },
    {
      "n": 3,
      "epsilon": 0.08333333333333333,
      "maximum_scalar_recurrence_residual": 1.1102230246251565e-16,
      "maximum_surviving_paths_length_2n": 36,
      "path_bound": 63,
      "maximum_sampled_filter_error": 0.011783183691677857
    },
    {
      "n": 8,
      "epsilon": 0.03125,
      "maximum_scalar_recurrence_residual": 2.220446049250313e-16,
      "maximum_surviving_paths_length_2n": 59108,
      "path_bound": 65535,
      "maximum_sampled_filter_error": 0.0017251013282435224
    }
  ],
  "samples": [
    {
      "lambda": 0.0,
      "limit": 1.0,
      "f_n": {
        "1": 1.0,
        "3": 1.0,
        "8": 1.0
      }
    },
    {
      "lambda": 0.5,
      "limit": 0.9922380414751257,
      "f_n": {
        "1": 0.9922480620155039,
        "3": 0.9922391569205501,
        "8": 0.9922381983657136
      }
    },
    {
      "lambda": 2.0,
      "limit": 0.886818883970074,
      "f_n": {
        "1": 0.8888888888888888,
        "3": 0.8870552223056668,
        "8": 0.8868522184082106
      }
    },
    {
      "lambda": 7.0,
      "limit": 0.33736048304290506,
      "f_n": {
        "1": 0.3950617283950617,
        "3": 0.3450278089166594,
        "8": 0.3384642326371663
      }
    },
    {
      "lambda": 12.0,
      "limit": 0.0993279274194332,
      "f_n": {
        "1": 0.18181818181818177,
        "3": 0.11111111111111106,
        "8": 0.10105302874767673
      }
    }
  ]
}