{
  "source_sha256": "b0b2e13c3cd35512ee5955a2d9a56c22d7410e283d35dd9c90abbaa7b99279eb",
  "scope": {
    "LP2_pages": [
      0,
      55
    ],
    "runes": 12956,
    "one_rune_word_tokens": 83,
    "one_rune_word_types": 28,
    "model": "One ciphertext rune decodes to one plaintext rune through a fixed table. Many ciphertext types may decode to the same plaintext type. Encoder may choose homophones using state, but decoding table is fixed within each stated key group.",
    "assumptions": "Retained separators are plaintext word boundaries; every ordinary one-rune word is in the specified A/I or A/I/O set; no nulls, variable-length decoding, context-dependent decoding or state-selected table inside a key group",
    "limits": "Necessary mass constraints only; exception budgets are not English decipherments; reference shares are empirical, not universal English limits"
  },
  "benchmarks": {
    "AI": {
      "allowed_values": [
        24,
        10
      ],
      "groups": [
        {
          "group": "warning",
          "runes": 184,
          "allowed_positions": 20,
          "allowed_share": 0.10869565217391304,
          "plaintext_types": 24
        },
        {
          "group": "wisdom",
          "runes": 157,
          "allowed_positions": 20,
          "allowed_share": 0.12738853503184713,
          "plaintext_types": 25
        },
        {
          "group": "koan",
          "runes": 778,
          "allowed_positions": 108,
          "allowed_share": 0.13881748071979436,
          "plaintext_types": 24
        },
        {
          "group": "divinity",
          "runes": 755,
          "allowed_positions": 85,
          "allowed_share": 0.11258278145695365,
          "plaintext_types": 24
        },
        {
          "group": "instruction",
          "runes": 89,
          "allowed_positions": 8,
          "allowed_share": 0.0898876404494382,
          "plaintext_types": 20
        }
      ],
      "pooled_ratio": [
        241,
        1963
      ],
      "pooled_share": 0.12277126846663271,
      "largest_individual_ratio": [
        54,
        389
      ],
      "largest_individual_share": 0.13881748071979436
    },
    "AIO": {
      "allowed_values": [
        24,
        10,
        3
      ],
      "groups": [
        {
          "group": "warning",
          "runes": 184,
          "allowed_positions": 40,
          "allowed_share": 0.21739130434782608,
          "plaintext_types": 24
        },
        {
          "group": "wisdom",
          "runes": 157,
          "allowed_positions": 33,
          "allowed_share": 0.21019108280254778,
          "plaintext_types": 25
        },
        {
          "group": "koan",
          "runes": 778,
          "allowed_positions": 185,
          "allowed_share": 0.2377892030848329,
          "plaintext_types": 24
        },
        {
          "group": "divinity",
          "runes": 755,
          "allowed_positions": 155,
          "allowed_share": 0.2052980132450331,
          "plaintext_types": 24
        },
        {
          "group": "instruction",
          "runes": 89,
          "allowed_positions": 18,
          "allowed_share": 0.20224719101123595,
          "plaintext_types": 20
        }
      ],
      "pooled_ratio": [
        431,
        1963
      ],
      "pooled_share": 0.2195618950585838,
      "largest_individual_ratio": [
        185,
        778
      ],
      "largest_individual_share": 0.2377892030848329
    }
  },
  "results": [
    {
      "runes": 12956,
      "key_scope": "shared",
      "allowed_output_types": 2,
      "singleton_tokens": 83,
      "forced_positions": 12513,
      "minimum_allowed_letter_share": 0.9658073479468972,
      "groups": [
        {
          "group": "all",
          "sections": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8
          ],
          "runes": 12956,
          "singleton_tokens": 83,
          "singleton_cipher_types": 28,
          "active_cipher_types": 29,
          "forced_positions": 12513,
          "maximum_distinct_output_runes": 3,
          "cipher_histogram": [
            458,
            450,
            455,
            458,
            424,
            443,
            438,
            401,
            414,
            446,
            471,
            450,
            399,
            445,
            458,
            434,
            442,
            445,
            439,
            436,
            460,
            454,
            492,
            439,
            482,
            445,
            448,
            470,
            460
          ],
          "singleton_counts_by_cipher_type": [
            1,
            3,
            3,
            3,
            3,
            0,
            3,
            4,
            4,
            4,
            5,
            3,
            1,
            5,
            1,
            2,
            5,
            3,
            1,
            5,
            2,
            3,
            3,
            3,
            2,
            1,
            5,
            1,
            4
          ]
        }
      ],
      "constraint_units": [
        {
          "group": "all",
          "cipher": 0,
          "label": "F",
          "exception_token_cost": 1,
          "freed_corpus_positions": 458
        },
        {
          "group": "all",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 3,
          "freed_corpus_positions": 450
        },
        {
          "group": "all",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 3,
          "freed_corpus_positions": 455
        },
        {
          "group": "all",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 3,
          "freed_corpus_positions": 458
        },
        {
          "group": "all",
          "cipher": 4,
          "label": "R",
          "exception_token_cost": 3,
          "freed_corpus_positions": 424
        },
        {
          "group": "all",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 3,
          "freed_corpus_positions": 438
        },
        {
          "group": "all",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 4,
          "freed_corpus_positions": 401
        },
        {
          "group": "all",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 4,
          "freed_corpus_positions": 414
        },
        {
          "group": "all",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 4,
          "freed_corpus_positions": 446
        },
        {
          "group": "all",
          "cipher": 10,
          "label": "I",
          "exception_token_cost": 5,
          "freed_corpus_positions": 471
        },
        {
          "group": "all",
          "cipher": 11,
          "label": "J",
          "exception_token_cost": 3,
          "freed_corpus_positions": 450
        },
        {
          "group": "all",
          "cipher": 12,
          "label": "EO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 399
        },
        {
          "group": "all",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 5,
          "freed_corpus_positions": 445
        },
        {
          "group": "all",
          "cipher": 14,
          "label": "X",
          "exception_token_cost": 1,
          "freed_corpus_positions": 458
        },
        {
          "group": "all",
          "cipher": 15,
          "label": "S",
          "exception_token_cost": 2,
          "freed_corpus_positions": 434
        },
        {
          "group": "all",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 5,
          "freed_corpus_positions": 442
        },
        {
          "group": "all",
          "cipher": 17,
          "label": "B",
          "exception_token_cost": 3,
          "freed_corpus_positions": 445
        },
        {
          "group": "all",
          "cipher": 18,
          "label": "E",
          "exception_token_cost": 1,
          "freed_corpus_positions": 439
        },
        {
          "group": "all",
          "cipher": 19,
          "label": "M",
          "exception_token_cost": 5,
          "freed_corpus_positions": 436
        },
        {
          "group": "all",
          "cipher": 20,
          "label": "L",
          "exception_token_cost": 2,
          "freed_corpus_positions": 460
        },
        {
          "group": "all",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 3,
          "freed_corpus_positions": 454
        },
        {
          "group": "all",
          "cipher": 22,
          "label": "OE",
          "exception_token_cost": 3,
          "freed_corpus_positions": 492
        },
        {
          "group": "all",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 3,
          "freed_corpus_positions": 439
        },
        {
          "group": "all",
          "cipher": 24,
          "label": "A",
          "exception_token_cost": 2,
          "freed_corpus_positions": 482
        },
        {
          "group": "all",
          "cipher": 25,
          "label": "AE",
          "exception_token_cost": 1,
          "freed_corpus_positions": 445
        },
        {
          "group": "all",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 5,
          "freed_corpus_positions": 448
        },
        {
          "group": "all",
          "cipher": 27,
          "label": "IO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 470
        },
        {
          "group": "all",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 4,
          "freed_corpus_positions": 460
        }
      ],
      "maximum_position_release_by_exact_exception_cost": [
        0,
        470,
        928,
        1386,
        1831,
        2270,
        2669,
        2752,
        3151,
        3212,
        3611,
        3646,
        4045,
        4103,
        4138,
        4537,
        4561,
        4596,
        4995,
        5016,
        5051,
        5450,
        5470,
        5505,
        5904,
        5920,
        5955,
        6354,
        6370,
        6405,
        6804,
        6815,
        6850,
        7249,
        7264,
        7289,
        7688,
        7709,
        7727,
        8126,
        8148,
        8159,
        8550,
        8586,
        8597,
        8619,
        9010,
        9032,
        9057,
        9065,
        9456,
        9481,
        9503,
        9505,
        9870,
        9927,
        9929,
        9951,
        10271,
        10341,
        10375,
        10374,
        10396,
        10742,
        10789,
        10820,
        10816,
        10838,
        11190,
        11234,
        11262,
        11252,
        11274,
        11635,
        11676,
        11698,
        11688,
        11678,
        12077,
        12112,
        12089,
        12079,
        12114,
        12513
      ],
      "singleton_sensitivity": "all_audited",
      "allowed_letters": "AI",
      "requirements": {
        "pooled": {
          "reference_ratio": [
            241,
            1963
          ],
          "maximum_allowed_positions": 1590,
          "required_position_release": 10923,
          "minimum_exception_tokens": 68,
          "freed_constraint_types": 25,
          "witness_units": [
            {
              "group": "all",
              "cipher": 0,
              "label": "F",
              "exception_token_cost": 1,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 3,
              "freed_corpus_positions": 450
            },
            {
              "group": "all",
              "cipher": 2,
              "label": "TH",
              "exception_token_cost": 3,
              "freed_corpus_positions": 455
            },
            {
              "group": "all",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 3,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 4,
              "label": "R",
              "exception_token_cost": 3,
              "freed_corpus_positions": 424
            },
            {
              "group": "all",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 3,
              "freed_corpus_positions": 438
            },
            {
              "group": "all",
              "cipher": 7,
              "label": "W",
              "exception_token_cost": 4,
              "freed_corpus_positions": 401
            },
            {
              "group": "all",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 4,
              "freed_corpus_positions": 414
            },
            {
              "group": "all",
              "cipher": 9,
              "label": "N",
              "exception_token_cost": 4,
              "freed_corpus_positions": 446
            },
            {
              "group": "all",
              "cipher": 10,
              "label": "I",
              "exception_token_cost": 5,
              "freed_corpus_positions": 471
            },
            {
              "group": "all",
              "cipher": 11,
              "label": "J",
              "exception_token_cost": 3,
              "freed_corpus_positions": 450
            },
            {
              "group": "all",
              "cipher": 12,
              "label": "EO",
              "exception_token_cost": 1,
              "freed_corpus_positions": 399
            },
            {
              "group": "all",
              "cipher": 14,
              "label": "X",
              "exception_token_cost": 1,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 15,
              "label": "S",
              "exception_token_cost": 2,
              "freed_corpus_positions": 434
            },
            {
              "group": "all",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 3,
              "freed_corpus_positions": 445
            },
            {
              "group": "all",
              "cipher": 18,
              "label": "E",
              "exception_token_cost": 1,
              "freed_corpus_positions": 439
            },
            {
              "group": "all",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 2,
              "freed_corpus_positions": 460
            },
            {
              "group": "all",
              "cipher": 21,
              "label": "ING",
              "exception_token_cost": 3,
              "freed_corpus_positions": 454
            },
            {
              "group": "all",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 3,
              "freed_corpus_positions": 492
            },
            {
              "group": "all",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 3,
              "freed_corpus_positions": 439
            },
            {
              "group": "all",
              "cipher": 24,
              "label": "A",
              "exception_token_cost": 2,
              "freed_corpus_positions": 482
            },
            {
              "group": "all",
              "cipher": 25,
              "label": "AE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 445
            },
            {
              "group": "all",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 5,
              "freed_corpus_positions": 448
            },
            {
              "group": "all",
              "cipher": 27,
              "label": "IO",
              "exception_token_cost": 1,
              "freed_corpus_positions": 470
            },
            {
              "group": "all",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 4,
              "freed_corpus_positions": 460
            }
          ],
          "remaining_forced_positions": 1323,
          "remaining_forced_share": 0.10211485026242667,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        },
        "largest_individual": {
          "reference_ratio": [
            54,
            389
          ],
          "maximum_allowed_positions": 1798,
          "required_position_release": 10715,
          "minimum_exception_tokens": 63,
          "freed_constraint_types": 24,
          "witness_units": [
            {
              "group": "all",
              "cipher": 0,
              "label": "F",
              "exception_token_cost": 1,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 3,
              "freed_corpus_positions": 450
            },
            {
              "group": "all",
              "cipher": 2,
              "label": "TH",
              "exception_token_cost": 3,
              "freed_corpus_positions": 455
            },
            {
              "group": "all",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 3,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 4,
              "label": "R",
              "exception_token_cost": 3,
              "freed_corpus_positions": 424
            },
            {
              "group": "all",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 3,
              "freed_corpus_positions": 438
            },
            {
              "group": "all",
              "cipher": 7,
              "label": "W",
              "exception_token_cost": 4,
              "freed_corpus_positions": 401
            },
            {
              "group": "all",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 4,
              "freed_corpus_positions": 414
            },
            {
              "group": "all",
              "cipher": 9,
              "label": "N",
              "exception_token_cost": 4,
              "freed_corpus_positions": 446
            },
            {
              "group": "all",
              "cipher": 10,
              "label": "I",
              "exception_token_cost": 5,
              "freed_corpus_positions": 471
            },
            {
              "group": "all",
              "cipher": 11,
              "label": "J",
              "exception_token_cost": 3,
              "freed_corpus_positions": 450
            },
            {
              "group": "all",
              "cipher": 12,
              "label": "EO",
              "exception_token_cost": 1,
              "freed_corpus_positions": 399
            },
            {
              "group": "all",
              "cipher": 14,
              "label": "X",
              "exception_token_cost": 1,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 15,
              "label": "S",
              "exception_token_cost": 2,
              "freed_corpus_positions": 434
            },
            {
              "group": "all",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 3,
              "freed_corpus_positions": 445
            },
            {
              "group": "all",
              "cipher": 18,
              "label": "E",
              "exception_token_cost": 1,
              "freed_corpus_positions": 439
            },
            {
              "group": "all",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 2,
              "freed_corpus_positions": 460
            },
            {
              "group": "all",
              "cipher": 21,
              "label": "ING",
              "exception_token_cost": 3,
              "freed_corpus_positions": 454
            },
            {
              "group": "all",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 3,
              "freed_corpus_positions": 492
            },
            {
              "group": "all",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 3,
              "freed_corpus_positions": 439
            },
            {
              "group": "all",
              "cipher": 24,
              "label": "A",
              "exception_token_cost": 2,
              "freed_corpus_positions": 482
            },
            {
              "group": "all",
              "cipher": 25,
              "label": "AE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 445
            },
            {
              "group": "all",
              "cipher": 27,
              "label": "IO",
              "exception_token_cost": 1,
              "freed_corpus_positions": 470
            },
            {
              "group": "all",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 4,
              "freed_corpus_positions": 460
            }
          ],
          "remaining_forced_positions": 1771,
          "remaining_forced_share": 0.13669342389626427,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        }
      }
    },
    {
      "runes": 12956,
      "key_scope": "shared",
      "allowed_output_types": 3,
      "singleton_tokens": 83,
      "forced_positions": 12513,
      "minimum_allowed_letter_share": 0.9658073479468972,
      "groups": [
        {
          "group": "all",
          "sections": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8
          ],
          "runes": 12956,
          "singleton_tokens": 83,
          "singleton_cipher_types": 28,
          "active_cipher_types": 29,
          "forced_positions": 12513,
          "maximum_distinct_output_runes": 4,
          "cipher_histogram": [
            458,
            450,
            455,
            458,
            424,
            443,
            438,
            401,
            414,
            446,
            471,
            450,
            399,
            445,
            458,
            434,
            442,
            445,
            439,
            436,
            460,
            454,
            492,
            439,
            482,
            445,
            448,
            470,
            460
          ],
          "singleton_counts_by_cipher_type": [
            1,
            3,
            3,
            3,
            3,
            0,
            3,
            4,
            4,
            4,
            5,
            3,
            1,
            5,
            1,
            2,
            5,
            3,
            1,
            5,
            2,
            3,
            3,
            3,
            2,
            1,
            5,
            1,
            4
          ]
        }
      ],
      "constraint_units": [
        {
          "group": "all",
          "cipher": 0,
          "label": "F",
          "exception_token_cost": 1,
          "freed_corpus_positions": 458
        },
        {
          "group": "all",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 3,
          "freed_corpus_positions": 450
        },
        {
          "group": "all",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 3,
          "freed_corpus_positions": 455
        },
        {
          "group": "all",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 3,
          "freed_corpus_positions": 458
        },
        {
          "group": "all",
          "cipher": 4,
          "label": "R",
          "exception_token_cost": 3,
          "freed_corpus_positions": 424
        },
        {
          "group": "all",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 3,
          "freed_corpus_positions": 438
        },
        {
          "group": "all",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 4,
          "freed_corpus_positions": 401
        },
        {
          "group": "all",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 4,
          "freed_corpus_positions": 414
        },
        {
          "group": "all",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 4,
          "freed_corpus_positions": 446
        },
        {
          "group": "all",
          "cipher": 10,
          "label": "I",
          "exception_token_cost": 5,
          "freed_corpus_positions": 471
        },
        {
          "group": "all",
          "cipher": 11,
          "label": "J",
          "exception_token_cost": 3,
          "freed_corpus_positions": 450
        },
        {
          "group": "all",
          "cipher": 12,
          "label": "EO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 399
        },
        {
          "group": "all",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 5,
          "freed_corpus_positions": 445
        },
        {
          "group": "all",
          "cipher": 14,
          "label": "X",
          "exception_token_cost": 1,
          "freed_corpus_positions": 458
        },
        {
          "group": "all",
          "cipher": 15,
          "label": "S",
          "exception_token_cost": 2,
          "freed_corpus_positions": 434
        },
        {
          "group": "all",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 5,
          "freed_corpus_positions": 442
        },
        {
          "group": "all",
          "cipher": 17,
          "label": "B",
          "exception_token_cost": 3,
          "freed_corpus_positions": 445
        },
        {
          "group": "all",
          "cipher": 18,
          "label": "E",
          "exception_token_cost": 1,
          "freed_corpus_positions": 439
        },
        {
          "group": "all",
          "cipher": 19,
          "label": "M",
          "exception_token_cost": 5,
          "freed_corpus_positions": 436
        },
        {
          "group": "all",
          "cipher": 20,
          "label": "L",
          "exception_token_cost": 2,
          "freed_corpus_positions": 460
        },
        {
          "group": "all",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 3,
          "freed_corpus_positions": 454
        },
        {
          "group": "all",
          "cipher": 22,
          "label": "OE",
          "exception_token_cost": 3,
          "freed_corpus_positions": 492
        },
        {
          "group": "all",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 3,
          "freed_corpus_positions": 439
        },
        {
          "group": "all",
          "cipher": 24,
          "label": "A",
          "exception_token_cost": 2,
          "freed_corpus_positions": 482
        },
        {
          "group": "all",
          "cipher": 25,
          "label": "AE",
          "exception_token_cost": 1,
          "freed_corpus_positions": 445
        },
        {
          "group": "all",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 5,
          "freed_corpus_positions": 448
        },
        {
          "group": "all",
          "cipher": 27,
          "label": "IO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 470
        },
        {
          "group": "all",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 4,
          "freed_corpus_positions": 460
        }
      ],
      "maximum_position_release_by_exact_exception_cost": [
        0,
        470,
        928,
        1386,
        1831,
        2270,
        2669,
        2752,
        3151,
        3212,
        3611,
        3646,
        4045,
        4103,
        4138,
        4537,
        4561,
        4596,
        4995,
        5016,
        5051,
        5450,
        5470,
        5505,
        5904,
        5920,
        5955,
        6354,
        6370,
        6405,
        6804,
        6815,
        6850,
        7249,
        7264,
        7289,
        7688,
        7709,
        7727,
        8126,
        8148,
        8159,
        8550,
        8586,
        8597,
        8619,
        9010,
        9032,
        9057,
        9065,
        9456,
        9481,
        9503,
        9505,
        9870,
        9927,
        9929,
        9951,
        10271,
        10341,
        10375,
        10374,
        10396,
        10742,
        10789,
        10820,
        10816,
        10838,
        11190,
        11234,
        11262,
        11252,
        11274,
        11635,
        11676,
        11698,
        11688,
        11678,
        12077,
        12112,
        12089,
        12079,
        12114,
        12513
      ],
      "singleton_sensitivity": "all_audited",
      "allowed_letters": "AIO",
      "requirements": {
        "pooled": {
          "reference_ratio": [
            431,
            1963
          ],
          "maximum_allowed_positions": 2844,
          "required_position_release": 9669,
          "minimum_exception_tokens": 54,
          "freed_constraint_types": 22,
          "witness_units": [
            {
              "group": "all",
              "cipher": 0,
              "label": "F",
              "exception_token_cost": 1,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 3,
              "freed_corpus_positions": 450
            },
            {
              "group": "all",
              "cipher": 2,
              "label": "TH",
              "exception_token_cost": 3,
              "freed_corpus_positions": 455
            },
            {
              "group": "all",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 3,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 4,
              "label": "R",
              "exception_token_cost": 3,
              "freed_corpus_positions": 424
            },
            {
              "group": "all",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 3,
              "freed_corpus_positions": 438
            },
            {
              "group": "all",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 4,
              "freed_corpus_positions": 414
            },
            {
              "group": "all",
              "cipher": 9,
              "label": "N",
              "exception_token_cost": 4,
              "freed_corpus_positions": 446
            },
            {
              "group": "all",
              "cipher": 11,
              "label": "J",
              "exception_token_cost": 3,
              "freed_corpus_positions": 450
            },
            {
              "group": "all",
              "cipher": 12,
              "label": "EO",
              "exception_token_cost": 1,
              "freed_corpus_positions": 399
            },
            {
              "group": "all",
              "cipher": 14,
              "label": "X",
              "exception_token_cost": 1,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 15,
              "label": "S",
              "exception_token_cost": 2,
              "freed_corpus_positions": 434
            },
            {
              "group": "all",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 3,
              "freed_corpus_positions": 445
            },
            {
              "group": "all",
              "cipher": 18,
              "label": "E",
              "exception_token_cost": 1,
              "freed_corpus_positions": 439
            },
            {
              "group": "all",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 2,
              "freed_corpus_positions": 460
            },
            {
              "group": "all",
              "cipher": 21,
              "label": "ING",
              "exception_token_cost": 3,
              "freed_corpus_positions": 454
            },
            {
              "group": "all",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 3,
              "freed_corpus_positions": 492
            },
            {
              "group": "all",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 3,
              "freed_corpus_positions": 439
            },
            {
              "group": "all",
              "cipher": 24,
              "label": "A",
              "exception_token_cost": 2,
              "freed_corpus_positions": 482
            },
            {
              "group": "all",
              "cipher": 25,
              "label": "AE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 445
            },
            {
              "group": "all",
              "cipher": 27,
              "label": "IO",
              "exception_token_cost": 1,
              "freed_corpus_positions": 470
            },
            {
              "group": "all",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 4,
              "freed_corpus_positions": 460
            }
          ],
          "remaining_forced_positions": 2643,
          "remaining_forced_share": 0.20399814757641246,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        },
        "largest_individual": {
          "reference_ratio": [
            185,
            778
          ],
          "maximum_allowed_positions": 3080,
          "required_position_release": 9433,
          "minimum_exception_tokens": 50,
          "freed_constraint_types": 21,
          "witness_units": [
            {
              "group": "all",
              "cipher": 0,
              "label": "F",
              "exception_token_cost": 1,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 3,
              "freed_corpus_positions": 450
            },
            {
              "group": "all",
              "cipher": 2,
              "label": "TH",
              "exception_token_cost": 3,
              "freed_corpus_positions": 455
            },
            {
              "group": "all",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 3,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 4,
              "label": "R",
              "exception_token_cost": 3,
              "freed_corpus_positions": 424
            },
            {
              "group": "all",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 3,
              "freed_corpus_positions": 438
            },
            {
              "group": "all",
              "cipher": 9,
              "label": "N",
              "exception_token_cost": 4,
              "freed_corpus_positions": 446
            },
            {
              "group": "all",
              "cipher": 11,
              "label": "J",
              "exception_token_cost": 3,
              "freed_corpus_positions": 450
            },
            {
              "group": "all",
              "cipher": 12,
              "label": "EO",
              "exception_token_cost": 1,
              "freed_corpus_positions": 399
            },
            {
              "group": "all",
              "cipher": 14,
              "label": "X",
              "exception_token_cost": 1,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 15,
              "label": "S",
              "exception_token_cost": 2,
              "freed_corpus_positions": 434
            },
            {
              "group": "all",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 3,
              "freed_corpus_positions": 445
            },
            {
              "group": "all",
              "cipher": 18,
              "label": "E",
              "exception_token_cost": 1,
              "freed_corpus_positions": 439
            },
            {
              "group": "all",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 2,
              "freed_corpus_positions": 460
            },
            {
              "group": "all",
              "cipher": 21,
              "label": "ING",
              "exception_token_cost": 3,
              "freed_corpus_positions": 454
            },
            {
              "group": "all",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 3,
              "freed_corpus_positions": 492
            },
            {
              "group": "all",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 3,
              "freed_corpus_positions": 439
            },
            {
              "group": "all",
              "cipher": 24,
              "label": "A",
              "exception_token_cost": 2,
              "freed_corpus_positions": 482
            },
            {
              "group": "all",
              "cipher": 25,
              "label": "AE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 445
            },
            {
              "group": "all",
              "cipher": 27,
              "label": "IO",
              "exception_token_cost": 1,
              "freed_corpus_positions": 470
            },
            {
              "group": "all",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 4,
              "freed_corpus_positions": 460
            }
          ],
          "remaining_forced_positions": 3057,
          "remaining_forced_share": 0.23595245446125349,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        }
      }
    },
    {
      "runes": 12956,
      "key_scope": "per_section",
      "allowed_output_types": 2,
      "singleton_tokens": 83,
      "forced_positions": 4310,
      "minimum_allowed_letter_share": 0.332664402593393,
      "groups": [
        {
          "group": "0",
          "sections": [
