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  "seed": 3301033,
  "formula": "p[i] = (pi[c[i]] - pi[c[i-1]] + r) mod 29",
  "assumptions": [
    "One fixed permutation pi and one fixed r shared across the selected sections.",
    "One plaintext rune per ciphertext rune, same 29-symbol alphabet.",
    "Only previous ciphertext rune affects decoding; punctuation and pages do not alter the mapping.",
    "First rune of each section excluded: initial state cannot affect the scored bounds.",
    "Plaintext benchmark is solved LP rune text; this is not a theorem about every language or intentionally balanced text."
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  "scope": "Eight substantial unsolved sections. Training/evaluation names retain the established split; no key is fitted. These are retrospective diagnostics on previously examined data.",
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  "evaluation_sections": [
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          9,
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          16
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        [
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          15,
          16,
          19,
          17,
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          10,
          10,
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          21,
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          13,
          23,
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          17,
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          12,
          3,
          23,
          11,
          20
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        [
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          18,
          21,
          13,
          10,
          10,
          15,
          15,
          15,
          17,
          19,
          13,
          18,
          19,
          20,
          15,
          18,
          9,
          10,
          23,
          12,
          17,
          18,
          16,
          11,
          13,
          4,
          13,
          12
        ],
        [
          17,
          21,
          17,
          5,
          15,
          22,
          16,
          18,
          9,
          13,
          11,
          17,
          17,
          10,
          15,
          20,
          19,
          20,
          17,
          15,
          14,
          13,
          12,
          23,
          14,
          20,
          19,
          3,
          16
        ],
        [
          15,
          15,
          16,
          16,
          17,
          18,
          17,
          15,
          14,
          13,
          10,
          21,
          17,
          9,
          17,
          16,
          16,
          16,
          13,
          18,
          13,
          9,
          14,
          12,
          13,
          12,
          9,
          12,
          2
        ]
      ]
    },
    "note": "Deliberately outside tested family. Changing per-position key recovers plaintext below the fixed-row bound and preserves rare doubles. The bound must not be generalized to this cipher."
  },
  "exhaustive_small_alphabet_checks": [
    {
      "matrix": [
        [
          2,
          7,
          1
        ],
        [
          3,
          1,
          5
        ],
        [
          6,
          2,
          0
        ]
      ],
      "unrestricted_assignments": 216,
      "shared_diagonal_assignments": 8,
      "exact_unrestricted_minimum": 1.173030669557363,
      "exact_shared_diagonal_minimum": 1.224394445405986
    },
    {
      "matrix": [
        [
          0,
          0,
          3
        ],
        [
          2,
          0,
          0
        ],
        [
          0,
          1,
          0
        ]
      ],
      "unrestricted_assignments": 216,
      "shared_diagonal_assignments": 8,
      "exact_unrestricted_minimum": -0.0,
      "exact_shared_diagonal_minimum": -0.0
    }
  ],
  "repeated_phrase_fixture": {
    "pi": [
      11,
      5,
      28,
      25,
      19,
      22,
      16,
      4,
      2,
      27,
      23,
      13,
      3,
      26,
      6,
      14,
      24,
      9,
      8,
      1,
      0,
      18,
      15,
      7,
      10,
      17,
      12,
      21,
      20
    ],
    "r": 28,
    "cipher_a": [
      0,
      23,
      11,
      1,
      17,
      18,
      10
    ],
    "cipher_b": [
      14,
      23,
      11,
      1,
      17,
      18,
      10
    ],
    "decoded_a": [
      28,
      24,
      5,
      20,
      3,
      27,
      14
    ],
    "decoded_b": [
      23,
      0,
      5,
      20,
      3,
      27,
      14
    ],
    "first_plaintext_of_phrase_differs": true,
    "last_five_plaintext_runes_equal": true
  },
  "no_unknown_key_search": true,
  "transcript_sha256": "b0b2e13c3cd35512ee5955a2d9a56c22d7410e283d35dd9c90abbaa7b99279eb",
  "script_sha256": "c4587042c8d272cd241d03fd2a80f9772862f2bf526df4f2f3bfe27dcfd499d0",
  "limits": [
    "Exact empirical bounds, not p-values or population entropy estimates.",
    "The relaxed rowwise optimum need not be achievable by any single permutation pi; it only makes the candidate look more favorable.",
    "A common mapping is assumed when pooling sections. Per-section values are supplied, but no claim that all separate-key models are excluded.",
    "Controls cycle solved rune streams and are deliberately constructed, not fresh natural-language samples.",
    "Positive controls check known-key inversion and mathematical bounds, not cryptanalytic key recovery.",
    "Additional key streams, position-dependent mappings, larger state, null insertion, and other intermediate encodings are outside scope."
  ]
}