{
  "status": "passed",
  "record_count": 147,
  "all_invertible_orbits_returned_to_start": true,
  "all_preperiods_zero": true,
  "density_monotonicity_violations": [],
  "independent_small_modulus_crosscheck": {
    "rows_checked": 78,
    "maximum_modulus": 400,
    "errors": []
  },
  "published_fibonacci_limit_comparison": [
    {
      "prime": 2,
      "max_k": 10,
      "observed_fraction": "21/32",
      "published_limit": "21/32",
      "observed_minus_limit": 0.0
    },
    {
      "prime": 3,
      "max_k": 8,
      "observed_fraction": "1",
      "published_limit": "1",
      "observed_minus_limit": 0.0
    },
    {
      "prime": 5,
      "max_k": 7,
      "observed_fraction": "1",
      "published_limit": "1",
      "observed_minus_limit": 0.0
    },
    {
      "prime": 7,
      "max_k": 6,
      "observed_fraction": "86137/117649",
      "published_limit": "41/56",
      "observed_minus_limit": 9.562342221353348e-06
    },
    {
      "prime": 11,
      "max_k": 5,
      "observed_fraction": "88457/161051",
      "published_limit": "145/264",
      "observed_minus_limit": 5.950496012650237e-06
    },
    {
      "prime": 13,
      "max_k": 5,
      "observed_fraction": "9/13",
      "published_limit": "9/13",
      "observed_minus_limit": 0.0
    },
    {
      "prime": 19,
      "max_k": 4,
      "observed_fraction": "75621/130321",
      "published_limit": "441/760",
      "observed_minus_limit": 4.028514207226771e-06
    },
    {
      "prime": 31,
      "max_k": 4,
      "observed_fraction": "19/31",
      "published_limit": "19/31",
      "observed_minus_limit": 0.0
    }
  ],
  "interpretation": "Finite densities must be at or above their limit. Exact agreement at the tested maximum is expected for p=2,3,5,13,31; other tested primes converge from above."
}