{
  "status": "passed",
  "scope": "Finite construction identities n=2..6 and volume inequalities at powers of two 64..4096; not an unrestricted or formal lower-bound proof",
  "row_parity": [
    {
      "n": 2,
      "all_queries_checked": 16,
      "maximum_probes": 2
    },
    {
      "n": 3,
      "all_queries_checked": 64,
      "maximum_probes": 6
    },
    {
      "n": 4,
      "all_queries_checked": 256,
      "maximum_probes": 8
    },
    {
      "n": 5,
      "all_queries_checked": 1024,
      "maximum_probes": 15
    },
    {
      "n": 6,
      "all_queries_checked": 4096,
      "maximum_probes": 18
    }
  ],
  "volume_checks": [
    {
      "n": 64,
      "k": 2048,
      "h": 22,
      "binomial_bit_length": 172,
      "required_bit_length_greater_than": 64
    },
    {
      "n": 128,
      "k": 8192,
      "h": 37,
      "binomial_bit_length": 338,
      "required_bit_length_greater_than": 128
    },
    {
      "n": 256,
      "k": 32768,
      "h": 64,
      "binomial_bit_length": 664,
      "required_bit_length_greater_than": 256
    },
    {
      "n": 512,
      "k": 131072,
      "h": 114,
      "binomial_bit_length": 1319,
      "required_bit_length_greater_than": 512
    },
    {
      "n": 1024,
      "k": 524288,
      "h": 205,
      "binomial_bit_length": 2612,
      "required_bit_length_greater_than": 1024
    },
    {
      "n": 2048,
      "k": 2097152,
      "h": 373,
      "binomial_bit_length": 5179,
      "required_bit_length_greater_than": 2048
    },
    {
      "n": 4096,
      "k": 8388608,
      "h": 683,
      "binomial_bit_length": 10258,
      "required_bit_length_greater_than": 4096
    }
  ]
}