            0
          ],
          "runes": 729,
          "singleton_tokens": 5,
          "singleton_cipher_types": 5,
          "active_cipher_types": 29,
          "forced_positions": 134,
          "maximum_distinct_output_runes": 26,
          "cipher_histogram": [
            34,
            21,
            30,
            20,
            22,
            28,
            29,
            22,
            30,
            28,
            24,
            24,
            17,
            27,
            28,
            23,
            23,
            23,
            24,
            18,
            30,
            29,
            25,
            31,
            19,
            24,
            25,
            23,
            28
          ],
          "singleton_counts_by_cipher_type": [
            1,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1
          ]
        },
        {
          "group": "1",
          "sections": [
            1
          ],
          "runes": 1145,
          "singleton_tokens": 8,
          "singleton_cipher_types": 7,
          "active_cipher_types": 29,
          "forced_positions": 271,
          "maximum_distinct_output_runes": 24,
          "cipher_histogram": [
            26,
            34,
            34,
            30,
            36,
            52,
            43,
            30,
            38,
            37,
            43,
            43,
            49,
            44,
            49,
            34,
            37,
            31,
            32,
            39,
            50,
            42,
            40,
            38,
            35,
            41,
            42,
            46,
            50
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            1,
            2,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            1,
            0,
            0,
            0,
            0,
            1,
            1,
            0
          ]
        },
        {
          "group": "2",
          "sections": [
            2
          ],
          "runes": 1729,
          "singleton_tokens": 11,
          "singleton_cipher_types": 9,
          "active_cipher_types": 29,
          "forced_positions": 545,
          "maximum_distinct_output_runes": 22,
          "cipher_histogram": [
            66,
            69,
            69,
            61,
            50,
            63,
            58,
            55,
            52,
            69,
            50,
            44,
            52,
            55,
            78,
            61,
            61,
            55,
            56,
            57,
            63,
            58,
            67,
            51,
            64,
            52,
            61,
            68,
            64
          ],
          "singleton_counts_by_cipher_type": [
            0,
            1,
            0,
            1,
            0,
            0,
            1,
            1,
            0,
            1,
            3,
            1,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0
          ]
        },
        {
          "group": "3",
          "sections": [
            3
          ],
          "runes": 9,
          "singleton_tokens": 0,
          "singleton_cipher_types": 0,
          "active_cipher_types": 8,
          "forced_positions": 0,
          "maximum_distinct_output_runes": 8,
          "cipher_histogram": [
            1,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            0,
            1,
            0,
            2,
            0,
            1,
            0,
            1
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0
          ]
        },
        {
          "group": "4",
          "sections": [
            4
          ],
          "runes": 1894,
          "singleton_tokens": 18,
          "singleton_cipher_types": 12,
          "active_cipher_types": 29,
          "forced_positions": 773,
          "maximum_distinct_output_runes": 19,
          "cipher_histogram": [
            71,
            63,
            75,
            75,
            64,
            70,
            71,
            50,
            52,
            57,
            73,
            76,
            52,
            72,
            63,
            56,
            60,
            63,
            54,
            62,
            63,
            69,
            74,
            70,
            73,
            67,
            54,
            77,
            68
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            2,
            0,
            0,
            1,
            0,
            2,
            2,
            0,
            0,
            1,
            0,
            0,
            2,
            2,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            1,
            1,
            0,
            2
          ]
        },
        {
          "group": "5",
          "sections": [
            5
          ],
          "runes": 1021,
          "singleton_tokens": 5,
          "singleton_cipher_types": 5,
          "active_cipher_types": 29,
          "forced_positions": 178,
          "maximum_distinct_output_runes": 26,
          "cipher_histogram": [
            37,
            44,
            37,
            40,
            34,
            30,
            37,
            33,
            33,
            39,
            35,
            27,
            21,
            34,
            32,
            43,
            38,
            37,
            42,
            32,
            34,
            37,
            35,
            25,
            41,
            31,
            37,
            35,
            41
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            0,
            1,
            0,
            0
          ]
        },
        {
          "group": "6",
          "sections": [
            6
          ],
          "runes": 1524,
          "singleton_tokens": 12,
          "singleton_cipher_types": 8,
          "active_cipher_types": 29,
          "forced_positions": 421,
          "maximum_distinct_output_runes": 23,
          "cipher_histogram": [
            55,
            45,
            50,
            53,
            57,
            40,
            47,
            61,
            52,
            43,
            58,
            56,
            48,
            51,
            47,
            49,
            50,
            64,
            58,
            54,
            55,
            51,
            56,
            60,
            57,
            50,
            48,
            56,
            53
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            2,
            0,
            2,
            0,
            1,
            0,
            0,
            0,
            3,
            1,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0
          ]
        },
        {
          "group": "7",
          "sections": [
            7
          ],
          "runes": 1589,
          "singleton_tokens": 9,
          "singleton_cipher_types": 9,
          "active_cipher_types": 29,
          "forced_positions": 480,
          "maximum_distinct_output_runes": 22,
          "cipher_histogram": [
            37,
            64,
            50,
            47,
            54,
            61,
            56,
            55,
            57,
            59,
            66,
            50,
            47,
            51,
            55,
            57,
            57,
            52,
            47,
            54,
            55,
            55,
            63,
            56,
            68,
            60,
            58,
            49,
            49
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            1,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            0,
            0
          ]
        },
        {
          "group": "8",
          "sections": [
            8
          ],
          "runes": 3316,
          "singleton_tokens": 15,
          "singleton_cipher_types": 13,
          "active_cipher_types": 29,
          "forced_positions": 1508,
          "maximum_distinct_output_runes": 18,
          "cipher_histogram": [
            131,
            109,
            110,
            132,
            107,
            99,
            97,
            95,
            100,
            114,
            122,
            130,
            113,
            111,
            106,
            111,
            116,
            120,
            126,
            119,
            109,
            113,
            131,
            108,
            123,
            120,
            122,
            116,
            106
          ],
          "singleton_counts_by_cipher_type": [
            0,
            1,
            0,
            1,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            2,
            1,
            0,
            1,
            1,
            1,
            2,
            0,
            1,
            0,
            1,
            0,
            1
          ]
        }
      ],
      "constraint_units": [
        {
          "group": "0",
          "cipher": 0,
          "label": "F",
          "exception_token_cost": 1,
          "freed_corpus_positions": 34
        },
        {
          "group": "0",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 21
        },
        {
          "group": "0",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 1,
          "freed_corpus_positions": 28
        },
        {
          "group": "0",
          "cipher": 15,
          "label": "S",
          "exception_token_cost": 1,
          "freed_corpus_positions": 23
        },
        {
          "group": "0",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 1,
          "freed_corpus_positions": 28
        },
        {
          "group": "1",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 34
        },
        {
          "group": "1",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 30
        },
        {
          "group": "1",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 2,
          "freed_corpus_positions": 38
        },
        {
          "group": "1",
          "cipher": 19,
          "label": "M",
          "exception_token_cost": 1,
          "freed_corpus_positions": 39
        },
        {
          "group": "1",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 1,
          "freed_corpus_positions": 42
        },
        {
          "group": "1",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 42
        },
        {
          "group": "1",
          "cipher": 27,
          "label": "IO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 46
        },
        {
          "group": "2",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 69
        },
        {
          "group": "2",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 1,
          "freed_corpus_positions": 61
        },
        {
          "group": "2",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 58
        },
        {
          "group": "2",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 55
        },
        {
          "group": "2",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 1,
          "freed_corpus_positions": 69
        },
        {
          "group": "2",
          "cipher": 10,
          "label": "I",
          "exception_token_cost": 3,
          "freed_corpus_positions": 50
        },
        {
          "group": "2",
          "cipher": 11,
          "label": "J",
          "exception_token_cost": 1,
          "freed_corpus_positions": 44
        },
        {
          "group": "2",
          "cipher": 14,
          "label": "X",
          "exception_token_cost": 1,
          "freed_corpus_positions": 78
        },
        {
          "group": "2",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 61
        },
        {
          "group": "4",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 75
        },
        {
          "group": "4",
          "cipher": 4,
          "label": "R",
          "exception_token_cost": 2,
          "freed_corpus_positions": 64
        },
        {
          "group": "4",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 50
        },
        {
          "group": "4",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 2,
          "freed_corpus_positions": 57
        },
        {
          "group": "4",
          "cipher": 10,
          "label": "I",
          "exception_token_cost": 2,
          "freed_corpus_positions": 73
        },
        {
          "group": "4",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 1,
          "freed_corpus_positions": 72
        },
        {
          "group": "4",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 2,
          "freed_corpus_positions": 60
        },
        {
          "group": "4",
          "cipher": 17,
          "label": "B",
          "exception_token_cost": 2,
          "freed_corpus_positions": 63
        },
        {
          "group": "4",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 70
        },
        {
          "group": "4",
          "cipher": 25,
          "label": "AE",
          "exception_token_cost": 1,
          "freed_corpus_positions": 67
        },
        {
          "group": "4",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 54
        },
        {
          "group": "4",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 2,
          "freed_corpus_positions": 68
        },
        {
          "group": "5",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 37
        },
        {
          "group": "5",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 1,
          "freed_corpus_positions": 38
        },
        {
          "group": "5",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 25
        },
        {
          "group": "5",
          "cipher": 24,
          "label": "A",
          "exception_token_cost": 1,
          "freed_corpus_positions": 41
        },
        {
          "group": "5",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 37
        },
        {
          "group": "6",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 1,
          "freed_corpus_positions": 53
        },
        {
          "group": "6",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 1,
          "freed_corpus_positions": 52
        },
        {
          "group": "6",
          "cipher": 11,
          "label": "J",
          "exception_token_cost": 2,
          "freed_corpus_positions": 56
        },
        {
          "group": "6",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 2,
          "freed_corpus_positions": 51
        },
        {
          "group": "6",
          "cipher": 15,
          "label": "S",
          "exception_token_cost": 1,
          "freed_corpus_positions": 49
        },
        {
          "group": "6",
          "cipher": 19,
          "label": "M",
          "exception_token_cost": 3,
          "freed_corpus_positions": 54
        },
        {
          "group": "6",
          "cipher": 20,
          "label": "L",
          "exception_token_cost": 1,
          "freed_corpus_positions": 55
        },
        {
          "group": "6",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 1,
          "freed_corpus_positions": 51
        },
        {
          "group": "7",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 50
        },
        {
          "group": "7",
          "cipher": 4,
          "label": "R",
          "exception_token_cost": 1,
          "freed_corpus_positions": 54
        },
        {
          "group": "7",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 55
        },
        {
          "group": "7",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 1,
          "freed_corpus_positions": 57
        },
        {
          "group": "7",
          "cipher": 12,
          "label": "EO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 47
        },
        {
          "group": "7",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 1,
          "freed_corpus_positions": 51
        },
        {
          "group": "7",
          "cipher": 18,
          "label": "E",
          "exception_token_cost": 1,
          "freed_corpus_positions": 47
        },
        {
          "group": "7",
          "cipher": 22,
          "label": "OE",
          "exception_token_cost": 1,
          "freed_corpus_positions": 63
        },
        {
          "group": "7",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 56
        },
        {
          "group": "8",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 109
        },
        {
          "group": "8",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 1,
          "freed_corpus_positions": 132
        },
        {
          "group": "8",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 97
        },
        {
          "group": "8",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 1,
          "freed_corpus_positions": 111
        },
        {
          "group": "8",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 2,
          "freed_corpus_positions": 116
        },
        {
          "group": "8",
          "cipher": 17,
          "label": "B",
          "exception_token_cost": 1,
          "freed_corpus_positions": 120
        },
        {
          "group": "8",
          "cipher": 19,
          "label": "M",
          "exception_token_cost": 1,
          "freed_corpus_positions": 119
        },
        {
          "group": "8",
          "cipher": 20,
          "label": "L",
          "exception_token_cost": 1,
          "freed_corpus_positions": 109
        },
        {
          "group": "8",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 1,
          "freed_corpus_positions": 113
        },
        {
          "group": "8",
          "cipher": 22,
          "label": "OE",
          "exception_token_cost": 2,
          "freed_corpus_positions": 131
        },
        {
          "group": "8",
          "cipher": 24,
          "label": "A",
          "exception_token_cost": 1,
          "freed_corpus_positions": 123
        },
        {
          "group": "8",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 122
        },
        {
          "group": "8",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 1,
          "freed_corpus_positions": 106
        }
      ],
      "maximum_position_release_by_exact_exception_cost": [
        0,
        132,
        255,
        377,
        497,
        616,
        729,
        840,
        949,
        1058,
        1164,
        1261,
        1339,
        1414,
        1486,
        1556,
        1625,
        1694,
        1761,
        1825,
        1892,
        1955,
        2016,
        2077,
        2135,
        2193,
        2251,
        2308,
        2364,
        2419,
        2474,
        2529,
        2583,
        2637,
        2690,
        2742,
        2793,
        2844,
        2894,
        2944,
        2993,
        3040,
        3087,
        3133,
        3177,
        3219,
        3261,
        3302,
        3341,
        3379,
        3416,
        3453,
        3489,
        3526,
        3560,
        3594,
        3628,
        3662,
        3692,
        3726,
        3756,
        3789,
        3819,
        3849,
        3879,
        3907,
        3936,
        3964,
        3992,
        4020,
        4048,
        4073,
        4099,
        4124,
        4147,
        4168,
        4185,
        4206,
        4222,
        4239,
        4260,
        4272,
        4289,
        4310
      ],
      "singleton_sensitivity": "all_audited",
      "allowed_letters": "AI",
      "requirements": {
        "pooled": {
          "reference_ratio": [
            241,
            1963
          ],
          "maximum_allowed_positions": 1590,
          "required_position_release": 2720,
          "minimum_exception_tokens": 35,
          "freed_constraint_types": 33,
          "witness_units": [
            {
              "group": "2",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 69
            },
            {
              "group": "2",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 1,
              "freed_corpus_positions": 61
            },
            {
              "group": "2",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 58
            },
            {
              "group": "2",
              "cipher": 7,
              "label": "W",
              "exception_token_cost": 1,
              "freed_corpus_positions": 55
            },
            {
              "group": "2",
              "cipher": 9,
              "label": "N",
              "exception_token_cost": 1,
              "freed_corpus_positions": 69
            },
            {
              "group": "2",
              "cipher": 14,
              "label": "X",
              "exception_token_cost": 1,
              "freed_corpus_positions": 78
            },
            {
              "group": "2",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 61
            },
            {
              "group": "4",
              "cipher": 2,
              "label": "TH",
              "exception_token_cost": 1,
              "freed_corpus_positions": 75
            },
            {
              "group": "4",
              "cipher": 13,
              "label": "P",
              "exception_token_cost": 1,
              "freed_corpus_positions": 72
            },
            {
              "group": "4",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 1,
              "freed_corpus_positions": 70
            },
            {
              "group": "4",
              "cipher": 25,
              "label": "AE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 67
            },
            {
              "group": "4",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 54
            },
            {
              "group": "6",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 1,
              "freed_corpus_positions": 53
            },
            {
              "group": "6",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 1,
              "freed_corpus_positions": 52
            },
            {
              "group": "6",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 1,
              "freed_corpus_positions": 55
            },
            {
              "group": "7",
              "cipher": 4,
              "label": "R",
              "exception_token_cost": 1,
              "freed_corpus_positions": 54
            },
            {
              "group": "7",
              "cipher": 7,
              "label": "W",
              "exception_token_cost": 1,
              "freed_corpus_positions": 55
            },
            {
              "group": "7",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 1,
              "freed_corpus_positions": 57
            },
            {
              "group": "7",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 63
            },
            {
              "group": "7",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 1,
              "freed_corpus_positions": 56
            },
            {
              "group": "8",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 109
            },
            {
              "group": "8",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 1,
              "freed_corpus_positions": 132
            },
            {
              "group": "8",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 97
            },
            {
              "group": "8",
              "cipher": 13,
              "label": "P",
              "exception_token_cost": 1,
              "freed_corpus_positions": 111
            },
            {
              "group": "8",
              "cipher": 16,
              "label": "T",
              "exception_token_cost": 2,
              "freed_corpus_positions": 116
            },
            {
              "group": "8",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 1,
              "freed_corpus_positions": 120
            },
            {
              "group": "8",
              "cipher": 19,
              "label": "M",
              "exception_token_cost": 1,
              "freed_corpus_positions": 119
            },
            {
              "group": "8",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 1,
              "freed_corpus_positions": 109
            },
            {
              "group": "8",
              "cipher": 21,
              "label": "ING",
              "exception_token_cost": 1,
              "freed_corpus_positions": 113
            },
            {
              "group": "8",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 2,
              "freed_corpus_positions": 131
            },
            {
              "group": "8",
              "cipher": 24,
              "label": "A",
              "exception_token_cost": 1,
              "freed_corpus_positions": 123
            },
            {
              "group": "8",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 122
            },
            {
              "group": "8",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 1,
              "freed_corpus_positions": 106
            }
          ],
          "remaining_forced_positions": 1568,
          "remaining_forced_share": 0.12102500771843161,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        },
        "largest_individual": {
          "reference_ratio": [
            54,
            389
          ],
          "maximum_allowed_positions": 1798,
          "required_position_release": 2512,
          "minimum_exception_tokens": 31,
          "freed_constraint_types": 29,
          "witness_units": [
            {
              "group": "2",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 69
            },
            {
              "group": "2",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 1,
              "freed_corpus_positions": 61
            },
            {
              "group": "2",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 58
            },
            {
              "group": "2",
              "cipher": 7,
              "label": "W",
              "exception_token_cost": 1,
              "freed_corpus_positions": 55
            },
            {
              "group": "2",
              "cipher": 9,
              "label": "N",
              "exception_token_cost": 1,
              "freed_corpus_positions": 69
            },
            {
              "group": "2",
              "cipher": 14,
              "label": "X",
              "exception_token_cost": 1,
              "freed_corpus_positions": 78
            },
            {
              "group": "2",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 61
            },
            {
              "group": "4",
              "cipher": 2,
              "label": "TH",
              "exception_token_cost": 1,
              "freed_corpus_positions": 75
            },
            {
              "group": "4",
              "cipher": 13,
              "label": "P",
              "exception_token_cost": 1,
              "freed_corpus_positions": 72
            },
            {
              "group": "4",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 1,
              "freed_corpus_positions": 70
            },
            {
              "group": "4",
              "cipher": 25,
              "label": "AE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 67
            },
            {
              "group": "6",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 1,
              "freed_corpus_positions": 55
            },
            {
              "group": "7",
              "cipher": 7,
              "label": "W",
              "exception_token_cost": 1,
              "freed_corpus_positions": 55
            },
            {
              "group": "7",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 1,
              "freed_corpus_positions": 57
            },
            {
              "group": "7",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 63
            },
            {
              "group": "7",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 1,
              "freed_corpus_positions": 56
            },
            {
              "group": "8",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 109
            },
            {
              "group": "8",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 1,
              "freed_corpus_positions": 132
            },
            {
              "group": "8",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 97
            },
            {
              "group": "8",
              "cipher": 13,
              "label": "P",
              "exception_token_cost": 1,
              "freed_corpus_positions": 111
            },
            {
              "group": "8",
              "cipher": 16,
              "label": "T",
              "exception_token_cost": 2,
              "freed_corpus_positions": 116
            },
            {
              "group": "8",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 1,
              "freed_corpus_positions": 120
            },
            {
              "group": "8",
              "cipher": 19,
              "label": "M",
              "exception_token_cost": 1,
              "freed_corpus_positions": 119
            },
            {
              "group": "8",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 1,
              "freed_corpus_positions": 109
            },
            {
              "group": "8",
              "cipher": 21,
              "label": "ING",
              "exception_token_cost": 1,
              "freed_corpus_positions": 113
            },
            {
              "group": "8",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 2,
              "freed_corpus_positions": 131
            },
            {
              "group": "8",
              "cipher": 24,
              "label": "A",
              "exception_token_cost": 1,
              "freed_corpus_positions": 123
            },
            {
              "group": "8",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 122
            },
            {
              "group": "8",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 1,
              "freed_corpus_positions": 106
            }
          ],
          "remaining_forced_positions": 1781,
          "remaining_forced_share": 0.13746526705773388,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        }
      }
    },
    {
      "runes": 12956,
      "key_scope": "per_section",
      "allowed_output_types": 3,
      "singleton_tokens": 83,
      "forced_positions": 4310,
      "minimum_allowed_letter_share": 0.332664402593393,
      "groups": [
        {
          "group": "0",
          "sections": [
            0
          ],
          "runes": 729,
          "singleton_tokens": 5,
          "singleton_cipher_types": 5,
          "active_cipher_types": 29,
          "forced_positions": 134,
          "maximum_distinct_output_runes": 27,
          "cipher_histogram": [
            34,
            21,
            30,
            20,
            22,
            28,
            29,
            22,
            30,
            28,
            24,
            24,
            17,
            27,
            28,
            23,
            23,
            23,
            24,
            18,
            30,
            29,
            25,
            31,
            19,
            24,
            25,
            23,
            28
          ],
          "singleton_counts_by_cipher_type": [
            1,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1
          ]
        },
        {
          "group": "1",
          "sections": [
            1
          ],
          "runes": 1145,
          "singleton_tokens": 8,
          "singleton_cipher_types": 7,
          "active_cipher_types": 29,
          "forced_positions": 271,
          "maximum_distinct_output_runes": 25,
          "cipher_histogram": [
            26,
            34,
            34,
            30,
            36,
            52,
            43,
            30,
            38,
            37,
            43,
            43,
            49,
            44,
            49,
            34,
            37,
            31,
            32,
            39,
            50,
            42,
            40,
            38,
            35,
            41,
            42,
            46,
            50
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            1,
            2,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            1,
            0,
            0,
            0,
            0,
            1,
            1,
            0
          ]
        },
        {
          "group": "2",
          "sections": [
            2
          ],
          "runes": 1729,
          "singleton_tokens": 11,
          "singleton_cipher_types": 9,
          "active_cipher_types": 29,
          "forced_positions": 545,
          "maximum_distinct_output_runes": 23,
          "cipher_histogram": [
            66,
            69,
            69,
            61,
            50,
            63,
            58,
            55,
            52,
            69,
            50,
            44,
            52,
            55,
            78,
            61,
            61,
            55,
            56,
            57,
            63,
            58,
            67,
            51,
            64,
            52,
            61,
            68,
            64
          ],
          "singleton_counts_by_cipher_type": [
            0,
            1,
            0,
            1,
            0,
            0,
            1,
            1,
            0,
            1,
            3,
            1,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0
          ]
        },
        {
          "group": "3",
          "sections": [
            3
          ],
          "runes": 9,
          "singleton_tokens": 0,
          "singleton_cipher_types": 0,
          "active_cipher_types": 8,
          "forced_positions": 0,
          "maximum_distinct_output_runes": 8,
          "cipher_histogram": [
            1,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            0,
            1,
            0,
            2,
            0,
            1,
            0,
            1
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0
          ]
        },
        {
          "group": "4",
          "sections": [
            4
          ],
          "runes": 1894,
          "singleton_tokens": 18,
          "singleton_cipher_types": 12,
          "active_cipher_types": 29,
          "forced_positions": 773,
          "maximum_distinct_output_runes": 20,
          "cipher_histogram": [
            71,
            63,
            75,
            75,
            64,
            70,
            71,
            50,
            52,
            57,
            73,
            76,
            52,
            72,
            63,
            56,
            60,
            63,
            54,
            62,
            63,
            69,
            74,
            70,
            73,
            67,
            54,
            77,
            68
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            2,
            0,
            0,
            1,
            0,
            2,
            2,
            0,
            0,
            1,
            0,
            0,
            2,
            2,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            1,
            1,
            0,
            2
          ]
        },
        {
          "group": "5",
          "sections": [
            5
          ],
          "runes": 1021,
          "singleton_tokens": 5,
          "singleton_cipher_types": 5,
          "active_cipher_types": 29,
          "forced_positions": 178,
          "maximum_distinct_output_runes": 27,
          "cipher_histogram": [
            37,
            44,
            37,
            40,
            34,
            30,
            37,
            33,
            33,
            39,
            35,
            27,
            21,
            34,
            32,
            43,
            38,
            37,
            42,
            32,
            34,
            37,
            35,
            25,
            41,
            31,
            37,
            35,
            41
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            0,
            1,
            0,
            0
          ]
        },
        {
          "group": "6",
          "sections": [
            6
          ],
          "runes": 1524,
          "singleton_tokens": 12,
          "singleton_cipher_types": 8,
          "active_cipher_types": 29,
          "forced_positions": 421,
          "maximum_distinct_output_runes": 24,
          "cipher_histogram": [
            55,
            45,
            50,
            53,
            57,
            40,
            47,
            61,
            52,
            43,
            58,
            56,
            48,
            51,
            47,
            49,
            50,
            64,
            58,
            54,
            55,
            51,
            56,
            60,
            57,
            50,
            48,
            56,
            53
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            2,
            0,
            2,
            0,
            1,
            0,
            0,
            0,
            3,
            1,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0
          ]
        },
        {
          "group": "7",
          "sections": [
            7
          ],
          "runes": 1589,
          "singleton_tokens": 9,
          "singleton_cipher_types": 9,
          "active_cipher_types": 29,
          "forced_positions": 480,
          "maximum_distinct_output_runes": 23,
          "cipher_histogram": [
            37,
            64,
            50,
            47,
            54,
            61,
            56,
            55,
            57,
            59,
            66,
            50,
            47,
            51,
            55,
            57,
            57,
            52,
            47,
            54,
            55,
            55,
            63,
            56,
            68,
            60,
            58,
            49,
            49
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            1,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            0,
            0
          ]
        },
        {
          "group": "8",
          "sections": [
            8
          ],
          "runes": 3316,
          "singleton_tokens": 15,
          "singleton_cipher_types": 13,
          "active_cipher_types": 29,
          "forced_positions": 1508,
          "maximum_distinct_output_runes": 19,
          "cipher_histogram": [
            131,
            109,
            110,
            132,
            107,
            99,
            97,
            95,
            100,
            114,
            122,
            130,
            113,
            111,
            106,
            111,
            116,
            120,
            126,
            119,
            109,
            113,
            131,
            108,
            123,
            120,
            122,
            116,
            106
          ],
          "singleton_counts_by_cipher_type": [
            0,
            1,
            0,
            1,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            2,
            1,
            0,
            1,
            1,
            1,
            2,
            0,
            1,
            0,
            1,
            0,
            1
          ]
        }
      ],
      "constraint_units": [
        {
          "group": "0",
          "cipher": 0,
          "label": "F",
          "exception_token_cost": 1,
          "freed_corpus_positions": 34
        },
        {
          "group": "0",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 21
        },
        {
          "group": "0",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 1,
          "freed_corpus_positions": 28
        },
        {
          "group": "0",
          "cipher": 15,
          "label": "S",
          "exception_token_cost": 1,
          "freed_corpus_positions": 23
        },
        {
          "group": "0",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 1,
          "freed_corpus_positions": 28
        },
        {
          "group": "1",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 34
        },
        {
          "group": "1",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 30
        },
        {
          "group": "1",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 2,
          "freed_corpus_positions": 38
        },
        {
          "group": "1",
          "cipher": 19,
          "label": "M",
          "exception_token_cost": 1,
          "freed_corpus_positions": 39
        },
        {
          "group": "1",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 1,
          "freed_corpus_positions": 42
        },
        {
          "group": "1",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 42
        },
        {
          "group": "1",
          "cipher": 27,
          "label": "IO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 46
        },
        {
          "group": "2",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 69
        },
        {
          "group": "2",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 1,
          "freed_corpus_positions": 61
        },
        {
          "group": "2",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 58
        },
        {
          "group": "2",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 55
        },
        {
          "group": "2",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 1,
          "freed_corpus_positions": 69
        },
        {
          "group": "2",
          "cipher": 10,
          "label": "I",
          "exception_token_cost": 3,
          "freed_corpus_positions": 50
        },
        {
          "group": "2",
          "cipher": 11,
          "label": "J",
          "exception_token_cost": 1,
          "freed_corpus_positions": 44
        },
        {
          "group": "2",
          "cipher": 14,
          "label": "X",
          "exception_token_cost": 1,
          "freed_corpus_positions": 78
        },
        {
          "group": "2",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 61
        },
        {
          "group": "4",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 75
        },
        {
          "group": "4",
          "cipher": 4,
          "label": "R",
          "exception_token_cost": 2,
          "freed_corpus_positions": 64
        },
        {
          "group": "4",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 50
        },
        {
          "group": "4",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 2,
          "freed_corpus_positions": 57
        },
        {
          "group": "4",
          "cipher": 10,
          "label": "I",
          "exception_token_cost": 2,
          "freed_corpus_positions": 73
        },
        {
          "group": "4",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 1,
          "freed_corpus_positions": 72
        },
        {
          "group": "4",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 2,
          "freed_corpus_positions": 60
        },
        {
          "group": "4",
          "cipher": 17,
          "label": "B",
          "exception_token_cost": 2,
          "freed_corpus_positions": 63
        },
        {
          "group": "4",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 70
        },
        {
          "group": "4",
          "cipher": 25,
          "label": "AE",
          "exception_token_cost": 1,
          "freed_corpus_positions": 67
        },
        {
          "group": "4",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 54
        },
        {
          "group": "4",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 2,
          "freed_corpus_positions": 68
        },
        {
          "group": "5",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 37
        },
        {
          "group": "5",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 1,
          "freed_corpus_positions": 38
        },
        {
          "group": "5",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 25
        },
        {
          "group": "5",
          "cipher": 24,
          "label": "A",
          "exception_token_cost": 1,
          "freed_corpus_positions": 41
        },
        {
          "group": "5",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 37
        },
        {
          "group": "6",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 1,
          "freed_corpus_positions": 53
        },
        {
          "group": "6",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 1,
          "freed_corpus_positions": 52
        },
        {
          "group": "6",
          "cipher": 11,
          "label": "J",
          "exception_token_cost": 2,
          "freed_corpus_positions": 56
        },
        {
          "group": "6",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 2,
          "freed_corpus_positions": 51
        },
        {
          "group": "6",
          "cipher": 15,
          "label": "S",
          "exception_token_cost": 1,
          "freed_corpus_positions": 49
        },
        {
          "group": "6",
          "cipher": 19,
          "label": "M",
          "exception_token_cost": 3,
          "freed_corpus_positions": 54
        },
        {
          "group": "6",
          "cipher": 20,
          "label": "L",
          "exception_token_cost": 1,
          "freed_corpus_positions": 55
        },
        {
          "group": "6",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 1,
          "freed_corpus_positions": 51
        },
        {
          "group": "7",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 50
        },
        {
          "group": "7",
          "cipher": 4,
          "label": "R",
          "exception_token_cost": 1,
          "freed_corpus_positions": 54
        },
        {
          "group": "7",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 55
        },
        {
          "group": "7",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 1,
          "freed_corpus_positions": 57
        },
        {
          "group": "7",
          "cipher": 12,
          "label": "EO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 47
        },
        {
          "group": "7",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 1,
          "freed_corpus_positions": 51
        },
        {
          "group": "7",
          "cipher": 18,
          "label": "E",
          "exception_token_cost": 1,
          "freed_corpus_positions": 47
        },
        {
          "group": "7",
          "cipher": 22,
          "label": "OE",
          "exception_token_cost": 1,
          "freed_corpus_positions": 63
        },
        {
          "group": "7",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 56
        },
        {
          "group": "8",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 109
        },
        {
          "group": "8",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 1,
          "freed_corpus_positions": 132
        },
        {
          "group": "8",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 97
        },
        {
          "group": "8",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 1,
          "freed_corpus_positions": 111
        },
        {
          "group": "8",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 2,
          "freed_corpus_positions": 116
        },
        {
          "group": "8",
          "cipher": 17,
          "label": "B",
          "exception_token_cost": 1,
          "freed_corpus_positions": 120
        },
        {
          "group": "8",
          "cipher": 19,
          "label": "M",
          "exception_token_cost": 1,
          "freed_corpus_positions": 119
        },
        {
          "group": "8",
          "cipher": 20,
          "label": "L",
          "exception_token_cost": 1,
          "freed_corpus_positions": 109
        },
        {
          "group": "8",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 1,
          "freed_corpus_positions": 113
        },
        {
          "group": "8",
          "cipher": 22,
          "label": "OE",
          "exception_token_cost": 2,
          "freed_corpus_positions": 131
        },
        {
          "group": "8",
          "cipher": 24,
          "label": "A",
          "exception_token_cost": 1,
          "freed_corpus_positions": 123
        },
        {
          "group": "8",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 122
        },
        {
          "group": "8",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 1,
          "freed_corpus_positions": 106
        }
      ],
      "maximum_position_release_by_exact_exception_cost": [
        0,
        132,
        255,
        377,
        497,
        616,
        729,
        840,
        949,
        1058,
        1164,
        1261,
        1339,
        1414,
        1486,
        1556,
        1625,
        1694,
        1761,
        1825,
        1892,
        1955,
        2016,
        2077,
        2135,
        2193,
        2251,
        2308,
        2364,
        2419,
        2474,
        2529,
        2583,
        2637,
        2690,
        2742,
        2793,
        2844,
        2894,
        2944,
        2993,
        3040,
        3087,
        3133,
        3177,
        3219,
        3261,
        3302,
        3341,
        3379,
        3416,
        3453,
        3489,
        3526,
        3560,
        3594,
        3628,
        3662,
        3692,
        3726,
        3756,
        3789,
        3819,
        3849,
        3879,
        3907,
        3936,
        3964,
        3992,
        4020,
        4048,
        4073,
        4099,
        4124,
        4147,
        4168,
        4185,
        4206,
        4222,
        4239,
        4260,
        4272,
        4289,
        4310
      ],
      "singleton_sensitivity": "all_audited",
      "allowed_letters": "AIO",
      "requirements": {
        "pooled": {
          "reference_ratio": [
            431,
            1963
          ],
          "maximum_allowed_positions": 2844,
          "required_position_release": 1466,
          "minimum_exception_tokens": 14,
          "freed_constraint_types": 14,
          "witness_units": [
            {
              "group": "2",
              "cipher": 14,
              "label": "X",
              "exception_token_cost": 1,
              "freed_corpus_positions": 78
            },
            {
              "group": "4",
              "cipher": 2,
              "label": "TH",
              "exception_token_cost": 1,
              "freed_corpus_positions": 75
            },
            {
              "group": "4",
              "cipher": 13,
              "label": "P",
              "exception_token_cost": 1,
              "freed_corpus_positions": 72
            },
            {
              "group": "8",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 109
            },
            {
              "group": "8",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 1,
              "freed_corpus_positions": 132
            },
            {
              "group": "8",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 97
            },
            {
              "group": "8",
              "cipher": 13,
              "label": "P",
              "exception_token_cost": 1,
              "freed_corpus_positions": 111
            },
            {
              "group": "8",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 1,
              "freed_corpus_positions": 120
            },
            {
              "group": "8",
              "cipher": 19,
              "label": "M",
              "exception_token_cost": 1,
              "freed_corpus_positions": 119
            },
            {
              "group": "8",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 1,
              "freed_corpus_positions": 109
            },
            {
              "group": "8",
              "cipher": 21,
              "label": "ING",
              "exception_token_cost": 1,
              "freed_corpus_positions": 113
            },
            {
              "group": "8",
              "cipher": 24,
              "label": "A",
              "exception_token_cost": 1,
              "freed_corpus_positions": 123
            },
            {
              "group": "8",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 122
            },
            {
              "group": "8",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 1,
              "freed_corpus_positions": 106
            }
          ],
          "remaining_forced_positions": 2824,
          "remaining_forced_share": 0.21796850879901203,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        },
        "largest_individual": {
          "reference_ratio": [
            185,
            778
          ],
          "maximum_allowed_positions": 3080,
          "required_position_release": 1230,
          "minimum_exception_tokens": 11,
          "freed_constraint_types": 11,
          "witness_units": [
            {
              "group": "8",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 109
            },
            {
              "group": "8",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 1,
              "freed_corpus_positions": 132
            },
            {
              "group": "8",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 97
            },
            {
              "group": "8",
              "cipher": 13,
              "label": "P",
              "exception_token_cost": 1,
              "freed_corpus_positions": 111
            },
            {
              "group": "8",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 1,
              "freed_corpus_positions": 120
            },
            {
              "group": "8",
              "cipher": 19,
              "label": "M",
              "exception_token_cost": 1,
              "freed_corpus_positions": 119
            },
            {
              "group": "8",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 1,
              "freed_corpus_positions": 109
            },
            {
              "group": "8",
              "cipher": 21,
              "label": "ING",
              "exception_token_cost": 1,
              "freed_corpus_positions": 113
            },
            {
              "group": "8",
              "cipher": 24,
              "label": "A",
              "exception_token_cost": 1,
              "freed_corpus_positions": 123
            },
            {
              "group": "8",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 122
            },
            {
              "group": "8",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 1,
              "freed_corpus_positions": 106
            }
          ],
          "remaining_forced_positions": 3049,
          "remaining_forced_share": 0.2353349799320778,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        }
      }
    },
    {
      "runes": 12956,
      "key_scope": "anchor_shared",
      "allowed_output_types": 2,
      "singleton_tokens": 83,
      "forced_positions": 5071,
      "minimum_allowed_letter_share": 0.39140166718122876,
      "groups": [
        {
          "group": "0",
          "sections": [
            0
          ],
          "runes": 729,
          "singleton_tokens": 5,
          "singleton_cipher_types": 5,
          "active_cipher_types": 29,
          "forced_positions": 134,
          "maximum_distinct_output_runes": 26,
          "cipher_histogram": [
            34,
            21,
            30,
            20,
            22,
            28,
            29,
            22,
            30,
            28,
            24,
            24,
            17,
            27,
            28,
            23,
            23,
            23,
            24,
            18,
            30,
            29,
            25,
            31,
            19,
            24,
            25,
            23,
            28
          ],
          "singleton_counts_by_cipher_type": [
            1,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1
          ]
        },
        {
          "group": "1",
          "sections": [
            1
          ],
          "runes": 1145,
          "singleton_tokens": 8,
          "singleton_cipher_types": 7,
          "active_cipher_types": 29,
          "forced_positions": 271,
          "maximum_distinct_output_runes": 24,
          "cipher_histogram": [
            26,
            34,
            34,
            30,
            36,
            52,
            43,
            30,
            38,
            37,
            43,
            43,
            49,
            44,
            49,
            34,
            37,
            31,
            32,
            39,
            50,
            42,
            40,
            38,
            35,
            41,
            42,
            46,
            50
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            1,
            2,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            1,
            0,
            0,
            0,
            0,
            1,
            1,
            0
          ]
        },
        {
          "group": "2",
          "sections": [
            2
          ],
          "runes": 1729,
          "singleton_tokens": 11,
          "singleton_cipher_types": 9,
          "active_cipher_types": 29,
          "forced_positions": 545,
          "maximum_distinct_output_runes": 22,
          "cipher_histogram": [
            66,
            69,
            69,
            61,
            50,
            63,
            58,
            55,
            52,
            69,
            50,
            44,
            52,
            55,
            78,
            61,
            61,
            55,
            56,
            57,
            63,
            58,
            67,
            51,
            64,
            52,
            61,
            68,
            64
          ],
          "singleton_counts_by_cipher_type": [
            0,
            1,
            0,
            1,
            0,
            0,
            1,
            1,
            0,
            1,
            3,
            1,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0
          ]
        },
        {
          "group": "3",
          "sections": [
            3
          ],
          "runes": 9,
          "singleton_tokens": 0,
          "singleton_cipher_types": 0,
          "active_cipher_types": 8,
          "forced_positions": 0,
          "maximum_distinct_output_runes": 8,
          "cipher_histogram": [
            1,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            0,
            1,
            0,
            2,
            0,
            1,
            0,
            1
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0
          ]
        },
        {
          "group": "4",
          "sections": [
            4
          ],
          "runes": 1894,
          "singleton_tokens": 18,
          "singleton_cipher_types": 12,
          "active_cipher_types": 29,
          "forced_positions": 773,
          "maximum_distinct_output_runes": 19,
          "cipher_histogram": [
            71,
            63,
            75,
            75,
            64,
            70,
            71,
            50,
            52,
            57,
            73,
            76,
            52,
            72,
            63,
            56,
            60,
            63,
            54,
            62,
            63,
            69,
            74,
            70,
            73,
            67,
            54,
            77,
            68
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            2,
            0,
            0,
            1,
            0,
            2,
            2,
            0,
            0,
            1,
            0,
            0,
            2,
            2,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            1,
            1,
            0,
            2
          ]
        },
        {
          "group": "5",
          "sections": [
            5
          ],
          "runes": 1021,
          "singleton_tokens": 5,
          "singleton_cipher_types": 5,
          "active_cipher_types": 29,
          "forced_positions": 178,
          "maximum_distinct_output_runes": 26,
          "cipher_histogram": [
            37,
            44,
            37,
            40,
            34,
            30,
            37,
            33,
            33,
            39,
            35,
            27,
            21,
            34,
            32,
            43,
            38,
            37,
            42,
            32,
            34,
            37,
            35,
            25,
            41,
            31,
            37,
            35,
            41
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            0,
            1,
            0,
            0
          ]
        },
        {
          "group": "6+8",
          "sections": [
            6,
            8
          ],
          "runes": 4840,
          "singleton_tokens": 27,
          "singleton_cipher_types": 16,
          "active_cipher_types": 29,
          "forced_positions": 2690,
          "maximum_distinct_output_runes": 15,
          "cipher_histogram": [
            186,
            154,
            160,
            185,
            164,
            139,
            144,
            156,
            152,
            157,
            180,
            186,
            161,
            162,
            153,
            160,
            166,
            184,
            184,
            173,
            164,
            164,
            187,
            168,
            180,
            170,
            170,
            172,
            159
          ],
          "singleton_counts_by_cipher_type": [
            0,
            1,
            0,
            2,
            0,
            0,
            1,
            0,
            1,
            0,
            0,
            2,
            0,
            3,
            0,
            1,
            2,
            1,
            0,
            4,
            2,
            2,
            2,
            0,
            1,
            0,
            1,
            0,
            1
          ]
        },
        {
          "group": "7",
          "sections": [
            7
          ],
          "runes": 1589,
          "singleton_tokens": 9,
          "singleton_cipher_types": 9,
          "active_cipher_types": 29,
          "forced_positions": 480,
          "maximum_distinct_output_runes": 22,
          "cipher_histogram": [
            37,
            64,
            50,
            47,
            54,
            61,
            56,
            55,
            57,
            59,
            66,
            50,
            47,
            51,
            55,
            57,
            57,
            52,
            47,
            54,
            55,
            55,
            63,
            56,
            68,
            60,
            58,
            49,
            49
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            1,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            0,
            0
          ]
        }
      ],
      "constraint_units": [
        {
          "group": "0",
          "cipher": 0,
          "label": "F",
          "exception_token_cost": 1,
          "freed_corpus_positions": 34
        },
        {
          "group": "0",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 21
        },
        {
          "group": "0",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 1,
          "freed_corpus_positions": 28
        },
        {
          "group": "0",
          "cipher": 15,
          "label": "S",
          "exception_token_cost": 1,
          "freed_corpus_positions": 23
        },
        {
          "group": "0",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 1,
          "freed_corpus_positions": 28
        },
        {
          "group": "1",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 34
        },
        {
          "group": "1",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 30
        },
        {
          "group": "1",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 2,
          "freed_corpus_positions": 38
        },
        {
          "group": "1",
          "cipher": 19,
          "label": "M",
          "exception_token_cost": 1,
          "freed_corpus_positions": 39
        },
        {
          "group": "1",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 1,
          "freed_corpus_positions": 42
        },
        {
          "group": "1",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 42
        },
        {
          "group": "1",
          "cipher": 27,
          "label": "IO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 46
        },
        {
          "group": "2",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 69
        },
        {
          "group": "2",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 1,
          "freed_corpus_positions": 61
        },
        {
          "group": "2",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 58
        },
        {
          "group": "2",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 55
        },
        {
          "group": "2",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 1,
          "freed_corpus_positions": 69
        },
        {
          "group": "2",
          "cipher": 10,
          "label": "I",
          "exception_token_cost": 3,
          "freed_corpus_positions": 50
        },
        {
          "group": "2",
          "cipher": 11,
          "label": "J",
          "exception_token_cost": 1,
          "freed_corpus_positions": 44
        },
        {
          "group": "2",
          "cipher": 14,
          "label": "X",
          "exception_token_cost": 1,
          "freed_corpus_positions": 78
        },
        {
          "group": "2",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 61
        },
        {
          "group": "4",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 75
        },
        {
          "group": "4",
          "cipher": 4,
          "label": "R",
          "exception_token_cost": 2,
          "freed_corpus_positions": 64
        },
        {
          "group": "4",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 50
        },
        {
          "group": "4",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 2,
          "freed_corpus_positions": 57
        },
        {
          "group": "4",
          "cipher": 10,
          "label": "I",
          "exception_token_cost": 2,
          "freed_corpus_positions": 73
        },
        {
          "group": "4",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 1,
          "freed_corpus_positions": 72
        },
        {
          "group": "4",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 2,
          "freed_corpus_positions": 60
        },
        {
          "group": "4",
          "cipher": 17,
          "label": "B",
          "exception_token_cost": 2,
          "freed_corpus_positions": 63
        },
        {
          "group": "4",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 70
        },
        {
          "group": "4",
          "cipher": 25,
          "label": "AE",
          "exception_token_cost": 1,
          "freed_corpus_positions": 67
        },
        {
          "group": "4",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 54
        },
        {
          "group": "4",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 2,
          "freed_corpus_positions": 68
        },
        {
          "group": "5",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 37
        },
        {
          "group": "5",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 1,
          "freed_corpus_positions": 38
        },
        {
          "group": "5",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 25
        },
        {
          "group": "5",
          "cipher": 24,
          "label": "A",
          "exception_token_cost": 1,
          "freed_corpus_positions": 41
        },
        {
          "group": "5",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 37
        },
        {
          "group": "6+8",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 154
        },
        {
          "group": "6+8",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 2,
          "freed_corpus_positions": 185
        },
        {
          "group": "6+8",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 144
        },
        {
          "group": "6+8",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 1,
          "freed_corpus_positions": 152
        },
        {
          "group": "6+8",
          "cipher": 11,
          "label": "J",
          "exception_token_cost": 2,
          "freed_corpus_positions": 186
        },
        {
          "group": "6+8",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 3,
          "freed_corpus_positions": 162
        },
        {
          "group": "6+8",
          "cipher": 15,
          "label": "S",
          "exception_token_cost": 1,
          "freed_corpus_positions": 160
        },
        {
          "group": "6+8",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 2,
          "freed_corpus_positions": 166
        },
        {
          "group": "6+8",
          "cipher": 17,
          "label": "B",
          "exception_token_cost": 1,
          "freed_corpus_positions": 184
        },
        {
          "group": "6+8",
          "cipher": 19,
          "label": "M",
          "exception_token_cost": 4,
          "freed_corpus_positions": 173
        },
        {
          "group": "6+8",
          "cipher": 20,
          "label": "L",
          "exception_token_cost": 2,
          "freed_corpus_positions": 164
        },
        {
          "group": "6+8",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 2,
          "freed_corpus_positions": 164
        },
        {
          "group": "6+8",
          "cipher": 22,
          "label": "OE",
          "exception_token_cost": 2,
          "freed_corpus_positions": 187
        },
        {
          "group": "6+8",
          "cipher": 24,
          "label": "A",
          "exception_token_cost": 1,
          "freed_corpus_positions": 180
        },
        {
          "group": "6+8",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 170
        },
        {
          "group": "6+8",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 1,
          "freed_corpus_positions": 159
        },
        {
          "group": "7",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 50
        },
        {
          "group": "7",
          "cipher": 4,
          "label": "R",
          "exception_token_cost": 1,
          "freed_corpus_positions": 54
        },
        {
          "group": "7",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 55
        },
        {
          "group": "7",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 1,
          "freed_corpus_positions": 57
        },
        {
          "group": "7",
          "cipher": 12,
          "label": "EO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 47
        },
        {
          "group": "7",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 1,
          "freed_corpus_positions": 51
        },
        {
          "group": "7",
          "cipher": 18,
          "label": "E",
          "exception_token_cost": 1,
          "freed_corpus_positions": 47
        },
        {
          "group": "7",
          "cipher": 22,
          "label": "OE",
          "exception_token_cost": 1,
          "freed_corpus_positions": 63
        },
        {
          "group": "7",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 56
        }
      ],
      "maximum_position_release_by_exact_exception_cost": [
        0,
        184,
        364,
        534,
        694,
        853,
        1007,
        1159,
        1303,
        1381,
        1490,
        1568,
        1676,
        1754,
        1861,
        1939,
        2027,
        2105,
        2191,
        2269,
        2355,
        2433,
        2508,
        2580,
        2650,
        2719,
        2788,
        2855,
        2918,
        2979,
        3040,
        3098,
        3155,
        3211,
        3266,
        3321,
        3375,
        3429,
        3483,
        3537,
        3591,
        3642,
        3692,
        3742,
        3789,
        3836,
        3882,
        3926,
        3968,
        4010,
        4055,
        4099,
        4141,
        4183,
        4224,
        4263,
        4301,
        4338,
        4375,
        4411,
        4448,
        4482,
        4516,
        4550,
        4584,
        4614,
        4648,
        4678,
        4711,
        4741,
        4771,
        4801,
        4829,
        4858,
        4886,
        4914,
        4939,
        4962,
        4983,
        5000,
        5021,
        5033,
        5050,
        5071
      ],
      "singleton_sensitivity": "all_audited",
      "allowed_letters": "AI",
      "requirements": {
        "pooled": {
          "reference_ratio": [
            241,
            1963
          ],
          "maximum_allowed_positions": 1590,
          "required_position_release": 3481,
          "minimum_exception_tokens": 38,
          "freed_constraint_types": 30,
          "witness_units": [
            {
              "group": "2",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 69
            },
            {
              "group": "2",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 1,
              "freed_corpus_positions": 61
            },
            {
              "group": "2",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 58
            },
            {
              "group": "2",
              "cipher": 7,
              "label": "W",
              "exception_token_cost": 1,
              "freed_corpus_positions": 55
            },
            {
              "group": "2",
              "cipher": 9,
              "label": "N",
              "exception_token_cost": 1,
              "freed_corpus_positions": 69
            },
            {
              "group": "2",
              "cipher": 14,
              "label": "X",
              "exception_token_cost": 1,
              "freed_corpus_positions": 78
            },
            {
              "group": "2",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 61
            },
            {
              "group": "4",
              "cipher": 2,
              "label": "TH",
              "exception_token_cost": 1,
              "freed_corpus_positions": 75
            },
            {
              "group": "4",
              "cipher": 13,
              "label": "P",
              "exception_token_cost": 1,
              "freed_corpus_positions": 72
            },
            {
              "group": "4",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 1,
              "freed_corpus_positions": 70
            },
            {
              "group": "4",
              "cipher": 25,
              "label": "AE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 67
            },
            {
              "group": "6+8",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 154
            },
            {
              "group": "6+8",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 2,
              "freed_corpus_positions": 185
            },
            {
              "group": "6+8",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 144
            },
            {
              "group": "6+8",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 1,
              "freed_corpus_positions": 152
            },
            {
              "group": "6+8",
              "cipher": 11,
              "label": "J",
              "exception_token_cost": 2,
              "freed_corpus_positions": 186
            },
            {
              "group": "6+8",
              "cipher": 13,
              "label": "P",
              "exception_token_cost": 3,
              "freed_corpus_positions": 162
            },
            {
              "group": "6+8",
              "cipher": 15,
              "label": "S",
              "exception_token_cost": 1,
              "freed_corpus_positions": 160
            },
            {
              "group": "6+8",
              "cipher": 16,
              "label": "T",
              "exception_token_cost": 2,
              "freed_corpus_positions": 166
            },
            {
              "group": "6+8",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 1,
              "freed_corpus_positions": 184
            },
            {
              "group": "6+8",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 2,
              "freed_corpus_positions": 164
            },
            {
              "group": "6+8",
              "cipher": 21,
              "label": "ING",
              "exception_token_cost": 2,
              "freed_corpus_positions": 164
            },
            {
              "group": "6+8",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 2,
              "freed_corpus_positions": 187
            },
            {
              "group": "6+8",
              "cipher": 24,
              "label": "A",
              "exception_token_cost": 1,
              "freed_corpus_positions": 180
            },
            {
              "group": "6+8",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 170
            },
            {
              "group": "6+8",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 1,
              "freed_corpus_positions": 159
            },
            {
              "group": "7",
              "cipher": 7,
              "label": "W",
              "exception_token_cost": 1,
              "freed_corpus_positions": 55
            },
            {
              "group": "7",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 1,
              "freed_corpus_positions": 57
            },
            {
              "group": "7",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 63
            },
            {
              "group": "7",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 1,
              "freed_corpus_positions": 56
            }
          ],
          "remaining_forced_positions": 1588,
          "remaining_forced_share": 0.12256869404137079,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        },
        "largest_individual": {
          "reference_ratio": [
            54,
            389
          ],
          "maximum_allowed_positions": 1798,
          "required_position_release": 3273,
          "minimum_exception_tokens": 35,
          "freed_constraint_types": 29,
          "witness_units": [
            {
              "group": "2",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 69
            },
            {
              "group": "2",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 1,
              "freed_corpus_positions": 61
            },
            {
              "group": "2",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 58
            },
            {
              "group": "2",
              "cipher": 7,
              "label": "W",
              "exception_token_cost": 1,
              "freed_corpus_positions": 55
            },
            {
              "group": "2",
              "cipher": 9,
              "label": "N",
              "exception_token_cost": 1,
              "freed_corpus_positions": 69
            },
            {
              "group": "2",
              "cipher": 14,
              "label": "X",
              "exception_token_cost": 1,
              "freed_corpus_positions": 78
            },
            {
              "group": "2",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 61
            },
            {
              "group": "4",
              "cipher": 2,
              "label": "TH",
              "exception_token_cost": 1,
              "freed_corpus_positions": 75
            },
            {
              "group": "4",
              "cipher": 13,
              "label": "P",
              "exception_token_cost": 1,
              "freed_corpus_positions": 72
            },
            {
              "group": "4",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 1,
              "freed_corpus_positions": 70
            },
            {
              "group": "4",
              "cipher": 25,
              "label": "AE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 67
            },
            {
              "group": "6+8",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 154
            },
            {
              "group": "6+8",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 2,
              "freed_corpus_positions": 185
            },
            {
              "group": "6+8",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 144
            },
            {
              "group": "6+8",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 1,
              "freed_corpus_positions": 152
            },
            {
              "group": "6+8",
              "cipher": 11,
              "label": "J",
              "exception_token_cost": 2,
              "freed_corpus_positions": 186
            },
            {
              "group": "6+8",
              "cipher": 15,
              "label": "S",
              "exception_token_cost": 1,
              "freed_corpus_positions": 160
            },
            {
              "group": "6+8",
              "cipher": 16,
              "label": "T",
              "exception_token_cost": 2,
              "freed_corpus_positions": 166
            },
            {
              "group": "6+8",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 1,
              "freed_corpus_positions": 184
            },
            {
              "group": "6+8",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 2,
              "freed_corpus_positions": 164
            },
            {
              "group": "6+8",
              "cipher": 21,
              "label": "ING",
              "exception_token_cost": 2,
              "freed_corpus_positions": 164
            },
            {
              "group": "6+8",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 2,
              "freed_corpus_positions": 187
            },
            {
              "group": "6+8",
              "cipher": 24,
              "label": "A",
              "exception_token_cost": 1,
              "freed_corpus_positions": 180
            },
            {
              "group": "6+8",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 170
            },
            {
              "group": "6+8",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 1,
              "freed_corpus_positions": 159
            },
            {
              "group": "7",
              "cipher": 7,
              "label": "W",
              "exception_token_cost": 1,
              "freed_corpus_positions": 55
            },
            {
              "group": "7",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 1,
              "freed_corpus_positions": 57
            },
            {
              "group": "7",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 63
            },
            {
              "group": "7",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 1,
              "freed_corpus_positions": 56
            }
          ],
          "remaining_forced_positions": 1750,
          "remaining_forced_share": 0.13507255325717815,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        }
      }
    },
    {
      "runes": 12956,
      "key_scope": "anchor_shared",
      "allowed_output_types": 3,
      "singleton_tokens": 83,
      "forced_positions": 5071,
      "minimum_allowed_letter_share": 0.39140166718122876,
      "groups": [
        {
          "group": "0",
          "sections": [
            0
          ],
          "runes": 729,
          "singleton_tokens": 5,
          "singleton_cipher_types": 5,
          "active_cipher_types": 29,
          "forced_positions": 134,
          "maximum_distinct_output_runes": 27,
          "cipher_histogram": [
            34,
            21,
            30,
            20,
            22,
            28,
            29,
            22,
            30,
            28,
            24,
            24,
            17,
            27,
            28,
            23,
            23,
            23,
            24,
            18,
            30,
            29,
            25,
            31,
            19,
            24,
            25,
            23,
            28
          ],
          "singleton_counts_by_cipher_type": [
            1,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1
          ]
        },
        {
          "group": "1",
          "sections": [
            1
          ],
          "runes": 1145,
          "singleton_tokens": 8,
          "singleton_cipher_types": 7,
          "active_cipher_types": 29,
          "forced_positions": 271,
          "maximum_distinct_output_runes": 25,
          "cipher_histogram": [
            26,
            34,
            34,
            30,
            36,
            52,
            43,
            30,
            38,
            37,
            43,
            43,
            49,
            44,
            49,
            34,
            37,
            31,
            32,
            39,
            50,
            42,
            40,
            38,
            35,
            41,
            42,
            46,
            50
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            1,
            2,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            1,
            0,
            0,
            0,
            0,
            1,
            1,
            0
          ]
        },
        {
          "group": "2",
          "sections": [
            2
          ],
          "runes": 1729,
          "singleton_tokens": 11,
          "singleton_cipher_types": 9,
          "active_cipher_types": 29,
          "forced_positions": 545,
          "maximum_distinct_output_runes": 23,
          "cipher_histogram": [
            66,
            69,
            69,
            61,
            50,
            63,
            58,
            55,
            52,
            69,
            50,
            44,
            52,
            55,
            78,
            61,
            61,
            55,
            56,
            57,
            63,
            58,
            67,
            51,
            64,
            52,
            61,
            68,
            64
          ],
          "singleton_counts_by_cipher_type": [
            0,
            1,
            0,
            1,
            0,
            0,
            1,
            1,
            0,
            1,
            3,
            1,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0
          ]
        },
        {
          "group": "3",
          "sections": [
            3
          ],
          "runes": 9,
          "singleton_tokens": 0,
          "singleton_cipher_types": 0,
          "active_cipher_types": 8,
          "forced_positions": 0,
          "maximum_distinct_output_runes": 8,
          "cipher_histogram": [
            1,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            0,
            1,
            0,
            2,
            0,
            1,
            0,
            1
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0
          ]
        },
        {
          "group": "4",
          "sections": [
            4
          ],
          "runes": 1894,
          "singleton_tokens": 18,
          "singleton_cipher_types": 12,
          "active_cipher_types": 29,
          "forced_positions": 773,
          "maximum_distinct_output_runes": 20,
          "cipher_histogram": [
            71,
            63,
            75,
            75,
            64,
            70,
            71,
            50,
            52,
            57,
            73,
            76,
            52,
            72,
            63,
            56,
            60,
            63,
            54,
            62,
            63,
            69,
            74,
            70,
            73,
            67,
            54,
            77,
            68
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            2,
            0,
            0,
            1,
            0,
            2,
            2,
            0,
            0,
            1,
            0,
            0,
            2,
            2,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            1,
            1,
            0,
            2
          ]
        },
        {
          "group": "5",
          "sections": [
            5
          ],
          "runes": 1021,
          "singleton_tokens": 5,
          "singleton_cipher_types": 5,
          "active_cipher_types": 29,
          "forced_positions": 178,
          "maximum_distinct_output_runes": 27,
          "cipher_histogram": [
            37,
            44,
            37,
            40,
            34,
            30,
            37,
            33,
            33,
            39,
            35,
            27,
            21,
            34,
            32,
            43,
            38,
            37,
            42,
            32,
            34,
            37,
            35,
            25,
            41,
            31,
            37,
            35,
            41
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            0,
            1,
            0,
            0
          ]
        },
        {
          "group": "6+8",
          "sections": [
            6,
            8
          ],
          "runes": 4840,
          "singleton_tokens": 27,
          "singleton_cipher_types": 16,
          "active_cipher_types": 29,
          "forced_positions": 2690,
          "maximum_distinct_output_runes": 16,
          "cipher_histogram": [
            186,
            154,
            160,
            185,
            164,
            139,
            144,
            156,
            152,
            157,
            180,
            186,
            161,
            162,
            153,
            160,
            166,
            184,
            184,
            173,
            164,
            164,
            187,
            168,
            180,
            170,
            170,
            172,
            159
          ],
          "singleton_counts_by_cipher_type": [
            0,
            1,
            0,
            2,
            0,
            0,
            1,
            0,
            1,
            0,
            0,
            2,
            0,
            3,
            0,
            1,
            2,
            1,
            0,
            4,
            2,
            2,
            2,
            0,
            1,
            0,
            1,
            0,
            1
          ]
        },
        {
          "group": "7",
          "sections": [
            7
          ],
          "runes": 1589,
          "singleton_tokens": 9,
          "singleton_cipher_types": 9,
          "active_cipher_types": 29,
          "forced_positions": 480,
          "maximum_distinct_output_runes": 23,
          "cipher_histogram": [
            37,
            64,
            50,
            47,
            54,
            61,
            56,
            55,
            57,
            59,
            66,
            50,
            47,
            51,
            55,
            57,
            57,
            52,
            47,
            54,
            55,
            55,
            63,
            56,
            68,
            60,
            58,
            49,
            49
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            1,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            0,
            0
          ]
        }
      ],
      "constraint_units": [
        {
          "group": "0",
          "cipher": 0,
          "label": "F",
          "exception_token_cost": 1,
          "freed_corpus_positions": 34
        },
        {
          "group": "0",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 21
        },
        {
          "group": "0",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 1,
          "freed_corpus_positions": 28
        },
        {
          "group": "0",
          "cipher": 15,
          "label": "S",
          "exception_token_cost": 1,
          "freed_corpus_positions": 23
        },
        {
          "group": "0",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 1,
          "freed_corpus_positions": 28
        },
        {
          "group": "1",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 34
        },
        {
          "group": "1",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 30
        },
        {
          "group": "1",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 2,
          "freed_corpus_positions": 38
        },
        {
          "group": "1",
          "cipher": 19,
          "label": "M",
          "exception_token_cost": 1,
          "freed_corpus_positions": 39
        },
        {
          "group": "1",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 1,
          "freed_corpus_positions": 42
        },
        {
          "group": "1",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 42
        },
        {
          "group": "1",
          "cipher": 27,
          "label": "IO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 46
        },
        {
          "group": "2",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 69
        },
        {
          "group": "2",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 1,
          "freed_corpus_positions": 61
        },
        {
          "group": "2",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 58
        },
        {
          "group": "2",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 55
        },
        {
          "group": "2",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 1,
          "freed_corpus_positions": 69
        },
        {
          "group": "2",
          "cipher": 10,
          "label": "I",
          "exception_token_cost": 3,
          "freed_corpus_positions": 50
        },
        {
          "group": "2",
          "cipher": 11,
          "label": "J",
          "exception_token_cost": 1,
          "freed_corpus_positions": 44
        },
        {
          "group": "2",
          "cipher": 14,
          "label": "X",
          "exception_token_cost": 1,
          "freed_corpus_positions": 78
        },
        {
          "group": "2",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 61
        },
        {
          "group": "4",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 75
        },
        {
          "group": "4",
          "cipher": 4,
          "label": "R",
          "exception_token_cost": 2,
          "freed_corpus_positions": 64
        },
        {
          "group": "4",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 50
        },
        {
          "group": "4",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 2,
          "freed_corpus_positions": 57
        },
        {
          "group": "4",
          "cipher": 10,
          "label": "I",
          "exception_token_cost": 2,
          "freed_corpus_positions": 73
        },
        {
          "group": "4",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 1,
          "freed_corpus_positions": 72
        },
        {
          "group": "4",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 2,
          "freed_corpus_positions": 60
        },
        {
          "group": "4",
          "cipher": 17,
          "label": "B",
          "exception_token_cost": 2,
          "freed_corpus_positions": 63
        },
        {
          "group": "4",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 70
        },
        {
          "group": "4",
          "cipher": 25,
          "label": "AE",
          "exception_token_cost": 1,
          "freed_corpus_positions": 67
        },
        {
          "group": "4",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 54
        },
        {
          "group": "4",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 2,
          "freed_corpus_positions": 68
        },
        {
          "group": "5",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 37
        },
        {
          "group": "5",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 1,
          "freed_corpus_positions": 38
        },
        {
          "group": "5",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 25
        },
        {
          "group": "5",
          "cipher": 24,
          "label": "A",
          "exception_token_cost": 1,
          "freed_corpus_positions": 41
        },
        {
          "group": "5",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 37
        },
        {
          "group": "6+8",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 154
        },
        {
          "group": "6+8",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 2,
          "freed_corpus_positions": 185
        },
        {
          "group": "6+8",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 144
        },
        {
          "group": "6+8",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 1,
          "freed_corpus_positions": 152
        },
        {
          "group": "6+8",
          "cipher": 11,
          "label": "J",
          "exception_token_cost": 2,
          "freed_corpus_positions": 186
        },
        {
          "group": "6+8",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 3,
          "freed_corpus_positions": 162
        },
        {
          "group": "6+8",
          "cipher": 15,
          "label": "S",
          "exception_token_cost": 1,
          "freed_corpus_positions": 160
        },
        {
          "group": "6+8",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 2,
          "freed_corpus_positions": 166
        },
        {
          "group": "6+8",
          "cipher": 17,
          "label": "B",
          "exception_token_cost": 1,
          "freed_corpus_positions": 184
        },
        {
          "group": "6+8",
          "cipher": 19,
          "label": "M",
          "exception_token_cost": 4,
          "freed_corpus_positions": 173
        },
        {
          "group": "6+8",
          "cipher": 20,
          "label": "L",
          "exception_token_cost": 2,
          "freed_corpus_positions": 164
        },
        {
          "group": "6+8",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 2,
          "freed_corpus_positions": 164
        },
        {
          "group": "6+8",
          "cipher": 22,
          "label": "OE",
          "exception_token_cost": 2,
          "freed_corpus_positions": 187
        },
        {
          "group": "6+8",
          "cipher": 24,
          "label": "A",
          "exception_token_cost": 1,
          "freed_corpus_positions": 180
        },
        {
          "group": "6+8",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 170
        },
        {
          "group": "6+8",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 1,
          "freed_corpus_positions": 159
        },
        {
          "group": "7",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 50
        },
        {
          "group": "7",
          "cipher": 4,
          "label": "R",
          "exception_token_cost": 1,
          "freed_corpus_positions": 54
        },
        {
          "group": "7",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 55
        },
        {
          "group": "7",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 1,
          "freed_corpus_positions": 57
        },
        {
          "group": "7",
          "cipher": 12,
          "label": "EO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 47
        },
        {
          "group": "7",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 1,
          "freed_corpus_positions": 51
        },
        {
          "group": "7",
          "cipher": 18,
          "label": "E",
          "exception_token_cost": 1,
          "freed_corpus_positions": 47
        },
        {
          "group": "7",
          "cipher": 22,
          "label": "OE",
          "exception_token_cost": 1,
          "freed_corpus_positions": 63
        },
        {
          "group": "7",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 56
        }
      ],
      "maximum_position_release_by_exact_exception_cost": [
        0,
        184,
        364,
        534,
        694,
        853,
        1007,
        1159,
        1303,
        1381,
        1490,
        1568,
        1676,
        1754,
        1861,
        1939,
        2027,
        2105,
        2191,
        2269,
        2355,
        2433,
        2508,
        2580,
        2650,
        2719,
        2788,
        2855,
        2918,
        2979,
        3040,
        3098,
        3155,
        3211,
        3266,
        3321,
        3375,
        3429,
        3483,
        3537,
        3591,
        3642,
        3692,
        3742,
        3789,
        3836,
        3882,
        3926,
        3968,
        4010,
        4055,
        4099,
        4141,
        4183,
        4224,
        4263,
        4301,
        4338,
        4375,
        4411,
        4448,
        4482,
        4516,
        4550,
        4584,
        4614,
        4648,
        4678,
        4711,
        4741,
        4771,
        4801,
        4829,
        4858,
        4886,
        4914,
        4939,
        4962,
        4983,
        5000,
        5021,
        5033,
        5050,
        5071
      ],
      "singleton_sensitivity": "all_audited",
      "allowed_letters": "AIO",
      "requirements": {
        "pooled": {
          "reference_ratio": [
            431,
            1963
          ],
          "maximum_allowed_positions": 2844,
          "required_position_release": 2227,
          "minimum_exception_tokens": 19,
          "freed_constraint_types": 14,
          "witness_units": [
            {
              "group": "2",
              "cipher": 14,
              "label": "X",
              "exception_token_cost": 1,
              "freed_corpus_positions": 78
            },
            {
              "group": "6+8",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 154
            },
            {
              "group": "6+8",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 2,
              "freed_corpus_positions": 185
            },
            {
              "group": "6+8",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 144
            },
            {
              "group": "6+8",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 1,
              "freed_corpus_positions": 152
            },
            {
              "group": "6+8",
              "cipher": 11,
              "label": "J",
              "exception_token_cost": 2,
              "freed_corpus_positions": 186
            },
            {
              "group": "6+8",
              "cipher": 15,
              "label": "S",
              "exception_token_cost": 1,
              "freed_corpus_positions": 160
            },
            {
              "group": "6+8",
              "cipher": 16,
              "label": "T",
              "exception_token_cost": 2,
              "freed_corpus_positions": 166
            },
            {
              "group": "6+8",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 1,
              "freed_corpus_positions": 184
            },
            {
              "group": "6+8",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 2,
              "freed_corpus_positions": 164
            },
            {
              "group": "6+8",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 2,
              "freed_corpus_positions": 187
            },
            {
              "group": "6+8",
              "cipher": 24,
              "label": "A",
              "exception_token_cost": 1,
              "freed_corpus_positions": 180
            },
            {
              "group": "6+8",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 170
            },
            {
              "group": "6+8",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 1,
              "freed_corpus_positions": 159
            }
          ],
          "remaining_forced_positions": 2802,
          "remaining_forced_share": 0.21627045384377894,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        },
        "largest_individual": {
          "reference_ratio": [
            185,
            778
          ],
          "maximum_allowed_positions": 3080,
          "required_position_release": 1991,
          "minimum_exception_tokens": 16,
          "freed_constraint_types": 12,
          "witness_units": [
            {
              "group": "6+8",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 154
            },
            {
              "group": "6+8",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 2,
              "freed_corpus_positions": 185
            },
            {
              "group": "6+8",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 144
            },
            {
              "group": "6+8",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 1,
              "freed_corpus_positions": 152
            },
            {
              "group": "6+8",
              "cipher": 11,
              "label": "J",
              "exception_token_cost": 2,
              "freed_corpus_positions": 186
            },
            {
              "group": "6+8",
              "cipher": 15,
              "label": "S",
              "exception_token_cost": 1,
              "freed_corpus_positions": 160
            },
            {
              "group": "6+8",
              "cipher": 16,
              "label": "T",
              "exception_token_cost": 2,
              "freed_corpus_positions": 166
            },
            {
              "group": "6+8",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 1,
              "freed_corpus_positions": 184
            },
            {
              "group": "6+8",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 2,
              "freed_corpus_positions": 187
            },
            {
              "group": "6+8",
              "cipher": 24,
              "label": "A",
              "exception_token_cost": 1,
              "freed_corpus_positions": 180
            },
            {
              "group": "6+8",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 170
            },
            {
              "group": "6+8",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 1,
              "freed_corpus_positions": 159
            }
          ],
          "remaining_forced_positions": 3044,
          "remaining_forced_share": 0.234949058351343,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        }
      }
    },
    {
      "runes": 12956,
      "key_scope": "shared",
      "allowed_output_types": 2,
      "singleton_tokens": 81,
      "forced_positions": 12513,
      "minimum_allowed_letter_share": 0.9658073479468972,
      "groups": [
        {
          "group": "all",
          "sections": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8
          ],
          "runes": 12956,
          "singleton_tokens": 81,
          "singleton_cipher_types": 28,
          "active_cipher_types": 29,
          "forced_positions": 12513,
          "maximum_distinct_output_runes": 3,
          "cipher_histogram": [
            458,
            450,
            455,
            458,
            424,
            443,
            438,
            401,
            414,
            446,
            471,
            450,
            399,
            445,
            458,
            434,
            442,
            445,
            439,
            436,
            460,
            454,
            492,
            439,
            482,
            445,
            448,
            470,
            460
          ],
          "singleton_counts_by_cipher_type": [
            1,
            3,
            3,
            3,
            3,
            0,
            3,
            4,
            4,
            4,
            5,
            3,
            1,
            5,
            1,
            2,
            5,
            3,
            1,
            4,
            2,
            3,
            3,
            3,
            1,
            1,
            5,
            1,
            4
          ]
        }
      ],
      "constraint_units": [
        {
          "group": "all",
          "cipher": 0,
          "label": "F",
          "exception_token_cost": 1,
          "freed_corpus_positions": 458
        },
        {
          "group": "all",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 3,
          "freed_corpus_positions": 450
        },
        {
          "group": "all",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 3,
          "freed_corpus_positions": 455
        },
        {
          "group": "all",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 3,
          "freed_corpus_positions": 458
        },
        {
          "group": "all",
          "cipher": 4,
          "label": "R",
          "exception_token_cost": 3,
          "freed_corpus_positions": 424
        },
        {
          "group": "all",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 3,
          "freed_corpus_positions": 438
        },
        {
          "group": "all",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 4,
          "freed_corpus_positions": 401
        },
        {
          "group": "all",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 4,
          "freed_corpus_positions": 414
        },
        {
          "group": "all",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 4,
          "freed_corpus_positions": 446
        },
        {
          "group": "all",
          "cipher": 10,
          "label": "I",
          "exception_token_cost": 5,
          "freed_corpus_positions": 471
        },
        {
          "group": "all",
          "cipher": 11,
          "label": "J",
          "exception_token_cost": 3,
          "freed_corpus_positions": 450
        },
        {
          "group": "all",
          "cipher": 12,
          "label": "EO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 399
        },
        {
          "group": "all",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 5,
          "freed_corpus_positions": 445
        },
        {
          "group": "all",
          "cipher": 14,
          "label": "X",
          "exception_token_cost": 1,
          "freed_corpus_positions": 458
        },
        {
          "group": "all",
          "cipher": 15,
          "label": "S",
          "exception_token_cost": 2,
          "freed_corpus_positions": 434
        },
        {
          "group": "all",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 5,
          "freed_corpus_positions": 442
        },
        {
          "group": "all",
          "cipher": 17,
          "label": "B",
          "exception_token_cost": 3,
          "freed_corpus_positions": 445
        },
        {
          "group": "all",
          "cipher": 18,
          "label": "E",
          "exception_token_cost": 1,
          "freed_corpus_positions": 439
        },
        {
          "group": "all",
          "cipher": 19,
          "label": "M",
          "exception_token_cost": 4,
          "freed_corpus_positions": 436
        },
        {
          "group": "all",
          "cipher": 20,
          "label": "L",
          "exception_token_cost": 2,
          "freed_corpus_positions": 460
        },
        {
          "group": "all",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 3,
          "freed_corpus_positions": 454
        },
        {
          "group": "all",
          "cipher": 22,
          "label": "OE",
          "exception_token_cost": 3,
          "freed_corpus_positions": 492
        },
        {
          "group": "all",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 3,
          "freed_corpus_positions": 439
        },
        {
          "group": "all",
          "cipher": 24,
          "label": "A",
          "exception_token_cost": 1,
          "freed_corpus_positions": 482
        },
        {
          "group": "all",
          "cipher": 25,
          "label": "AE",
          "exception_token_cost": 1,
          "freed_corpus_positions": 445
        },
        {
          "group": "all",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 5,
          "freed_corpus_positions": 448
        },
        {
          "group": "all",
          "cipher": 27,
          "label": "IO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 470
        },
        {
          "group": "all",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 4,
          "freed_corpus_positions": 460
        }
      ],
      "maximum_position_release_by_exact_exception_cost": [
        0,
        482,
        952,
        1410,
        1868,
        2313,
        2752,
        3151,
        3212,
        3611,
        3646,
        4045,
        4103,
        4138,
        4537,
        4561,
        4596,
        4995,
        5016,
        5051,
        5450,
        5470,
        5505,
        5904,
        5920,
        5955,
        6354,
        6370,
        6405,
        6804,
        6815,
        6850,
        7249,
        7264,
        7289,
        7688,
        7709,
        7727,
        8126,
        8148,
        8159,
        8550,
        8586,
        8597,
        8619,
        9010,
        9032,
        9057,
        9065,
        9456,
        9481,
        9503,
        9505,
        9892,
        9927,
        9939,
        9951,
        10306,
        10363,
        10375,
        10387,
        10707,
        10777,
        10811,
        10820,
        10832,
        11178,
        11225,
        11256,
        11262,
        11274,
        11626,
        11670,
        11698,
        11688,
        11678,
        12071,
        12112,
        12089,
        12079,
        12114,
        12513
      ],
      "singleton_sensitivity": "exclude_red_initials",
      "allowed_letters": "AI",
      "requirements": {
        "pooled": {
          "reference_ratio": [
            241,
            1963
          ],
          "maximum_allowed_positions": 1590,
          "required_position_release": 10923,
          "minimum_exception_tokens": 66,
          "freed_constraint_types": 25,
          "witness_units": [
            {
              "group": "all",
              "cipher": 0,
              "label": "F",
              "exception_token_cost": 1,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 3,
              "freed_corpus_positions": 450
            },
            {
              "group": "all",
              "cipher": 2,
              "label": "TH",
              "exception_token_cost": 3,
              "freed_corpus_positions": 455
            },
            {
              "group": "all",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 3,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 4,
              "label": "R",
              "exception_token_cost": 3,
              "freed_corpus_positions": 424
            },
            {
              "group": "all",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 3,
              "freed_corpus_positions": 438
            },
            {
              "group": "all",
              "cipher": 7,
              "label": "W",
              "exception_token_cost": 4,
              "freed_corpus_positions": 401
            },
            {
              "group": "all",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 4,
              "freed_corpus_positions": 414
            },
            {
              "group": "all",
              "cipher": 9,
              "label": "N",
              "exception_token_cost": 4,
              "freed_corpus_positions": 446
            },
            {
              "group": "all",
              "cipher": 10,
              "label": "I",
              "exception_token_cost": 5,
              "freed_corpus_positions": 471
            },
            {
              "group": "all",
              "cipher": 11,
              "label": "J",
              "exception_token_cost": 3,
              "freed_corpus_positions": 450
            },
            {
              "group": "all",
              "cipher": 12,
              "label": "EO",
              "exception_token_cost": 1,
              "freed_corpus_positions": 399
            },
            {
              "group": "all",
              "cipher": 14,
              "label": "X",
              "exception_token_cost": 1,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 15,
              "label": "S",
              "exception_token_cost": 2,
              "freed_corpus_positions": 434
            },
            {
              "group": "all",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 3,
              "freed_corpus_positions": 445
            },
            {
              "group": "all",
              "cipher": 18,
              "label": "E",
              "exception_token_cost": 1,
              "freed_corpus_positions": 439
            },
            {
              "group": "all",
              "cipher": 19,
              "label": "M",
              "exception_token_cost": 4,
              "freed_corpus_positions": 436
            },
            {
              "group": "all",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 2,
              "freed_corpus_positions": 460
            },
            {
              "group": "all",
              "cipher": 21,
              "label": "ING",
              "exception_token_cost": 3,
              "freed_corpus_positions": 454
            },
            {
              "group": "all",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 3,
              "freed_corpus_positions": 492
            },
            {
              "group": "all",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 3,
              "freed_corpus_positions": 439
            },
            {
              "group": "all",
              "cipher": 24,
              "label": "A",
              "exception_token_cost": 1,
              "freed_corpus_positions": 482
            },
            {
              "group": "all",
              "cipher": 25,
              "label": "AE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 445
            },
            {
              "group": "all",
              "cipher": 27,
              "label": "IO",
              "exception_token_cost": 1,
              "freed_corpus_positions": 470
            },
            {
              "group": "all",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 4,
              "freed_corpus_positions": 460
            }
          ],
          "remaining_forced_positions": 1335,
          "remaining_forced_share": 0.10304106205619018,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        },
        "largest_individual": {
          "reference_ratio": [
            54,
            389
          ],
          "maximum_allowed_positions": 1798,
          "required_position_release": 10715,
          "minimum_exception_tokens": 62,
          "freed_constraint_types": 24,
          "witness_units": [
            {
              "group": "all",
              "cipher": 0,
              "label": "F",
              "exception_token_cost": 1,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 3,
              "freed_corpus_positions": 450
            },
            {
              "group": "all",
              "cipher": 2,
              "label": "TH",
              "exception_token_cost": 3,
              "freed_corpus_positions": 455
            },
            {
              "group": "all",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 3,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 4,
              "label": "R",
              "exception_token_cost": 3,
              "freed_corpus_positions": 424
            },
            {
              "group": "all",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 3,
              "freed_corpus_positions": 438
            },
            {
              "group": "all",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 4,
              "freed_corpus_positions": 414
            },
            {
              "group": "all",
              "cipher": 9,
              "label": "N",
              "exception_token_cost": 4,
              "freed_corpus_positions": 446
            },
            {
              "group": "all",
              "cipher": 10,
              "label": "I",
              "exception_token_cost": 5,
              "freed_corpus_positions": 471
            },
            {
              "group": "all",
              "cipher": 11,
              "label": "J",
              "exception_token_cost": 3,
              "freed_corpus_positions": 450
            },
            {
              "group": "all",
              "cipher": 12,
              "label": "EO",
              "exception_token_cost": 1,
              "freed_corpus_positions": 399
            },
            {
              "group": "all",
              "cipher": 14,
              "label": "X",
              "exception_token_cost": 1,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 15,
              "label": "S",
              "exception_token_cost": 2,
              "freed_corpus_positions": 434
            },
            {
              "group": "all",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 3,
              "freed_corpus_positions": 445
            },
            {
              "group": "all",
              "cipher": 18,
              "label": "E",
              "exception_token_cost": 1,
              "freed_corpus_positions": 439
            },
            {
              "group": "all",
              "cipher": 19,
              "label": "M",
              "exception_token_cost": 4,
              "freed_corpus_positions": 436
            },
            {
              "group": "all",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 2,
              "freed_corpus_positions": 460
            },
            {
              "group": "all",
              "cipher": 21,
              "label": "ING",
              "exception_token_cost": 3,
              "freed_corpus_positions": 454
            },
            {
              "group": "all",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 3,
              "freed_corpus_positions": 492
            },
            {
              "group": "all",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 3,
              "freed_corpus_positions": 439
            },
            {
              "group": "all",
              "cipher": 24,
              "label": "A",
              "exception_token_cost": 1,
              "freed_corpus_positions": 482
            },
            {
              "group": "all",
              "cipher": 25,
              "label": "AE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 445
            },
            {
              "group": "all",
              "cipher": 27,
              "label": "IO",
              "exception_token_cost": 1,
              "freed_corpus_positions": 470
            },
            {
              "group": "all",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 4,
              "freed_corpus_positions": 460
            }
          ],
          "remaining_forced_positions": 1736,
          "remaining_forced_share": 0.13399197283112071,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        }
      }
    },
    {
      "runes": 12956,
      "key_scope": "shared",
      "allowed_output_types": 3,
      "singleton_tokens": 81,
      "forced_positions": 12513,
      "minimum_allowed_letter_share": 0.9658073479468972,
      "groups": [
        {
          "group": "all",
          "sections": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8
          ],
          "runes": 12956,
          "singleton_tokens": 81,
          "singleton_cipher_types": 28,
          "active_cipher_types": 29,
          "forced_positions": 12513,
          "maximum_distinct_output_runes": 4,
          "cipher_histogram": [
            458,
            450,
            455,
            458,
            424,
            443,
            438,
            401,
            414,
            446,
            471,
            450,
            399,
            445,
            458,
            434,
            442,
            445,
            439,
            436,
            460,
            454,
            492,
            439,
            482,
            445,
            448,
            470,
            460
          ],
          "singleton_counts_by_cipher_type": [
            1,
            3,
            3,
            3,
            3,
            0,
            3,
            4,
            4,
            4,
            5,
            3,
            1,
            5,
            1,
            2,
            5,
            3,
            1,
            4,
            2,
            3,
            3,
            3,
            1,
            1,
            5,
            1,
            4
          ]
        }
      ],
      "constraint_units": [
        {
          "group": "all",
          "cipher": 0,
          "label": "F",
          "exception_token_cost": 1,
          "freed_corpus_positions": 458
        },
        {
          "group": "all",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 3,
          "freed_corpus_positions": 450
        },
        {
          "group": "all",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 3,
          "freed_corpus_positions": 455
        },
        {
          "group": "all",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 3,
          "freed_corpus_positions": 458
        },
        {
          "group": "all",
          "cipher": 4,
          "label": "R",
          "exception_token_cost": 3,
          "freed_corpus_positions": 424
        },
        {
          "group": "all",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 3,
          "freed_corpus_positions": 438
        },
        {
          "group": "all",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 4,
          "freed_corpus_positions": 401
        },
        {
          "group": "all",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 4,
          "freed_corpus_positions": 414
        },
        {
          "group": "all",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 4,
          "freed_corpus_positions": 446
        },
        {
          "group": "all",
          "cipher": 10,
          "label": "I",
          "exception_token_cost": 5,
          "freed_corpus_positions": 471
        },
        {
          "group": "all",
          "cipher": 11,
          "label": "J",
          "exception_token_cost": 3,
          "freed_corpus_positions": 450
        },
        {
          "group": "all",
          "cipher": 12,
          "label": "EO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 399
        },
        {
          "group": "all",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 5,
          "freed_corpus_positions": 445
        },
        {
          "group": "all",
          "cipher": 14,
          "label": "X",
          "exception_token_cost": 1,
          "freed_corpus_positions": 458
        },
        {
          "group": "all",
          "cipher": 15,
          "label": "S",
          "exception_token_cost": 2,
          "freed_corpus_positions": 434
        },
        {
          "group": "all",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 5,
          "freed_corpus_positions": 442
        },
        {
          "group": "all",
          "cipher": 17,
          "label": "B",
          "exception_token_cost": 3,
          "freed_corpus_positions": 445
        },
        {
          "group": "all",
          "cipher": 18,
          "label": "E",
          "exception_token_cost": 1,
          "freed_corpus_positions": 439
        },
        {
          "group": "all",
          "cipher": 19,
          "label": "M",
          "exception_token_cost": 4,
          "freed_corpus_positions": 436
        },
        {
          "group": "all",
          "cipher": 20,
          "label": "L",
          "exception_token_cost": 2,
          "freed_corpus_positions": 460
        },
        {
          "group": "all",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 3,
          "freed_corpus_positions": 454
        },
        {
          "group": "all",
          "cipher": 22,
          "label": "OE",
          "exception_token_cost": 3,
          "freed_corpus_positions": 492
        },
        {
          "group": "all",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 3,
          "freed_corpus_positions": 439
        },
        {
          "group": "all",
          "cipher": 24,
          "label": "A",
          "exception_token_cost": 1,
          "freed_corpus_positions": 482
        },
        {
          "group": "all",
          "cipher": 25,
          "label": "AE",
          "exception_token_cost": 1,
          "freed_corpus_positions": 445
        },
        {
          "group": "all",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 5,
          "freed_corpus_positions": 448
        },
        {
          "group": "all",
          "cipher": 27,
          "label": "IO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 470
        },
        {
          "group": "all",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 4,
          "freed_corpus_positions": 460
        }
      ],
      "maximum_position_release_by_exact_exception_cost": [
        0,
        482,
        952,
        1410,
        1868,
        2313,
        2752,
        3151,
        3212,
        3611,
        3646,
        4045,
        4103,
        4138,
        4537,
        4561,
        4596,
        4995,
        5016,
        5051,
        5450,
        5470,
        5505,
        5904,
        5920,
        5955,
        6354,
        6370,
        6405,
        6804,
        6815,
        6850,
        7249,
        7264,
        7289,
        7688,
        7709,
        7727,
        8126,
        8148,
        8159,
        8550,
        8586,
        8597,
        8619,
        9010,
        9032,
        9057,
        9065,
        9456,
        9481,
        9503,
        9505,
        9892,
        9927,
        9939,
        9951,
        10306,
        10363,
        10375,
        10387,
        10707,
        10777,
        10811,
        10820,
        10832,
        11178,
        11225,
        11256,
        11262,
        11274,
        11626,
        11670,
        11698,
        11688,
        11678,
        12071,
        12112,
        12089,
        12079,
        12114,
        12513
      ],
      "singleton_sensitivity": "exclude_red_initials",
      "allowed_letters": "AIO",
      "requirements": {
        "pooled": {
          "reference_ratio": [
            431,
            1963
          ],
          "maximum_allowed_positions": 2844,
          "required_position_release": 9669,
          "minimum_exception_tokens": 53,
          "freed_constraint_types": 22,
          "witness_units": [
            {
              "group": "all",
              "cipher": 0,
              "label": "F",
              "exception_token_cost": 1,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 3,
              "freed_corpus_positions": 450
            },
            {
              "group": "all",
              "cipher": 2,
              "label": "TH",
              "exception_token_cost": 3,
              "freed_corpus_positions": 455
            },
            {
              "group": "all",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 3,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 4,
              "label": "R",
              "exception_token_cost": 3,
              "freed_corpus_positions": 424
            },
            {
              "group": "all",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 3,
              "freed_corpus_positions": 438
            },
            {
              "group": "all",
              "cipher": 9,
              "label": "N",
              "exception_token_cost": 4,
              "freed_corpus_positions": 446
            },
            {
              "group": "all",
              "cipher": 11,
              "label": "J",
              "exception_token_cost": 3,
              "freed_corpus_positions": 450
            },
            {
              "group": "all",
              "cipher": 12,
              "label": "EO",
              "exception_token_cost": 1,
              "freed_corpus_positions": 399
            },
            {
              "group": "all",
              "cipher": 14,
              "label": "X",
              "exception_token_cost": 1,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 15,
              "label": "S",
              "exception_token_cost": 2,
              "freed_corpus_positions": 434
            },
            {
              "group": "all",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 3,
              "freed_corpus_positions": 445
            },
            {
              "group": "all",
              "cipher": 18,
              "label": "E",
              "exception_token_cost": 1,
              "freed_corpus_positions": 439
            },
            {
              "group": "all",
              "cipher": 19,
              "label": "M",
              "exception_token_cost": 4,
              "freed_corpus_positions": 436
            },
            {
              "group": "all",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 2,
              "freed_corpus_positions": 460
            },
            {
              "group": "all",
              "cipher": 21,
              "label": "ING",
              "exception_token_cost": 3,
              "freed_corpus_positions": 454
            },
            {
              "group": "all",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 3,
              "freed_corpus_positions": 492
            },
            {
              "group": "all",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 3,
              "freed_corpus_positions": 439
            },
            {
              "group": "all",
              "cipher": 24,
              "label": "A",
              "exception_token_cost": 1,
              "freed_corpus_positions": 482
            },
            {
              "group": "all",
              "cipher": 25,
              "label": "AE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 445
            },
            {
              "group": "all",
              "cipher": 27,
              "label": "IO",
              "exception_token_cost": 1,
              "freed_corpus_positions": 470
            },
            {
              "group": "all",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 4,
              "freed_corpus_positions": 460
            }
          ],
          "remaining_forced_positions": 2621,
          "remaining_forced_share": 0.20230009262117937,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        },
        "largest_individual": {
          "reference_ratio": [
            185,
            778
          ],
          "maximum_allowed_positions": 3080,
          "required_position_release": 9433,
          "minimum_exception_tokens": 49,
          "freed_constraint_types": 21,
          "witness_units": [
            {
              "group": "all",
              "cipher": 0,
              "label": "F",
              "exception_token_cost": 1,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 3,
              "freed_corpus_positions": 450
            },
            {
              "group": "all",
              "cipher": 2,
              "label": "TH",
              "exception_token_cost": 3,
              "freed_corpus_positions": 455
            },
            {
              "group": "all",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 3,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 4,
              "label": "R",
              "exception_token_cost": 3,
              "freed_corpus_positions": 424
            },
            {
              "group": "all",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 3,
              "freed_corpus_positions": 438
            },
            {
              "group": "all",
              "cipher": 9,
              "label": "N",
              "exception_token_cost": 4,
              "freed_corpus_positions": 446
            },
            {
              "group": "all",
              "cipher": 11,
              "label": "J",
              "exception_token_cost": 3,
              "freed_corpus_positions": 450
            },
            {
              "group": "all",
              "cipher": 12,
              "label": "EO",
              "exception_token_cost": 1,
              "freed_corpus_positions": 399
            },
            {
              "group": "all",
              "cipher": 14,
              "label": "X",
              "exception_token_cost": 1,
              "freed_corpus_positions": 458
            },
            {
              "group": "all",
              "cipher": 15,
              "label": "S",
              "exception_token_cost": 2,
              "freed_corpus_positions": 434
            },
            {
              "group": "all",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 3,
              "freed_corpus_positions": 445
            },
            {
              "group": "all",
              "cipher": 18,
              "label": "E",
              "exception_token_cost": 1,
              "freed_corpus_positions": 439
            },
            {
              "group": "all",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 2,
              "freed_corpus_positions": 460
            },
            {
              "group": "all",
              "cipher": 21,
              "label": "ING",
              "exception_token_cost": 3,
              "freed_corpus_positions": 454
            },
            {
              "group": "all",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 3,
              "freed_corpus_positions": 492
            },
            {
              "group": "all",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 3,
              "freed_corpus_positions": 439
            },
            {
              "group": "all",
              "cipher": 24,
              "label": "A",
              "exception_token_cost": 1,
              "freed_corpus_positions": 482
            },
            {
              "group": "all",
              "cipher": 25,
              "label": "AE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 445
            },
            {
              "group": "all",
              "cipher": 27,
              "label": "IO",
              "exception_token_cost": 1,
              "freed_corpus_positions": 470
            },
            {
              "group": "all",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 4,
              "freed_corpus_positions": 460
            }
          ],
          "remaining_forced_positions": 3057,
          "remaining_forced_share": 0.23595245446125349,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        }
      }
    },
    {
      "runes": 12956,
      "key_scope": "per_section",
      "allowed_output_types": 2,
      "singleton_tokens": 81,
      "forced_positions": 4148,
      "minimum_allowed_letter_share": 0.32016054337758565,
      "groups": [
        {
          "group": "0",
          "sections": [
            0
          ],
          "runes": 729,
          "singleton_tokens": 5,
          "singleton_cipher_types": 5,
          "active_cipher_types": 29,
          "forced_positions": 134,
          "maximum_distinct_output_runes": 26,
          "cipher_histogram": [
            34,
            21,
            30,
            20,
            22,
            28,
            29,
            22,
            30,
            28,
            24,
            24,
            17,
            27,
            28,
            23,
            23,
            23,
            24,
            18,
            30,
            29,
            25,
            31,
            19,
            24,
            25,
            23,
            28
          ],
          "singleton_counts_by_cipher_type": [
            1,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1
          ]
        },
        {
          "group": "1",
          "sections": [
            1
          ],
          "runes": 1145,
          "singleton_tokens": 7,
          "singleton_cipher_types": 6,
          "active_cipher_types": 29,
          "forced_positions": 232,
          "maximum_distinct_output_runes": 25,
          "cipher_histogram": [
            26,
            34,
            34,
            30,
            36,
            52,
            43,
            30,
            38,
            37,
            43,
            43,
            49,
            44,
            49,
            34,
            37,
            31,
            32,
            39,
            50,
            42,
            40,
            38,
            35,
            41,
            42,
            46,
            50
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            1,
            2,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            1,
            1,
            0
          ]
        },
        {
          "group": "2",
          "sections": [
            2
          ],
          "runes": 1729,
          "singleton_tokens": 11,
          "singleton_cipher_types": 9,
          "active_cipher_types": 29,
          "forced_positions": 545,
          "maximum_distinct_output_runes": 22,
          "cipher_histogram": [
            66,
            69,
            69,
            61,
            50,
            63,
            58,
            55,
            52,
            69,
            50,
            44,
            52,
            55,
            78,
            61,
            61,
            55,
            56,
            57,
            63,
            58,
            67,
            51,
            64,
            52,
            61,
            68,
            64
          ],
          "singleton_counts_by_cipher_type": [
            0,
            1,
            0,
            1,
            0,
            0,
            1,
            1,
            0,
            1,
            3,
            1,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0
          ]
        },
        {
          "group": "3",
          "sections": [
            3
          ],
          "runes": 9,
          "singleton_tokens": 0,
          "singleton_cipher_types": 0,
          "active_cipher_types": 8,
          "forced_positions": 0,
          "maximum_distinct_output_runes": 8,
          "cipher_histogram": [
            1,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            0,
            1,
            0,
            2,
            0,
            1,
            0,
            1
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0
          ]
        },
        {
          "group": "4",
          "sections": [
            4
          ],
          "runes": 1894,
          "singleton_tokens": 18,
          "singleton_cipher_types": 12,
          "active_cipher_types": 29,
          "forced_positions": 773,
          "maximum_distinct_output_runes": 19,
          "cipher_histogram": [
            71,
            63,
            75,
            75,
            64,
            70,
            71,
            50,
            52,
            57,
            73,
            76,
            52,
            72,
            63,
            56,
            60,
            63,
            54,
            62,
            63,
            69,
            74,
            70,
            73,
            67,
            54,
            77,
            68
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            2,
            0,
            0,
            1,
            0,
            2,
            2,
            0,
            0,
            1,
            0,
            0,
            2,
            2,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            1,
            1,
            0,
            2
          ]
        },
        {
          "group": "5",
          "sections": [
            5
          ],
          "runes": 1021,
          "singleton_tokens": 5,
          "singleton_cipher_types": 5,
          "active_cipher_types": 29,
          "forced_positions": 178,
          "maximum_distinct_output_runes": 26,
          "cipher_histogram": [
            37,
            44,
            37,
            40,
            34,
            30,
            37,
            33,
            33,
            39,
            35,
            27,
            21,
            34,
            32,
            43,
            38,
            37,
            42,
            32,
            34,
            37,
            35,
            25,
            41,
            31,
            37,
            35,
            41
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            0,
            1,
            0,
            0
          ]
        },
        {
          "group": "6",
          "sections": [
            6
          ],
          "runes": 1524,
          "singleton_tokens": 12,
          "singleton_cipher_types": 8,
          "active_cipher_types": 29,
          "forced_positions": 421,
          "maximum_distinct_output_runes": 23,
          "cipher_histogram": [
            55,
            45,
            50,
            53,
            57,
            40,
            47,
            61,
            52,
            43,
            58,
            56,
            48,
            51,
            47,
            49,
            50,
            64,
            58,
            54,
            55,
            51,
            56,
            60,
            57,
            50,
            48,
            56,
            53
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            2,
            0,
            2,
            0,
            1,
            0,
            0,
            0,
            3,
            1,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0
          ]
        },
        {
          "group": "7",
          "sections": [
            7
          ],
          "runes": 1589,
          "singleton_tokens": 9,
          "singleton_cipher_types": 9,
          "active_cipher_types": 29,
          "forced_positions": 480,
          "maximum_distinct_output_runes": 22,
          "cipher_histogram": [
            37,
            64,
            50,
            47,
            54,
            61,
            56,
            55,
            57,
            59,
            66,
            50,
            47,
            51,
            55,
            57,
            57,
            52,
            47,
            54,
            55,
            55,
            63,
            56,
            68,
            60,
            58,
            49,
            49
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            1,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            0,
            0
          ]
        },
        {
          "group": "8",
          "sections": [
            8
          ],
          "runes": 3316,
          "singleton_tokens": 14,
          "singleton_cipher_types": 12,
          "active_cipher_types": 29,
          "forced_positions": 1385,
          "maximum_distinct_output_runes": 19,
          "cipher_histogram": [
            131,
            109,
            110,
            132,
            107,
            99,
            97,
            95,
            100,
            114,
            122,
            130,
            113,
            111,
            106,
            111,
            116,
            120,
            126,
            119,
            109,
            113,
            131,
            108,
            123,
            120,
            122,
            116,
            106
          ],
          "singleton_counts_by_cipher_type": [
            0,
            1,
            0,
            1,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            2,
            1,
            0,
            1,
            1,
            1,
            2,
            0,
            0,
            0,
            1,
            0,
            1
          ]
        }
      ],
      "constraint_units": [
        {
          "group": "0",
          "cipher": 0,
          "label": "F",
          "exception_token_cost": 1,
          "freed_corpus_positions": 34
        },
        {
          "group": "0",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 21
        },
        {
          "group": "0",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 1,
          "freed_corpus_positions": 28
        },
        {
          "group": "0",
          "cipher": 15,
          "label": "S",
          "exception_token_cost": 1,
          "freed_corpus_positions": 23
        },
        {
          "group": "0",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 1,
          "freed_corpus_positions": 28
        },
        {
          "group": "1",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 34
        },
        {
          "group": "1",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 30
        },
        {
          "group": "1",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 2,
          "freed_corpus_positions": 38
        },
        {
          "group": "1",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 1,
          "freed_corpus_positions": 42
        },
        {
          "group": "1",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 42
        },
        {
          "group": "1",
          "cipher": 27,
          "label": "IO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 46
        },
        {
          "group": "2",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 69
        },
        {
          "group": "2",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 1,
          "freed_corpus_positions": 61
        },
        {
          "group": "2",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 58
        },
        {
          "group": "2",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 55
        },
        {
          "group": "2",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 1,
          "freed_corpus_positions": 69
        },
        {
          "group": "2",
          "cipher": 10,
          "label": "I",
          "exception_token_cost": 3,
          "freed_corpus_positions": 50
        },
        {
          "group": "2",
          "cipher": 11,
          "label": "J",
          "exception_token_cost": 1,
          "freed_corpus_positions": 44
        },
        {
          "group": "2",
          "cipher": 14,
          "label": "X",
          "exception_token_cost": 1,
          "freed_corpus_positions": 78
        },
        {
          "group": "2",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 61
        },
        {
          "group": "4",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 75
        },
        {
          "group": "4",
          "cipher": 4,
          "label": "R",
          "exception_token_cost": 2,
          "freed_corpus_positions": 64
        },
        {
          "group": "4",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 50
        },
        {
          "group": "4",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 2,
          "freed_corpus_positions": 57
        },
        {
          "group": "4",
          "cipher": 10,
          "label": "I",
          "exception_token_cost": 2,
          "freed_corpus_positions": 73
        },
        {
          "group": "4",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 1,
          "freed_corpus_positions": 72
        },
        {
          "group": "4",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 2,
          "freed_corpus_positions": 60
        },
        {
          "group": "4",
          "cipher": 17,
          "label": "B",
          "exception_token_cost": 2,
          "freed_corpus_positions": 63
        },
        {
          "group": "4",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 70
        },
        {
          "group": "4",
          "cipher": 25,
          "label": "AE",
          "exception_token_cost": 1,
          "freed_corpus_positions": 67
        },
        {
          "group": "4",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 54
        },
        {
          "group": "4",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 2,
          "freed_corpus_positions": 68
        },
        {
          "group": "5",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 37
        },
        {
          "group": "5",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 1,
          "freed_corpus_positions": 38
        },
        {
          "group": "5",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 25
        },
        {
          "group": "5",
          "cipher": 24,
          "label": "A",
          "exception_token_cost": 1,
          "freed_corpus_positions": 41
        },
        {
          "group": "5",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 37
        },
        {
          "group": "6",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 1,
          "freed_corpus_positions": 53
        },
        {
          "group": "6",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 1,
          "freed_corpus_positions": 52
        },
        {
          "group": "6",
          "cipher": 11,
          "label": "J",
          "exception_token_cost": 2,
          "freed_corpus_positions": 56
        },
        {
          "group": "6",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 2,
          "freed_corpus_positions": 51
        },
        {
          "group": "6",
          "cipher": 15,
          "label": "S",
          "exception_token_cost": 1,
          "freed_corpus_positions": 49
        },
        {
          "group": "6",
          "cipher": 19,
          "label": "M",
          "exception_token_cost": 3,
          "freed_corpus_positions": 54
        },
        {
          "group": "6",
          "cipher": 20,
          "label": "L",
          "exception_token_cost": 1,
          "freed_corpus_positions": 55
        },
        {
          "group": "6",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 1,
          "freed_corpus_positions": 51
        },
        {
          "group": "7",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 50
        },
        {
          "group": "7",
          "cipher": 4,
          "label": "R",
          "exception_token_cost": 1,
          "freed_corpus_positions": 54
        },
        {
          "group": "7",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 55
        },
        {
          "group": "7",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 1,
          "freed_corpus_positions": 57
        },
        {
          "group": "7",
          "cipher": 12,
          "label": "EO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 47
        },
        {
          "group": "7",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 1,
          "freed_corpus_positions": 51
        },
        {
          "group": "7",
          "cipher": 18,
          "label": "E",
          "exception_token_cost": 1,
          "freed_corpus_positions": 47
        },
        {
          "group": "7",
          "cipher": 22,
          "label": "OE",
          "exception_token_cost": 1,
          "freed_corpus_positions": 63
        },
        {
          "group": "7",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 56
        },
        {
          "group": "8",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 109
        },
        {
          "group": "8",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 1,
          "freed_corpus_positions": 132
        },
        {
          "group": "8",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 97
        },
        {
          "group": "8",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 1,
          "freed_corpus_positions": 111
        },
        {
          "group": "8",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 2,
          "freed_corpus_positions": 116
        },
        {
          "group": "8",
          "cipher": 17,
          "label": "B",
          "exception_token_cost": 1,
          "freed_corpus_positions": 120
        },
        {
          "group": "8",
          "cipher": 19,
          "label": "M",
          "exception_token_cost": 1,
          "freed_corpus_positions": 119
        },
        {
          "group": "8",
          "cipher": 20,
          "label": "L",
          "exception_token_cost": 1,
          "freed_corpus_positions": 109
        },
        {
          "group": "8",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 1,
          "freed_corpus_positions": 113
        },
        {
          "group": "8",
          "cipher": 22,
          "label": "OE",
          "exception_token_cost": 2,
          "freed_corpus_positions": 131
        },
        {
          "group": "8",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 122
        },
        {
          "group": "8",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 1,
          "freed_corpus_positions": 106
        }
      ],
      "maximum_position_release_by_exact_exception_cost": [
        0,
        132,
        254,
        374,
        493,
        606,
        717,
        826,
        935,
        1041,
        1138,
        1216,
        1291,
        1363,
        1433,
        1502,
        1571,
        1638,
        1702,
        1769,
        1832,
        1893,
        1954,
        2012,
        2070,
        2128,
        2185,
        2241,
        2296,
        2351,
        2406,
        2460,
        2514,
        2567,
        2619,
        2670,
        2721,
        2771,
        2821,
        2870,
        2917,
        2964,
        3010,
        3054,
        3096,
        3138,
        3179,
        3217,
        3254,
        3291,
        3327,
        3364,
        3398,
        3432,
        3466,
        3500,
        3530,
        3564,
        3594,
        3627,
        3657,
        3687,
        3717,
        3745,
        3774,
        3802,
        3830,
        3858,
        3886,
        3911,
        3937,
        3962,
        3985,
        4006,
        4023,
        4044,
        4060,
        4077,
        4098,
        4110,
        4127,
        4148
      ],
      "singleton_sensitivity": "exclude_red_initials",
      "allowed_letters": "AI",
      "requirements": {
        "pooled": {
          "reference_ratio": [
            241,
            1963
          ],
          "maximum_allowed_positions": 1590,
          "required_position_release": 2558,
          "minimum_exception_tokens": 33,
          "freed_constraint_types": 31,
          "witness_units": [
            {
              "group": "2",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 69
            },
            {
              "group": "2",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 1,
              "freed_corpus_positions": 61
            },
            {
              "group": "2",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 58
            },
            {
              "group": "2",
              "cipher": 7,
              "label": "W",
              "exception_token_cost": 1,
              "freed_corpus_positions": 55
            },
            {
              "group": "2",
              "cipher": 9,
              "label": "N",
              "exception_token_cost": 1,
              "freed_corpus_positions": 69
            },
            {
              "group": "2",
              "cipher": 14,
              "label": "X",
              "exception_token_cost": 1,
              "freed_corpus_positions": 78
            },
            {
              "group": "2",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 61
            },
            {
              "group": "4",
              "cipher": 2,
              "label": "TH",
              "exception_token_cost": 1,
              "freed_corpus_positions": 75
            },
            {
              "group": "4",
              "cipher": 13,
              "label": "P",
              "exception_token_cost": 1,
              "freed_corpus_positions": 72
            },
            {
              "group": "4",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 1,
              "freed_corpus_positions": 70
            },
            {
              "group": "4",
              "cipher": 25,
              "label": "AE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 67
            },
            {
              "group": "4",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 54
            },
            {
              "group": "6",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 1,
              "freed_corpus_positions": 53
            },
            {
              "group": "6",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 1,
              "freed_corpus_positions": 55
            },
            {
              "group": "7",
              "cipher": 4,
              "label": "R",
              "exception_token_cost": 1,
              "freed_corpus_positions": 54
            },
            {
              "group": "7",
              "cipher": 7,
              "label": "W",
              "exception_token_cost": 1,
              "freed_corpus_positions": 55
            },
            {
              "group": "7",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 1,
              "freed_corpus_positions": 57
            },
            {
              "group": "7",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 63
            },
            {
              "group": "7",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 1,
              "freed_corpus_positions": 56
            },
            {
              "group": "8",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 109
            },
            {
              "group": "8",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 1,
              "freed_corpus_positions": 132
            },
            {
              "group": "8",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 97
            },
            {
              "group": "8",
              "cipher": 13,
              "label": "P",
              "exception_token_cost": 1,
              "freed_corpus_positions": 111
            },
            {
              "group": "8",
              "cipher": 16,
              "label": "T",
              "exception_token_cost": 2,
              "freed_corpus_positions": 116
            },
            {
              "group": "8",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 1,
              "freed_corpus_positions": 120
            },
            {
              "group": "8",
              "cipher": 19,
              "label": "M",
              "exception_token_cost": 1,
              "freed_corpus_positions": 119
            },
            {
              "group": "8",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 1,
              "freed_corpus_positions": 109
            },
            {
              "group": "8",
              "cipher": 21,
              "label": "ING",
              "exception_token_cost": 1,
              "freed_corpus_positions": 113
            },
            {
              "group": "8",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 2,
              "freed_corpus_positions": 131
            },
            {
              "group": "8",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 122
            },
            {
              "group": "8",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 1,
              "freed_corpus_positions": 106
            }
          ],
          "remaining_forced_positions": 1581,
          "remaining_forced_share": 0.12202840382834208,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        },
        "largest_individual": {
          "reference_ratio": [
            54,
            389
          ],
          "maximum_allowed_positions": 1798,
          "required_position_release": 2350,
          "minimum_exception_tokens": 29,
          "freed_constraint_types": 27,
          "witness_units": [
            {
              "group": "2",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 69
            },
            {
              "group": "2",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 1,
              "freed_corpus_positions": 61
            },
            {
              "group": "2",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 58
            },
            {
              "group": "2",
              "cipher": 7,
              "label": "W",
              "exception_token_cost": 1,
              "freed_corpus_positions": 55
            },
            {
              "group": "2",
              "cipher": 9,
              "label": "N",
              "exception_token_cost": 1,
              "freed_corpus_positions": 69
            },
            {
              "group": "2",
              "cipher": 14,
              "label": "X",
              "exception_token_cost": 1,
              "freed_corpus_positions": 78
            },
            {
              "group": "2",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 61
            },
            {
              "group": "4",
              "cipher": 2,
              "label": "TH",
              "exception_token_cost": 1,
              "freed_corpus_positions": 75
            },
            {
              "group": "4",
              "cipher": 13,
              "label": "P",
              "exception_token_cost": 1,
              "freed_corpus_positions": 72
            },
            {
              "group": "4",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 1,
              "freed_corpus_positions": 70
            },
            {
              "group": "4",
              "cipher": 25,
              "label": "AE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 67
            },
            {
              "group": "6",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 1,
              "freed_corpus_positions": 55
            },
            {
              "group": "7",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 1,
              "freed_corpus_positions": 57
            },
            {
              "group": "7",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 63
            },
            {
              "group": "7",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 1,
              "freed_corpus_positions": 56
            },
            {
              "group": "8",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 109
            },
            {
              "group": "8",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 1,
              "freed_corpus_positions": 132
            },
            {
              "group": "8",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 97
            },
            {
              "group": "8",
              "cipher": 13,
              "label": "P",
              "exception_token_cost": 1,
              "freed_corpus_positions": 111
            },
            {
              "group": "8",
              "cipher": 16,
              "label": "T",
              "exception_token_cost": 2,
              "freed_corpus_positions": 116
            },
            {
              "group": "8",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 1,
              "freed_corpus_positions": 120
            },
            {
              "group": "8",
              "cipher": 19,
              "label": "M",
              "exception_token_cost": 1,
              "freed_corpus_positions": 119
            },
            {
              "group": "8",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 1,
              "freed_corpus_positions": 109
            },
            {
              "group": "8",
              "cipher": 21,
              "label": "ING",
              "exception_token_cost": 1,
              "freed_corpus_positions": 113
            },
            {
              "group": "8",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 2,
              "freed_corpus_positions": 131
            },
            {
              "group": "8",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 122
            },
            {
              "group": "8",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 1,
              "freed_corpus_positions": 106
            }
          ],
          "remaining_forced_positions": 1797,
          "remaining_forced_share": 0.1387002161160852,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        }
      }
    },
    {
      "runes": 12956,
      "key_scope": "per_section",
      "allowed_output_types": 3,
      "singleton_tokens": 81,
      "forced_positions": 4148,
      "minimum_allowed_letter_share": 0.32016054337758565,
      "groups": [
        {
          "group": "0",
          "sections": [
            0
          ],
          "runes": 729,
          "singleton_tokens": 5,
          "singleton_cipher_types": 5,
          "active_cipher_types": 29,
          "forced_positions": 134,
          "maximum_distinct_output_runes": 27,
          "cipher_histogram": [
            34,
            21,
            30,
            20,
            22,
            28,
            29,
            22,
            30,
            28,
            24,
            24,
            17,
            27,
            28,
            23,
            23,
            23,
            24,
            18,
            30,
            29,
            25,
            31,
            19,
            24,
            25,
            23,
            28
          ],
          "singleton_counts_by_cipher_type": [
            1,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1
          ]
        },
        {
          "group": "1",
          "sections": [
            1
          ],
          "runes": 1145,
          "singleton_tokens": 7,
          "singleton_cipher_types": 6,
          "active_cipher_types": 29,
          "forced_positions": 232,
          "maximum_distinct_output_runes": 26,
          "cipher_histogram": [
            26,
            34,
            34,
            30,
            36,
            52,
            43,
            30,
            38,
            37,
            43,
            43,
            49,
            44,
            49,
            34,
            37,
            31,
            32,
            39,
            50,
            42,
            40,
            38,
            35,
            41,
            42,
            46,
            50
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            1,
            2,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            1,
            1,
            0
          ]
        },
        {
          "group": "2",
          "sections": [
            2
          ],
          "runes": 1729,
          "singleton_tokens": 11,
          "singleton_cipher_types": 9,
          "active_cipher_types": 29,
          "forced_positions": 545,
          "maximum_distinct_output_runes": 23,
          "cipher_histogram": [
            66,
            69,
            69,
            61,
            50,
            63,
            58,
            55,
            52,
            69,
            50,
            44,
            52,
            55,
            78,
            61,
            61,
            55,
            56,
            57,
            63,
            58,
            67,
            51,
            64,
            52,
            61,
            68,
            64
          ],
          "singleton_counts_by_cipher_type": [
            0,
            1,
            0,
            1,
            0,
            0,
            1,
            1,
            0,
            1,
            3,
            1,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0
          ]
        },
        {
          "group": "3",
          "sections": [
            3
          ],
          "runes": 9,
          "singleton_tokens": 0,
          "singleton_cipher_types": 0,
          "active_cipher_types": 8,
          "forced_positions": 0,
          "maximum_distinct_output_runes": 8,
          "cipher_histogram": [
            1,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            0,
            1,
            0,
            2,
            0,
            1,
            0,
            1
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0
          ]
        },
        {
          "group": "4",
          "sections": [
            4
          ],
          "runes": 1894,
          "singleton_tokens": 18,
          "singleton_cipher_types": 12,
          "active_cipher_types": 29,
          "forced_positions": 773,
          "maximum_distinct_output_runes": 20,
          "cipher_histogram": [
            71,
            63,
            75,
            75,
            64,
            70,
            71,
            50,
            52,
            57,
            73,
            76,
            52,
            72,
            63,
            56,
            60,
            63,
            54,
            62,
            63,
            69,
            74,
            70,
            73,
            67,
            54,
            77,
            68
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            2,
            0,
            0,
            1,
            0,
            2,
            2,
            0,
            0,
            1,
            0,
            0,
            2,
            2,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            1,
            1,
            0,
            2
          ]
        },
        {
          "group": "5",
          "sections": [
            5
          ],
          "runes": 1021,
          "singleton_tokens": 5,
          "singleton_cipher_types": 5,
          "active_cipher_types": 29,
          "forced_positions": 178,
          "maximum_distinct_output_runes": 27,
          "cipher_histogram": [
            37,
            44,
            37,
            40,
            34,
            30,
            37,
            33,
            33,
            39,
            35,
            27,
            21,
            34,
            32,
            43,
            38,
            37,
            42,
            32,
            34,
            37,
            35,
            25,
            41,
            31,
            37,
            35,
            41
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            0,
            1,
            0,
            0
          ]
        },
        {
          "group": "6",
          "sections": [
            6
          ],
          "runes": 1524,
          "singleton_tokens": 12,
          "singleton_cipher_types": 8,
          "active_cipher_types": 29,
          "forced_positions": 421,
          "maximum_distinct_output_runes": 24,
          "cipher_histogram": [
            55,
            45,
            50,
            53,
            57,
            40,
            47,
            61,
            52,
            43,
            58,
            56,
            48,
            51,
            47,
            49,
            50,
            64,
            58,
            54,
            55,
            51,
            56,
            60,
            57,
            50,
            48,
            56,
            53
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            2,
            0,
            2,
            0,
            1,
            0,
            0,
            0,
            3,
            1,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0
          ]
        },
        {
          "group": "7",
          "sections": [
            7
          ],
          "runes": 1589,
          "singleton_tokens": 9,
          "singleton_cipher_types": 9,
          "active_cipher_types": 29,
          "forced_positions": 480,
          "maximum_distinct_output_runes": 23,
          "cipher_histogram": [
            37,
            64,
            50,
            47,
            54,
            61,
            56,
            55,
            57,
            59,
            66,
            50,
            47,
            51,
            55,
            57,
            57,
            52,
            47,
            54,
            55,
            55,
            63,
            56,
            68,
            60,
            58,
            49,
            49
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            1,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            0,
            0
          ]
        },
        {
          "group": "8",
          "sections": [
            8
          ],
          "runes": 3316,
          "singleton_tokens": 14,
          "singleton_cipher_types": 12,
          "active_cipher_types": 29,
          "forced_positions": 1385,
          "maximum_distinct_output_runes": 20,
          "cipher_histogram": [
            131,
            109,
            110,
            132,
            107,
            99,
            97,
            95,
            100,
            114,
            122,
            130,
            113,
            111,
            106,
            111,
            116,
            120,
            126,
            119,
            109,
            113,
            131,
            108,
            123,
            120,
            122,
            116,
            106
          ],
          "singleton_counts_by_cipher_type": [
            0,
            1,
            0,
            1,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            2,
            1,
            0,
            1,
            1,
            1,
            2,
            0,
            0,
            0,
            1,
            0,
            1
          ]
        }
      ],
      "constraint_units": [
        {
          "group": "0",
          "cipher": 0,
          "label": "F",
          "exception_token_cost": 1,
          "freed_corpus_positions": 34
        },
        {
          "group": "0",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 21
        },
        {
          "group": "0",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 1,
          "freed_corpus_positions": 28
        },
        {
          "group": "0",
          "cipher": 15,
          "label": "S",
          "exception_token_cost": 1,
          "freed_corpus_positions": 23
        },
        {
          "group": "0",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 1,
          "freed_corpus_positions": 28
        },
        {
          "group": "1",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 34
        },
        {
          "group": "1",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 30
        },
        {
          "group": "1",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 2,
          "freed_corpus_positions": 38
        },
        {
          "group": "1",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 1,
          "freed_corpus_positions": 42
        },
        {
          "group": "1",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 42
        },
        {
          "group": "1",
          "cipher": 27,
          "label": "IO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 46
        },
        {
          "group": "2",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 69
        },
        {
          "group": "2",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 1,
          "freed_corpus_positions": 61
        },
        {
          "group": "2",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 58
        },
        {
          "group": "2",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 55
        },
        {
          "group": "2",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 1,
          "freed_corpus_positions": 69
        },
        {
          "group": "2",
          "cipher": 10,
          "label": "I",
          "exception_token_cost": 3,
          "freed_corpus_positions": 50
        },
        {
          "group": "2",
          "cipher": 11,
          "label": "J",
          "exception_token_cost": 1,
          "freed_corpus_positions": 44
        },
        {
          "group": "2",
          "cipher": 14,
          "label": "X",
          "exception_token_cost": 1,
          "freed_corpus_positions": 78
        },
        {
          "group": "2",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 61
        },
        {
          "group": "4",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 75
        },
        {
          "group": "4",
          "cipher": 4,
          "label": "R",
          "exception_token_cost": 2,
          "freed_corpus_positions": 64
        },
        {
          "group": "4",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 50
        },
        {
          "group": "4",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 2,
          "freed_corpus_positions": 57
        },
        {
          "group": "4",
          "cipher": 10,
          "label": "I",
          "exception_token_cost": 2,
          "freed_corpus_positions": 73
        },
        {
          "group": "4",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 1,
          "freed_corpus_positions": 72
        },
        {
          "group": "4",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 2,
          "freed_corpus_positions": 60
        },
        {
          "group": "4",
          "cipher": 17,
          "label": "B",
          "exception_token_cost": 2,
          "freed_corpus_positions": 63
        },
        {
          "group": "4",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 70
        },
        {
          "group": "4",
          "cipher": 25,
          "label": "AE",
          "exception_token_cost": 1,
          "freed_corpus_positions": 67
        },
        {
          "group": "4",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 54
        },
        {
          "group": "4",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 2,
          "freed_corpus_positions": 68
        },
        {
          "group": "5",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 37
        },
        {
          "group": "5",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 1,
          "freed_corpus_positions": 38
        },
        {
          "group": "5",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 25
        },
        {
          "group": "5",
          "cipher": 24,
          "label": "A",
          "exception_token_cost": 1,
          "freed_corpus_positions": 41
        },
        {
          "group": "5",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 37
        },
        {
          "group": "6",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 1,
          "freed_corpus_positions": 53
        },
        {
          "group": "6",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 1,
          "freed_corpus_positions": 52
        },
        {
          "group": "6",
          "cipher": 11,
          "label": "J",
          "exception_token_cost": 2,
          "freed_corpus_positions": 56
        },
        {
          "group": "6",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 2,
          "freed_corpus_positions": 51
        },
        {
          "group": "6",
          "cipher": 15,
          "label": "S",
          "exception_token_cost": 1,
          "freed_corpus_positions": 49
        },
        {
          "group": "6",
          "cipher": 19,
          "label": "M",
          "exception_token_cost": 3,
          "freed_corpus_positions": 54
        },
        {
          "group": "6",
          "cipher": 20,
          "label": "L",
          "exception_token_cost": 1,
          "freed_corpus_positions": 55
        },
        {
          "group": "6",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 1,
          "freed_corpus_positions": 51
        },
        {
          "group": "7",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 50
        },
        {
          "group": "7",
          "cipher": 4,
          "label": "R",
          "exception_token_cost": 1,
          "freed_corpus_positions": 54
        },
        {
          "group": "7",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 55
        },
        {
          "group": "7",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 1,
          "freed_corpus_positions": 57
        },
        {
          "group": "7",
          "cipher": 12,
          "label": "EO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 47
        },
        {
          "group": "7",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 1,
          "freed_corpus_positions": 51
        },
        {
          "group": "7",
          "cipher": 18,
          "label": "E",
          "exception_token_cost": 1,
          "freed_corpus_positions": 47
        },
        {
          "group": "7",
          "cipher": 22,
          "label": "OE",
          "exception_token_cost": 1,
          "freed_corpus_positions": 63
        },
        {
          "group": "7",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 56
        },
        {
          "group": "8",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 109
        },
        {
          "group": "8",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 1,
          "freed_corpus_positions": 132
        },
        {
          "group": "8",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 97
        },
        {
          "group": "8",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 1,
          "freed_corpus_positions": 111
        },
        {
          "group": "8",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 2,
          "freed_corpus_positions": 116
        },
        {
          "group": "8",
          "cipher": 17,
          "label": "B",
          "exception_token_cost": 1,
          "freed_corpus_positions": 120
        },
        {
          "group": "8",
          "cipher": 19,
          "label": "M",
          "exception_token_cost": 1,
          "freed_corpus_positions": 119
        },
        {
          "group": "8",
          "cipher": 20,
          "label": "L",
          "exception_token_cost": 1,
          "freed_corpus_positions": 109
        },
        {
          "group": "8",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 1,
          "freed_corpus_positions": 113
        },
        {
          "group": "8",
          "cipher": 22,
          "label": "OE",
          "exception_token_cost": 2,
          "freed_corpus_positions": 131
        },
        {
          "group": "8",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 122
        },
        {
          "group": "8",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 1,
          "freed_corpus_positions": 106
        }
      ],
      "maximum_position_release_by_exact_exception_cost": [
        0,
        132,
        254,
        374,
        493,
        606,
        717,
        826,
        935,
        1041,
        1138,
        1216,
        1291,
        1363,
        1433,
        1502,
        1571,
        1638,
        1702,
        1769,
        1832,
        1893,
        1954,
        2012,
        2070,
        2128,
        2185,
        2241,
        2296,
        2351,
        2406,
        2460,
        2514,
        2567,
        2619,
        2670,
        2721,
        2771,
        2821,
        2870,
        2917,
        2964,
        3010,
        3054,
        3096,
        3138,
        3179,
        3217,
        3254,
        3291,
        3327,
        3364,
        3398,
        3432,
        3466,
        3500,
        3530,
        3564,
        3594,
        3627,
        3657,
        3687,
        3717,
        3745,
        3774,
        3802,
        3830,
        3858,
        3886,
        3911,
        3937,
        3962,
        3985,
        4006,
        4023,
        4044,
        4060,
        4077,
        4098,
        4110,
        4127,
        4148
      ],
      "singleton_sensitivity": "exclude_red_initials",
      "allowed_letters": "AIO",
      "requirements": {
        "pooled": {
          "reference_ratio": [
            431,
            1963
          ],
          "maximum_allowed_positions": 2844,
          "required_position_release": 1304,
          "minimum_exception_tokens": 13,
          "freed_constraint_types": 13,
          "witness_units": [
            {
              "group": "2",
              "cipher": 14,
              "label": "X",
              "exception_token_cost": 1,
              "freed_corpus_positions": 78
            },
            {
              "group": "4",
              "cipher": 2,
              "label": "TH",
              "exception_token_cost": 1,
              "freed_corpus_positions": 75
            },
            {
              "group": "4",
              "cipher": 13,
              "label": "P",
              "exception_token_cost": 1,
              "freed_corpus_positions": 72
            },
            {
              "group": "8",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 109
            },
            {
              "group": "8",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 1,
              "freed_corpus_positions": 132
            },
            {
              "group": "8",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 97
            },
            {
              "group": "8",
              "cipher": 13,
              "label": "P",
              "exception_token_cost": 1,
              "freed_corpus_positions": 111
            },
            {
              "group": "8",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 1,
              "freed_corpus_positions": 120
            },
            {
              "group": "8",
              "cipher": 19,
              "label": "M",
              "exception_token_cost": 1,
              "freed_corpus_positions": 119
            },
            {
              "group": "8",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 1,
              "freed_corpus_positions": 109
            },
            {
              "group": "8",
              "cipher": 21,
              "label": "ING",
              "exception_token_cost": 1,
              "freed_corpus_positions": 113
            },
            {
              "group": "8",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 122
            },
            {
              "group": "8",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 1,
              "freed_corpus_positions": 106
            }
          ],
          "remaining_forced_positions": 2785,
          "remaining_forced_share": 0.21495832046928065,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        },
        "largest_individual": {
          "reference_ratio": [
            185,
            778
          ],
          "maximum_allowed_positions": 3080,
          "required_position_release": 1068,
          "minimum_exception_tokens": 10,
          "freed_constraint_types": 10,
          "witness_units": [
            {
              "group": "8",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 109
            },
            {
              "group": "8",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 1,
              "freed_corpus_positions": 132
            },
            {
              "group": "8",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 97
            },
            {
              "group": "8",
              "cipher": 13,
              "label": "P",
              "exception_token_cost": 1,
              "freed_corpus_positions": 111
            },
            {
              "group": "8",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 1,
              "freed_corpus_positions": 120
            },
            {
              "group": "8",
              "cipher": 19,
              "label": "M",
              "exception_token_cost": 1,
              "freed_corpus_positions": 119
            },
            {
              "group": "8",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 1,
              "freed_corpus_positions": 109
            },
            {
              "group": "8",
              "cipher": 21,
              "label": "ING",
              "exception_token_cost": 1,
              "freed_corpus_positions": 113
            },
            {
              "group": "8",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 122
            },
            {
              "group": "8",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 1,
              "freed_corpus_positions": 106
            }
          ],
          "remaining_forced_positions": 3010,
          "remaining_forced_share": 0.2323247916023464,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        }
      }
    },
    {
      "runes": 12956,
      "key_scope": "anchor_shared",
      "allowed_output_types": 2,
      "singleton_tokens": 81,
      "forced_positions": 4852,
      "minimum_allowed_letter_share": 0.37449830194504474,
      "groups": [
        {
          "group": "0",
          "sections": [
            0
          ],
          "runes": 729,
          "singleton_tokens": 5,
          "singleton_cipher_types": 5,
          "active_cipher_types": 29,
          "forced_positions": 134,
          "maximum_distinct_output_runes": 26,
          "cipher_histogram": [
            34,
            21,
            30,
            20,
            22,
            28,
            29,
            22,
            30,
            28,
            24,
            24,
            17,
            27,
            28,
            23,
            23,
            23,
            24,
            18,
            30,
            29,
            25,
            31,
            19,
            24,
            25,
            23,
            28
          ],
          "singleton_counts_by_cipher_type": [
            1,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1
          ]
        },
        {
          "group": "1",
          "sections": [
            1
          ],
          "runes": 1145,
          "singleton_tokens": 7,
          "singleton_cipher_types": 6,
          "active_cipher_types": 29,
          "forced_positions": 232,
          "maximum_distinct_output_runes": 25,
          "cipher_histogram": [
            26,
            34,
            34,
            30,
            36,
            52,
            43,
            30,
            38,
            37,
            43,
            43,
            49,
            44,
            49,
            34,
            37,
            31,
            32,
            39,
            50,
            42,
            40,
            38,
            35,
            41,
            42,
            46,
            50
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            1,
            2,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            1,
            1,
            0
          ]
        },
        {
          "group": "2",
          "sections": [
            2
          ],
          "runes": 1729,
          "singleton_tokens": 11,
          "singleton_cipher_types": 9,
          "active_cipher_types": 29,
          "forced_positions": 545,
          "maximum_distinct_output_runes": 22,
          "cipher_histogram": [
            66,
            69,
            69,
            61,
            50,
            63,
            58,
            55,
            52,
            69,
            50,
            44,
            52,
            55,
            78,
            61,
            61,
            55,
            56,
            57,
            63,
            58,
            67,
            51,
            64,
            52,
            61,
            68,
            64
          ],
          "singleton_counts_by_cipher_type": [
            0,
            1,
            0,
            1,
            0,
            0,
            1,
            1,
            0,
            1,
            3,
            1,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0
          ]
        },
        {
          "group": "3",
          "sections": [
            3
          ],
          "runes": 9,
          "singleton_tokens": 0,
          "singleton_cipher_types": 0,
          "active_cipher_types": 8,
          "forced_positions": 0,
          "maximum_distinct_output_runes": 8,
          "cipher_histogram": [
            1,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            0,
            1,
            0,
            2,
            0,
            1,
            0,
            1
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0
          ]
        },
        {
          "group": "4",
          "sections": [
            4
          ],
          "runes": 1894,
          "singleton_tokens": 18,
          "singleton_cipher_types": 12,
          "active_cipher_types": 29,
          "forced_positions": 773,
          "maximum_distinct_output_runes": 19,
          "cipher_histogram": [
            71,
            63,
            75,
            75,
            64,
            70,
            71,
            50,
            52,
            57,
            73,
            76,
            52,
            72,
            63,
            56,
            60,
            63,
            54,
            62,
            63,
            69,
            74,
            70,
            73,
            67,
            54,
            77,
            68
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            2,
            0,
            0,
            1,
            0,
            2,
            2,
            0,
            0,
            1,
            0,
            0,
            2,
            2,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            1,
            1,
            0,
            2
          ]
        },
        {
          "group": "5",
          "sections": [
            5
          ],
          "runes": 1021,
          "singleton_tokens": 5,
          "singleton_cipher_types": 5,
          "active_cipher_types": 29,
          "forced_positions": 178,
          "maximum_distinct_output_runes": 26,
          "cipher_histogram": [
            37,
            44,
            37,
            40,
            34,
            30,
            37,
            33,
            33,
            39,
            35,
            27,
            21,
            34,
            32,
            43,
            38,
            37,
            42,
            32,
            34,
            37,
            35,
            25,
            41,
            31,
            37,
            35,
            41
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            0,
            1,
            0,
            0
          ]
        },
        {
          "group": "6+8",
          "sections": [
            6,
            8
          ],
          "runes": 4840,
          "singleton_tokens": 26,
          "singleton_cipher_types": 15,
          "active_cipher_types": 29,
          "forced_positions": 2510,
          "maximum_distinct_output_runes": 16,
          "cipher_histogram": [
            186,
            154,
            160,
            185,
            164,
            139,
            144,
            156,
            152,
            157,
            180,
            186,
            161,
            162,
            153,
            160,
            166,
            184,
            184,
            173,
            164,
            164,
            187,
            168,
            180,
            170,
            170,
            172,
            159
          ],
          "singleton_counts_by_cipher_type": [
            0,
            1,
            0,
            2,
            0,
            0,
            1,
            0,
            1,
            0,
            0,
            2,
            0,
            3,
            0,
            1,
            2,
            1,
            0,
            4,
            2,
            2,
            2,
            0,
            0,
            0,
            1,
            0,
            1
          ]
        },
        {
          "group": "7",
          "sections": [
            7
          ],
          "runes": 1589,
          "singleton_tokens": 9,
          "singleton_cipher_types": 9,
          "active_cipher_types": 29,
          "forced_positions": 480,
          "maximum_distinct_output_runes": 22,
          "cipher_histogram": [
            37,
            64,
            50,
            47,
            54,
            61,
            56,
            55,
            57,
            59,
            66,
            50,
            47,
            51,
            55,
            57,
            57,
            52,
            47,
            54,
            55,
            55,
            63,
            56,
            68,
            60,
            58,
            49,
            49
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            1,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            0,
            0
          ]
        }
      ],
      "constraint_units": [
        {
          "group": "0",
          "cipher": 0,
          "label": "F",
          "exception_token_cost": 1,
          "freed_corpus_positions": 34
        },
        {
          "group": "0",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 21
        },
        {
          "group": "0",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 1,
          "freed_corpus_positions": 28
        },
        {
          "group": "0",
          "cipher": 15,
          "label": "S",
          "exception_token_cost": 1,
          "freed_corpus_positions": 23
        },
        {
          "group": "0",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 1,
          "freed_corpus_positions": 28
        },
        {
          "group": "1",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 34
        },
        {
          "group": "1",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 30
        },
        {
          "group": "1",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 2,
          "freed_corpus_positions": 38
        },
        {
          "group": "1",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 1,
          "freed_corpus_positions": 42
        },
        {
          "group": "1",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 42
        },
        {
          "group": "1",
          "cipher": 27,
          "label": "IO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 46
        },
        {
          "group": "2",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 69
        },
        {
          "group": "2",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 1,
          "freed_corpus_positions": 61
        },
        {
          "group": "2",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 58
        },
        {
          "group": "2",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 55
        },
        {
          "group": "2",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 1,
          "freed_corpus_positions": 69
        },
        {
          "group": "2",
          "cipher": 10,
          "label": "I",
          "exception_token_cost": 3,
          "freed_corpus_positions": 50
        },
        {
          "group": "2",
          "cipher": 11,
          "label": "J",
          "exception_token_cost": 1,
          "freed_corpus_positions": 44
        },
        {
          "group": "2",
          "cipher": 14,
          "label": "X",
          "exception_token_cost": 1,
          "freed_corpus_positions": 78
        },
        {
          "group": "2",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 61
        },
        {
          "group": "4",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 75
        },
        {
          "group": "4",
          "cipher": 4,
          "label": "R",
          "exception_token_cost": 2,
          "freed_corpus_positions": 64
        },
        {
          "group": "4",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 50
        },
        {
          "group": "4",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 2,
          "freed_corpus_positions": 57
        },
        {
          "group": "4",
          "cipher": 10,
          "label": "I",
          "exception_token_cost": 2,
          "freed_corpus_positions": 73
        },
        {
          "group": "4",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 1,
          "freed_corpus_positions": 72
        },
        {
          "group": "4",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 2,
          "freed_corpus_positions": 60
        },
        {
          "group": "4",
          "cipher": 17,
          "label": "B",
          "exception_token_cost": 2,
          "freed_corpus_positions": 63
        },
        {
          "group": "4",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 70
        },
        {
          "group": "4",
          "cipher": 25,
          "label": "AE",
          "exception_token_cost": 1,
          "freed_corpus_positions": 67
        },
        {
          "group": "4",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 54
        },
        {
          "group": "4",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 2,
          "freed_corpus_positions": 68
        },
        {
          "group": "5",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 37
        },
        {
          "group": "5",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 1,
          "freed_corpus_positions": 38
        },
        {
          "group": "5",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 25
        },
        {
          "group": "5",
          "cipher": 24,
          "label": "A",
          "exception_token_cost": 1,
          "freed_corpus_positions": 41
        },
        {
          "group": "5",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 37
        },
        {
          "group": "6+8",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 154
        },
        {
          "group": "6+8",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 2,
          "freed_corpus_positions": 185
        },
        {
          "group": "6+8",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 144
        },
        {
          "group": "6+8",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 1,
          "freed_corpus_positions": 152
        },
        {
          "group": "6+8",
          "cipher": 11,
          "label": "J",
          "exception_token_cost": 2,
          "freed_corpus_positions": 186
        },
        {
          "group": "6+8",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 3,
          "freed_corpus_positions": 162
        },
        {
          "group": "6+8",
          "cipher": 15,
          "label": "S",
          "exception_token_cost": 1,
          "freed_corpus_positions": 160
        },
        {
          "group": "6+8",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 2,
          "freed_corpus_positions": 166
        },
        {
          "group": "6+8",
          "cipher": 17,
          "label": "B",
          "exception_token_cost": 1,
          "freed_corpus_positions": 184
        },
        {
          "group": "6+8",
          "cipher": 19,
          "label": "M",
          "exception_token_cost": 4,
          "freed_corpus_positions": 173
        },
        {
          "group": "6+8",
          "cipher": 20,
          "label": "L",
          "exception_token_cost": 2,
          "freed_corpus_positions": 164
        },
        {
          "group": "6+8",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 2,
          "freed_corpus_positions": 164
        },
        {
          "group": "6+8",
          "cipher": 22,
          "label": "OE",
          "exception_token_cost": 2,
          "freed_corpus_positions": 187
        },
        {
          "group": "6+8",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 170
        },
        {
          "group": "6+8",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 1,
          "freed_corpus_positions": 159
        },
        {
          "group": "7",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 50
        },
        {
          "group": "7",
          "cipher": 4,
          "label": "R",
          "exception_token_cost": 1,
          "freed_corpus_positions": 54
        },
        {
          "group": "7",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 55
        },
        {
          "group": "7",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 1,
          "freed_corpus_positions": 57
        },
        {
          "group": "7",
          "cipher": 12,
          "label": "EO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 47
        },
        {
          "group": "7",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 1,
          "freed_corpus_positions": 51
        },
        {
          "group": "7",
          "cipher": 18,
          "label": "E",
          "exception_token_cost": 1,
          "freed_corpus_positions": 47
        },
        {
          "group": "7",
          "cipher": 22,
          "label": "OE",
          "exception_token_cost": 1,
          "freed_corpus_positions": 63
        },
        {
          "group": "7",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 56
        }
      ],
      "maximum_position_release_by_exact_exception_cost": [
        0,
        184,
        354,
        514,
        673,
        827,
        979,
        1123,
        1201,
        1310,
        1388,
        1496,
        1574,
        1681,
        1759,
        1847,
        1925,
        2011,
        2089,
        2175,
        2253,
        2328,
        2400,
        2470,
        2539,
        2608,
        2675,
        2738,
        2799,
        2860,
        2918,
        2975,
        3031,
        3086,
        3141,
        3195,
        3249,
        3303,
        3357,
        3411,
        3462,
        3512,
        3562,
        3609,
        3656,
        3702,
        3746,
        3788,
        3830,
        3875,
        3919,
        3961,
        4003,
        4044,
        4082,
        4119,
        4156,
        4192,
        4229,
        4263,
        4297,
        4331,
        4365,
        4395,
        4429,
        4459,
        4492,
        4522,
        4552,
        4582,
        4610,
        4639,
        4667,
        4695,
        4720,
        4743,
        4764,
        4781,
        4802,
        4814,
        4831,
        4852
      ],
      "singleton_sensitivity": "exclude_red_initials",
      "allowed_letters": "AI",
      "requirements": {
        "pooled": {
          "reference_ratio": [
            241,
            1963
          ],
          "maximum_allowed_positions": 1590,
          "required_position_release": 3262,
          "minimum_exception_tokens": 37,
          "freed_constraint_types": 29,
          "witness_units": [
            {
              "group": "2",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 69
            },
            {
              "group": "2",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 1,
              "freed_corpus_positions": 61
            },
            {
              "group": "2",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 58
            },
            {
              "group": "2",
              "cipher": 7,
              "label": "W",
              "exception_token_cost": 1,
              "freed_corpus_positions": 55
            },
            {
              "group": "2",
              "cipher": 9,
              "label": "N",
              "exception_token_cost": 1,
              "freed_corpus_positions": 69
            },
            {
              "group": "2",
              "cipher": 14,
              "label": "X",
              "exception_token_cost": 1,
              "freed_corpus_positions": 78
            },
            {
              "group": "2",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 61
            },
            {
              "group": "4",
              "cipher": 2,
              "label": "TH",
              "exception_token_cost": 1,
              "freed_corpus_positions": 75
            },
            {
              "group": "4",
              "cipher": 13,
              "label": "P",
              "exception_token_cost": 1,
              "freed_corpus_positions": 72
            },
            {
              "group": "4",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 1,
              "freed_corpus_positions": 70
            },
            {
              "group": "4",
              "cipher": 25,
              "label": "AE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 67
            },
            {
              "group": "6+8",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 154
            },
            {
              "group": "6+8",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 2,
              "freed_corpus_positions": 185
            },
            {
              "group": "6+8",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 144
            },
            {
              "group": "6+8",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 1,
              "freed_corpus_positions": 152
            },
            {
              "group": "6+8",
              "cipher": 11,
              "label": "J",
              "exception_token_cost": 2,
              "freed_corpus_positions": 186
            },
            {
              "group": "6+8",
              "cipher": 13,
              "label": "P",
              "exception_token_cost": 3,
              "freed_corpus_positions": 162
            },
            {
              "group": "6+8",
              "cipher": 15,
              "label": "S",
              "exception_token_cost": 1,
              "freed_corpus_positions": 160
            },
            {
              "group": "6+8",
              "cipher": 16,
              "label": "T",
              "exception_token_cost": 2,
              "freed_corpus_positions": 166
            },
            {
              "group": "6+8",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 1,
              "freed_corpus_positions": 184
            },
            {
              "group": "6+8",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 2,
              "freed_corpus_positions": 164
            },
            {
              "group": "6+8",
              "cipher": 21,
              "label": "ING",
              "exception_token_cost": 2,
              "freed_corpus_positions": 164
            },
            {
              "group": "6+8",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 2,
              "freed_corpus_positions": 187
            },
            {
              "group": "6+8",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 170
            },
            {
              "group": "6+8",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 1,
              "freed_corpus_positions": 159
            },
            {
              "group": "7",
              "cipher": 7,
              "label": "W",
              "exception_token_cost": 1,
              "freed_corpus_positions": 55
            },
            {
              "group": "7",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 1,
              "freed_corpus_positions": 57
            },
            {
              "group": "7",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 63
            },
            {
              "group": "7",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 1,
              "freed_corpus_positions": 56
            }
          ],
          "remaining_forced_positions": 1549,
          "remaining_forced_share": 0.1195585057116394,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        },
        "largest_individual": {
          "reference_ratio": [
            54,
            389
          ],
          "maximum_allowed_positions": 1798,
          "required_position_release": 3054,
          "minimum_exception_tokens": 33,
          "freed_constraint_types": 27,
          "witness_units": [
            {
              "group": "2",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 69
            },
            {
              "group": "2",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 1,
              "freed_corpus_positions": 61
            },
            {
              "group": "2",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 58
            },
            {
              "group": "2",
              "cipher": 7,
              "label": "W",
              "exception_token_cost": 1,
              "freed_corpus_positions": 55
            },
            {
              "group": "2",
              "cipher": 9,
              "label": "N",
              "exception_token_cost": 1,
              "freed_corpus_positions": 69
            },
            {
              "group": "2",
              "cipher": 14,
              "label": "X",
              "exception_token_cost": 1,
              "freed_corpus_positions": 78
            },
            {
              "group": "2",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 61
            },
            {
              "group": "4",
              "cipher": 2,
              "label": "TH",
              "exception_token_cost": 1,
              "freed_corpus_positions": 75
            },
            {
              "group": "4",
              "cipher": 13,
              "label": "P",
              "exception_token_cost": 1,
              "freed_corpus_positions": 72
            },
            {
              "group": "4",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 1,
              "freed_corpus_positions": 70
            },
            {
              "group": "4",
              "cipher": 25,
              "label": "AE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 67
            },
            {
              "group": "6+8",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 154
            },
            {
              "group": "6+8",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 2,
              "freed_corpus_positions": 185
            },
            {
              "group": "6+8",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 144
            },
            {
              "group": "6+8",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 1,
              "freed_corpus_positions": 152
            },
            {
              "group": "6+8",
              "cipher": 11,
              "label": "J",
              "exception_token_cost": 2,
              "freed_corpus_positions": 186
            },
            {
              "group": "6+8",
              "cipher": 15,
              "label": "S",
              "exception_token_cost": 1,
              "freed_corpus_positions": 160
            },
            {
              "group": "6+8",
              "cipher": 16,
              "label": "T",
              "exception_token_cost": 2,
              "freed_corpus_positions": 166
            },
            {
              "group": "6+8",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 1,
              "freed_corpus_positions": 184
            },
            {
              "group": "6+8",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 2,
              "freed_corpus_positions": 164
            },
            {
              "group": "6+8",
              "cipher": 21,
              "label": "ING",
              "exception_token_cost": 2,
              "freed_corpus_positions": 164
            },
            {
              "group": "6+8",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 2,
              "freed_corpus_positions": 187
            },
            {
              "group": "6+8",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 170
            },
            {
              "group": "6+8",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 1,
              "freed_corpus_positions": 159
            },
            {
              "group": "7",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 1,
              "freed_corpus_positions": 57
            },
            {
              "group": "7",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 1,
              "freed_corpus_positions": 63
            },
            {
              "group": "7",
              "cipher": 23,
              "label": "D",
              "exception_token_cost": 1,
              "freed_corpus_positions": 56
            }
          ],
          "remaining_forced_positions": 1766,
          "remaining_forced_share": 0.1363075023155295,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        }
      }
    },
    {
      "runes": 12956,
      "key_scope": "anchor_shared",
      "allowed_output_types": 3,
      "singleton_tokens": 81,
      "forced_positions": 4852,
      "minimum_allowed_letter_share": 0.37449830194504474,
      "groups": [
        {
          "group": "0",
          "sections": [
            0
          ],
          "runes": 729,
          "singleton_tokens": 5,
          "singleton_cipher_types": 5,
          "active_cipher_types": 29,
          "forced_positions": 134,
          "maximum_distinct_output_runes": 27,
          "cipher_histogram": [
            34,
            21,
            30,
            20,
            22,
            28,
            29,
            22,
            30,
            28,
            24,
            24,
            17,
            27,
            28,
            23,
            23,
            23,
            24,
            18,
            30,
            29,
            25,
            31,
            19,
            24,
            25,
            23,
            28
          ],
          "singleton_counts_by_cipher_type": [
            1,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1
          ]
        },
        {
          "group": "1",
          "sections": [
            1
          ],
          "runes": 1145,
          "singleton_tokens": 7,
          "singleton_cipher_types": 6,
          "active_cipher_types": 29,
          "forced_positions": 232,
          "maximum_distinct_output_runes": 26,
          "cipher_histogram": [
            26,
            34,
            34,
            30,
            36,
            52,
            43,
            30,
            38,
            37,
            43,
            43,
            49,
            44,
            49,
            34,
            37,
            31,
            32,
            39,
            50,
            42,
            40,
            38,
            35,
            41,
            42,
            46,
            50
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            1,
            2,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            1,
            1,
            0
          ]
        },
        {
          "group": "2",
          "sections": [
            2
          ],
          "runes": 1729,
          "singleton_tokens": 11,
          "singleton_cipher_types": 9,
          "active_cipher_types": 29,
          "forced_positions": 545,
          "maximum_distinct_output_runes": 23,
          "cipher_histogram": [
            66,
            69,
            69,
            61,
            50,
            63,
            58,
            55,
            52,
            69,
            50,
            44,
            52,
            55,
            78,
            61,
            61,
            55,
            56,
            57,
            63,
            58,
            67,
            51,
            64,
            52,
            61,
            68,
            64
          ],
          "singleton_counts_by_cipher_type": [
            0,
            1,
            0,
            1,
            0,
            0,
            1,
            1,
            0,
            1,
            3,
            1,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0
          ]
        },
        {
          "group": "3",
          "sections": [
            3
          ],
          "runes": 9,
          "singleton_tokens": 0,
          "singleton_cipher_types": 0,
          "active_cipher_types": 8,
          "forced_positions": 0,
          "maximum_distinct_output_runes": 8,
          "cipher_histogram": [
            1,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            0,
            1,
            0,
            2,
            0,
            1,
            0,
            1
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0
          ]
        },
        {
          "group": "4",
          "sections": [
            4
          ],
          "runes": 1894,
          "singleton_tokens": 18,
          "singleton_cipher_types": 12,
          "active_cipher_types": 29,
          "forced_positions": 773,
          "maximum_distinct_output_runes": 20,
          "cipher_histogram": [
            71,
            63,
            75,
            75,
            64,
            70,
            71,
            50,
            52,
            57,
            73,
            76,
            52,
            72,
            63,
            56,
            60,
            63,
            54,
            62,
            63,
            69,
            74,
            70,
            73,
            67,
            54,
            77,
            68
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            2,
            0,
            0,
            1,
            0,
            2,
            2,
            0,
            0,
            1,
            0,
            0,
            2,
            2,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            1,
            1,
            0,
            2
          ]
        },
        {
          "group": "5",
          "sections": [
            5
          ],
          "runes": 1021,
          "singleton_tokens": 5,
          "singleton_cipher_types": 5,
          "active_cipher_types": 29,
          "forced_positions": 178,
          "maximum_distinct_output_runes": 27,
          "cipher_histogram": [
            37,
            44,
            37,
            40,
            34,
            30,
            37,
            33,
            33,
            39,
            35,
            27,
            21,
            34,
            32,
            43,
            38,
            37,
            42,
            32,
            34,
            37,
            35,
            25,
            41,
            31,
            37,
            35,
            41
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            0,
            1,
            0,
            0
          ]
        },
        {
          "group": "6+8",
          "sections": [
            6,
            8
          ],
          "runes": 4840,
          "singleton_tokens": 26,
          "singleton_cipher_types": 15,
          "active_cipher_types": 29,
          "forced_positions": 2510,
          "maximum_distinct_output_runes": 17,
          "cipher_histogram": [
            186,
            154,
            160,
            185,
            164,
            139,
            144,
            156,
            152,
            157,
            180,
            186,
            161,
            162,
            153,
            160,
            166,
            184,
            184,
            173,
            164,
            164,
            187,
            168,
            180,
            170,
            170,
            172,
            159
          ],
          "singleton_counts_by_cipher_type": [
            0,
            1,
            0,
            2,
            0,
            0,
            1,
            0,
            1,
            0,
            0,
            2,
            0,
            3,
            0,
            1,
            2,
            1,
            0,
            4,
            2,
            2,
            2,
            0,
            0,
            0,
            1,
            0,
            1
          ]
        },
        {
          "group": "7",
          "sections": [
            7
          ],
          "runes": 1589,
          "singleton_tokens": 9,
          "singleton_cipher_types": 9,
          "active_cipher_types": 29,
          "forced_positions": 480,
          "maximum_distinct_output_runes": 23,
          "cipher_histogram": [
            37,
            64,
            50,
            47,
            54,
            61,
            56,
            55,
            57,
            59,
            66,
            50,
            47,
            51,
            55,
            57,
            57,
            52,
            47,
            54,
            55,
            55,
            63,
            56,
            68,
            60,
            58,
            49,
            49
          ],
          "singleton_counts_by_cipher_type": [
            0,
            0,
            1,
            0,
            1,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            0,
            0
          ]
        }
      ],
      "constraint_units": [
        {
          "group": "0",
          "cipher": 0,
          "label": "F",
          "exception_token_cost": 1,
          "freed_corpus_positions": 34
        },
        {
          "group": "0",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 21
        },
        {
          "group": "0",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 1,
          "freed_corpus_positions": 28
        },
        {
          "group": "0",
          "cipher": 15,
          "label": "S",
          "exception_token_cost": 1,
          "freed_corpus_positions": 23
        },
        {
          "group": "0",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 1,
          "freed_corpus_positions": 28
        },
        {
          "group": "1",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 34
        },
        {
          "group": "1",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 30
        },
        {
          "group": "1",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 2,
          "freed_corpus_positions": 38
        },
        {
          "group": "1",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 1,
          "freed_corpus_positions": 42
        },
        {
          "group": "1",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 42
        },
        {
          "group": "1",
          "cipher": 27,
          "label": "IO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 46
        },
        {
          "group": "2",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 69
        },
        {
          "group": "2",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 1,
          "freed_corpus_positions": 61
        },
        {
          "group": "2",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 58
        },
        {
          "group": "2",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 55
        },
        {
          "group": "2",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 1,
          "freed_corpus_positions": 69
        },
        {
          "group": "2",
          "cipher": 10,
          "label": "I",
          "exception_token_cost": 3,
          "freed_corpus_positions": 50
        },
        {
          "group": "2",
          "cipher": 11,
          "label": "J",
          "exception_token_cost": 1,
          "freed_corpus_positions": 44
        },
        {
          "group": "2",
          "cipher": 14,
          "label": "X",
          "exception_token_cost": 1,
          "freed_corpus_positions": 78
        },
        {
          "group": "2",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 61
        },
        {
          "group": "4",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 75
        },
        {
          "group": "4",
          "cipher": 4,
          "label": "R",
          "exception_token_cost": 2,
          "freed_corpus_positions": 64
        },
        {
          "group": "4",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 50
        },
        {
          "group": "4",
          "cipher": 9,
          "label": "N",
          "exception_token_cost": 2,
          "freed_corpus_positions": 57
        },
        {
          "group": "4",
          "cipher": 10,
          "label": "I",
          "exception_token_cost": 2,
          "freed_corpus_positions": 73
        },
        {
          "group": "4",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 1,
          "freed_corpus_positions": 72
        },
        {
          "group": "4",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 2,
          "freed_corpus_positions": 60
        },
        {
          "group": "4",
          "cipher": 17,
          "label": "B",
          "exception_token_cost": 2,
          "freed_corpus_positions": 63
        },
        {
          "group": "4",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 70
        },
        {
          "group": "4",
          "cipher": 25,
          "label": "AE",
          "exception_token_cost": 1,
          "freed_corpus_positions": 67
        },
        {
          "group": "4",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 54
        },
        {
          "group": "4",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 2,
          "freed_corpus_positions": 68
        },
        {
          "group": "5",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 37
        },
        {
          "group": "5",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 1,
          "freed_corpus_positions": 38
        },
        {
          "group": "5",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 25
        },
        {
          "group": "5",
          "cipher": 24,
          "label": "A",
          "exception_token_cost": 1,
          "freed_corpus_positions": 41
        },
        {
          "group": "5",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 37
        },
        {
          "group": "6+8",
          "cipher": 1,
          "label": "U",
          "exception_token_cost": 1,
          "freed_corpus_positions": 154
        },
        {
          "group": "6+8",
          "cipher": 3,
          "label": "O",
          "exception_token_cost": 2,
          "freed_corpus_positions": 185
        },
        {
          "group": "6+8",
          "cipher": 6,
          "label": "G",
          "exception_token_cost": 1,
          "freed_corpus_positions": 144
        },
        {
          "group": "6+8",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 1,
          "freed_corpus_positions": 152
        },
        {
          "group": "6+8",
          "cipher": 11,
          "label": "J",
          "exception_token_cost": 2,
          "freed_corpus_positions": 186
        },
        {
          "group": "6+8",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 3,
          "freed_corpus_positions": 162
        },
        {
          "group": "6+8",
          "cipher": 15,
          "label": "S",
          "exception_token_cost": 1,
          "freed_corpus_positions": 160
        },
        {
          "group": "6+8",
          "cipher": 16,
          "label": "T",
          "exception_token_cost": 2,
          "freed_corpus_positions": 166
        },
        {
          "group": "6+8",
          "cipher": 17,
          "label": "B",
          "exception_token_cost": 1,
          "freed_corpus_positions": 184
        },
        {
          "group": "6+8",
          "cipher": 19,
          "label": "M",
          "exception_token_cost": 4,
          "freed_corpus_positions": 173
        },
        {
          "group": "6+8",
          "cipher": 20,
          "label": "L",
          "exception_token_cost": 2,
          "freed_corpus_positions": 164
        },
        {
          "group": "6+8",
          "cipher": 21,
          "label": "ING",
          "exception_token_cost": 2,
          "freed_corpus_positions": 164
        },
        {
          "group": "6+8",
          "cipher": 22,
          "label": "OE",
          "exception_token_cost": 2,
          "freed_corpus_positions": 187
        },
        {
          "group": "6+8",
          "cipher": 26,
          "label": "Y",
          "exception_token_cost": 1,
          "freed_corpus_positions": 170
        },
        {
          "group": "6+8",
          "cipher": 28,
          "label": "EA",
          "exception_token_cost": 1,
          "freed_corpus_positions": 159
        },
        {
          "group": "7",
          "cipher": 2,
          "label": "TH",
          "exception_token_cost": 1,
          "freed_corpus_positions": 50
        },
        {
          "group": "7",
          "cipher": 4,
          "label": "R",
          "exception_token_cost": 1,
          "freed_corpus_positions": 54
        },
        {
          "group": "7",
          "cipher": 7,
          "label": "W",
          "exception_token_cost": 1,
          "freed_corpus_positions": 55
        },
        {
          "group": "7",
          "cipher": 8,
          "label": "H",
          "exception_token_cost": 1,
          "freed_corpus_positions": 57
        },
        {
          "group": "7",
          "cipher": 12,
          "label": "EO",
          "exception_token_cost": 1,
          "freed_corpus_positions": 47
        },
        {
          "group": "7",
          "cipher": 13,
          "label": "P",
          "exception_token_cost": 1,
          "freed_corpus_positions": 51
        },
        {
          "group": "7",
          "cipher": 18,
          "label": "E",
          "exception_token_cost": 1,
          "freed_corpus_positions": 47
        },
        {
          "group": "7",
          "cipher": 22,
          "label": "OE",
          "exception_token_cost": 1,
          "freed_corpus_positions": 63
        },
        {
          "group": "7",
          "cipher": 23,
          "label": "D",
          "exception_token_cost": 1,
          "freed_corpus_positions": 56
        }
      ],
      "maximum_position_release_by_exact_exception_cost": [
        0,
        184,
        354,
        514,
        673,
        827,
        979,
        1123,
        1201,
        1310,
        1388,
        1496,
        1574,
        1681,
        1759,
        1847,
        1925,
        2011,
        2089,
        2175,
        2253,
        2328,
        2400,
        2470,
        2539,
        2608,
        2675,
        2738,
        2799,
        2860,
        2918,
        2975,
        3031,
        3086,
        3141,
        3195,
        3249,
        3303,
        3357,
        3411,
        3462,
        3512,
        3562,
        3609,
        3656,
        3702,
        3746,
        3788,
        3830,
        3875,
        3919,
        3961,
        4003,
        4044,
        4082,
        4119,
        4156,
        4192,
        4229,
        4263,
        4297,
        4331,
        4365,
        4395,
        4429,
        4459,
        4492,
        4522,
        4552,
        4582,
        4610,
        4639,
        4667,
        4695,
        4720,
        4743,
        4764,
        4781,
        4802,
        4814,
        4831,
        4852
      ],
      "singleton_sensitivity": "exclude_red_initials",
      "allowed_letters": "AIO",
      "requirements": {
        "pooled": {
          "reference_ratio": [
            431,
            1963
          ],
          "maximum_allowed_positions": 2844,
          "required_position_release": 2008,
          "minimum_exception_tokens": 17,
          "freed_constraint_types": 12,
          "witness_units": [
            {
              "group": "6+8",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 154
            },
            {
              "group": "6+8",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 2,
              "freed_corpus_positions": 185
            },
            {
              "group": "6+8",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 144
            },
            {
              "group": "6+8",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 1,
              "freed_corpus_positions": 152
            },
            {
              "group": "6+8",
              "cipher": 11,
              "label": "J",
              "exception_token_cost": 2,
              "freed_corpus_positions": 186
            },
            {
              "group": "6+8",
              "cipher": 15,
              "label": "S",
              "exception_token_cost": 1,
              "freed_corpus_positions": 160
            },
            {
              "group": "6+8",
              "cipher": 16,
              "label": "T",
              "exception_token_cost": 2,
              "freed_corpus_positions": 166
            },
            {
              "group": "6+8",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 1,
              "freed_corpus_positions": 184
            },
            {
              "group": "6+8",
              "cipher": 20,
              "label": "L",
              "exception_token_cost": 2,
              "freed_corpus_positions": 164
            },
            {
              "group": "6+8",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 2,
              "freed_corpus_positions": 187
            },
            {
              "group": "6+8",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 170
            },
            {
              "group": "6+8",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 1,
              "freed_corpus_positions": 159
            }
          ],
          "remaining_forced_positions": 2841,
          "remaining_forced_share": 0.21928064217351034,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        },
        "largest_individual": {
          "reference_ratio": [
            185,
            778
          ],
          "maximum_allowed_positions": 3080,
          "required_position_release": 1772,
          "minimum_exception_tokens": 15,
          "freed_constraint_types": 11,
          "witness_units": [
            {
              "group": "6+8",
              "cipher": 1,
              "label": "U",
              "exception_token_cost": 1,
              "freed_corpus_positions": 154
            },
            {
              "group": "6+8",
              "cipher": 3,
              "label": "O",
              "exception_token_cost": 2,
              "freed_corpus_positions": 185
            },
            {
              "group": "6+8",
              "cipher": 6,
              "label": "G",
              "exception_token_cost": 1,
              "freed_corpus_positions": 144
            },
            {
              "group": "6+8",
              "cipher": 8,
              "label": "H",
              "exception_token_cost": 1,
              "freed_corpus_positions": 152
            },
            {
              "group": "6+8",
              "cipher": 11,
              "label": "J",
              "exception_token_cost": 2,
              "freed_corpus_positions": 186
            },
            {
              "group": "6+8",
              "cipher": 15,
              "label": "S",
              "exception_token_cost": 1,
              "freed_corpus_positions": 160
            },
            {
              "group": "6+8",
              "cipher": 16,
              "label": "T",
              "exception_token_cost": 2,
              "freed_corpus_positions": 166
            },
            {
              "group": "6+8",
              "cipher": 17,
              "label": "B",
              "exception_token_cost": 1,
              "freed_corpus_positions": 184
            },
            {
              "group": "6+8",
              "cipher": 22,
              "label": "OE",
              "exception_token_cost": 2,
              "freed_corpus_positions": 187
            },
            {
              "group": "6+8",
              "cipher": 26,
              "label": "Y",
              "exception_token_cost": 1,
              "freed_corpus_positions": 170
            },
            {
              "group": "6+8",
              "cipher": 28,
              "label": "EA",
              "exception_token_cost": 1,
              "freed_corpus_positions": 159
            }
          ],
          "remaining_forced_positions": 3005,
          "remaining_forced_share": 0.23193887002161162,
          "necessary_mass_condition_only_not_a_full_plaintext_fit": true,
          "relaxed_mass_witness_verified": true
        }
      }
    }
  ],
  "small_exhaustive_controls": [
    {
      "cipher_and_output_alphabet_size": 5,
      "decoding_tables_exhausted": 3125,
      "exception_budgets_checked": 8,
      "exact_mass_and_alphabet_bounds_agree": true
    },
    {
      "cipher_and_output_alphabet_size": 4,
      "decoding_tables_exhausted": 256,
      "exception_budgets_checked": 6,
      "exact_mass_and_alphabet_bounds_agree": true
    }
  ],
  "homophonic_controls": [
    {
      "source_group": "warning",
      "runes": 184,
      "plaintext_types": 24,
      "homophone_classes": {
        "F": [
          14,
          20
        ],
        "U": [
          27,
          18
        ],
        "TH": [
          17
        ],
        "O": [
          8,
          28
        ],
        "R": [
          13
        ],
        "K": [
          25
        ],
        "G": [
          22
        ],
        "W": [
          1
        ],
        "H": [
          5
        ],
        "N": [
          19
        ],
        "I": [
          23
        ],
        "P": [
          11
        ],
        "X": [
          9
        ],
        "S": [
          10,
          12
        ],
        "T": [
          2
        ],
        "B": [
          26
        ],
        "E": [
          0
        ],
        "M": [
          16
        ],
        "L": [
          21,
          6
        ],
        "ING": [
          24
        ],
        "D": [
          3
        ],
        "A": [
          15
        ],
        "Y": [
          4
        ],
        "EA": [
          7
        ]
      },
      "stateful_homophone_choice_but_fixed_decoding_table": true,
      "exact_inverse_recovery": true,
      "plaintext_neighbor_repeats": 5,
      "ciphertext_neighbor_repeats": 0,
      "singleton_tokens": 1,
      "singleton_cipher_types": 1,
      "forced_AI_positions": 8,
      "true_AI_positions": 20,
      "alphabet_bound_preserves_true_alphabet": true
    },
    {
      "source_group": "koan",
      "runes": 778,
      "plaintext_types": 24,
      "homophone_classes": {
        "F": [
          7,
          23
        ],
        "U": [
          19
        ],
        "TH": [
          2
        ],
        "O": [
          28
        ],
        "R": [
          11,
          14
        ],
        "K": [
          18
        ],
        "G": [
          25
        ],
        "W": [
          10
        ],
        "H": [
          4
        ],
        "N": [
          3
        ],
        "I": [
          6
        ],
        "P": [
          17
        ],
        "S": [
          5,
          26
        ],
        "T": [
          0,
          27
        ],
        "B": [
          13
        ],
        "E": [
          1
        ],
        "M": [
          9
        ],
        "L": [
          20,
          21
        ],
        "ING": [
          15
        ],
        "D": [
          22
        ],
        "A": [
          24
        ],
        "Y": [
          16
        ],
        "IO": [
          12
        ],
        "EA": [
          8
        ]
      },
      "stateful_homophone_choice_but_fixed_decoding_table": true,
      "exact_inverse_recovery": true,
      "plaintext_neighbor_repeats": 14,
      "ciphertext_neighbor_repeats": 2,
      "singleton_tokens": 13,
      "singleton_cipher_types": 2,
      "forced_AI_positions": 108,
      "true_AI_positions": 108,
      "alphabet_bound_preserves_true_alphabet": true
    },
    {
      "source_group": "divinity",
      "runes": 755,
      "plaintext_types": 24,
      "homophone_classes": {
        "F": [
          15
        ],
        "U": [
          9
        ],
        "TH": [
          26
        ],
        "O": [
          21,
          5
        ],
        "R": [
          6
        ],
        "K": [
          8
        ],
        "G": [
          23
        ],
        "W": [
          0
        ],
        "H": [
          28
        ],
        "N": [
          1
        ],
        "I": [
          14
        ],
        "P": [
          7
        ],
        "S": [
          24,
          22
        ],
        "T": [
          13,
          4
        ],
        "B": [
          19
        ],
        "E": [
          25,
          27
        ],
        "M": [
          10
        ],
        "L": [
          11,
          2
        ],
        "ING": [
          20
        ],
        "D": [
          16
        ],
        "A": [
          17
        ],
        "Y": [
          3
        ],
        "IO": [
          12
        ],
        "EA": [
          18
        ]
      },
      "stateful_homophone_choice_but_fixed_decoding_table": true,
      "exact_inverse_recovery": true,
      "plaintext_neighbor_repeats": 18,
      "ciphertext_neighbor_repeats": 2,
      "singleton_tokens": 0,
      "singleton_cipher_types": 0,
      "forced_AI_positions": 0,
      "true_AI_positions": 85,
      "alphabet_bound_preserves_true_alphabet": true
    },
    {
      "source_group": "instruction",
      "runes": 89,
      "plaintext_types": 20,
      "homophone_classes": {
        "F": [
          25,
          22
        ],
        "U": [
          2,
          14
        ],
        "TH": [
          28,
          10
        ],
        "O": [
          4,
          6
        ],
        "R": [
          23,
          11
        ],
        "K": [
          13,
          5
        ],
        "W": [
          12,
          7
        ],
        "N": [
          20,
          24
        ],
        "I": [
          1
        ],
        "P": [
          18
        ],
        "S": [
          19
        ],
        "T": [
          8
        ],
        "E": [
          26
        ],
        "M": [
          16
        ],
        "L": [
          9,
          15
        ],
        "ING": [
          27
        ],
        "D": [
          3
        ],
        "A": [
          21
        ],
        "Y": [
          17
        ],
        "IO": [
          0
        ]
      },
      "stateful_homophone_choice_but_fixed_decoding_table": true,
      "exact_inverse_recovery": true,
      "plaintext_neighbor_repeats": 3,
      "ciphertext_neighbor_repeats": 0,
      "singleton_tokens": 0,
      "singleton_cipher_types": 0,
      "forced_AI_positions": 0,
      "true_AI_positions": 8,
      "alphabet_bound_preserves_true_alphabet": true
    }
  ],
  "state_dependent_counterexample": {
    "known_koan_copies": 3,
    "runes": 2334,
    "singletons": 39,
    "singleton_cipher_types": 28,
    "per_word_substitution_inverse_exact": true,
    "true_plaintext_types": 24,
    "incorrect_fixed_table_assumption_would_cap_output_types": 3,
    "fixed_table_bound_not_applicable": true,
    "a_scope_counterexample_not_a_proposed_Cicada_key": true
  }
}
