{
  "schema": 1,
  "purpose": "Reproduce the author-linked 2025 2222/4444/6666/8888 clue without treating it as a new plaintext.",
  "sources": {
    "transcription": {
      "path": "archive/gaps/tr1-02-files/DERIVED-2018-magic-square-16x16-transcription.txt",
      "sha256": "8ee668a011757a13ce42a34790a27991d6ffc44aba5ec0eb40747e28e5a03512"
    },
    "source_images": {
      "2018_original": {
        "path": "archive/gaps/seed-07-files/twimg-DlclzejWwAAL7AU.jpg",
        "sha256": "278b887087f41432a8f8a1badd1a33b0f5e58cc51b8bdec88f8eed7ced8bfe03"
      },
      "2025_repost": {
        "path": "archive/gaps/seed-07-files/twimg-GpMaU-NW8AAtwtj.jpg",
        "sha256": "2a7e1991019e1ff840907aef8470948d670a14464c806aab2cd925cd0ff4293c"
      }
    },
    "tweet_archive": {
      "path": "solution/tweets/666ab731-timeline.json",
      "sha256": "8241217e5bd14ca5db8e8414d11570d4b3c53219cf6d641b4f9d46a8cc0955a3"
    }
  },
  "author_linked_records": {
    "2018_original_image_tweet": {
      "id": "1033336220661809152",
      "created_utc": "2018-08-25T12:52:08Z"
    },
    "2025_repost": {
      "id": "1914903216644403468",
      "created_utc": "2025-04-23T04:44:38.000Z",
      "permalink": "https://x.com/666ab731/status/1914903216644403468",
      "text_verbatim": "@tactical_nook @hamptonism [MEDIA]",
      "media": [
        {
          "source_url": "https://pbs.twimg.com/media/GpMaU-NW8AAtwtj.jpg",
          "local_path": "media/GpMaU-NW8AAtwtj.jpg",
          "bytes": 241371,
          "sha256": "2a7e1991019e1ff840907aef8470948d670a14464c806aab2cd925cd0ff4293c"
        }
      ]
    },
    "2025_hint": {
      "id": "1914918471940350300",
      "created_utc": "2025-04-23T05:45:15.000Z",
      "permalink": "https://x.com/666ab731/status/1914918471940350300",
      "text_verbatim": "@tactical_nook Seek also for 2222, 4444, 6666 and 8888.",
      "reply_to": "@tactical_nook  (status 1914914213740392569)",
      "seconds_after_repost": 3637
    },
    "association_status": "Strong source-linked inference: same author, named recipient, and a 3,637-second gap. The preserved parent context does not explicitly say that the four numbers describe this table."
  },
  "table": {
    "dimensions": [
      16,
      16
    ],
    "range": [
      428,
      683
    ],
    "magic_constant": 8888,
    "row_sums": [
      8888,
      8888,
      8888,
      8888,
      8888,
      8888,
      8888,
      8888,
      8888,
      8888,
      8888,
      8888,
      8888,
      8888,
      8888,
      8888
    ],
    "column_sums": [
      8888,
      8888,
      8888,
      8888,
      8888,
      8888,
      8888,
      8888,
      8888,
      8888,
      8888,
      8888,
      8888,
      8888,
      8888,
      8888
    ],
    "broken_diagonal_sums": {
      "down_right": [
        8888,
        8888,
        8888,
        8888,
        8888,
        8888,
        8888,
        8888,
        8888,
        8888,
        8888,
        8888,
        8888,
        8888,
        8888,
        8888
      ],
      "down_left": [
        8888,
        8888,
        8888,
        8888,
        8888,
        8888,
        8888,
        8888,
        8888,
        8888,
        8888,
        8888,
        8888,
        8888,
        8888,
        8888
      ]
    },
    "classification": "pandiagonal magic square; it is not most-perfect because cyclic 2x2 sums vary"
  },
  "binary_construction": {
    "normalization": "n[row,column] = value[row,column] - 428",
    "formula": "n[row,column] = row_masks[row] XOR column_masks[column]",
    "row_masks": [
      191,
      96,
      131,
      92,
      187,
      100,
      135,
      88,
      183,
      104,
      139,
      84,
      179,
      108,
      143,
      80
    ],
    "column_masks": [
      0,
      112,
      204,
      188,
      1,
      113,
      205,
      189,
      2,
      114,
      206,
      190,
      3,
      115,
      207,
      191
    ],
    "row_coset_origin": 191,
    "translated_row_subspace": [
      0,
      223,
      60,
      227,
      4,
      219,
      56,
      231,
      8,
      215,
      52,
      235,
      12,
      211,
      48,
      239
    ],
    "row_basis_first_encountered": [
      223,
      60,
      4,
      8
    ],
    "column_basis_first_encountered": [
      112,
      204,
      1,
      2
    ],
    "row_subspace_size": 16,
    "column_subspace_size": 16,
    "intersection": [
      0
    ],
    "combined_xor_coverage": 256,
    "interpretation_limit": "This fully specifies a compact numerical construction. It does not specify a letter extraction, cipher key, or plaintext."
  },
  "block_sum_ladder": {
    "aligned_even_start_blocks": [
      {
        "shape": "2x2",
        "starts": 64,
        "distinct_sums": [
          2222
        ],
        "constant": true,
        "expected_sum": 2222,
        "matches_expected": true
      },
      {
        "shape": "2x2",
        "starts": 64,
        "distinct_sums": [
          2222
        ],
        "constant": true,
        "expected_sum": 2222,
        "matches_expected": true
      },
      {
        "shape": "2x4",
        "starts": 56,
        "distinct_sums": [
          4444
        ],
        "constant": true,
        "expected_sum": 4444,
        "matches_expected": true
      },
      {
        "shape": "4x2",
        "starts": 56,
        "distinct_sums": [
          4444
        ],
        "constant": true,
        "expected_sum": 4444,
        "matches_expected": true
      },
      {
        "shape": "2x6",
        "starts": 48,
        "distinct_sums": [
          6666
        ],
        "constant": true,
        "expected_sum": 6666,
        "matches_expected": true
      },
      {
        "shape": "6x2",
        "starts": 48,
        "distinct_sums": [
          6666
        ],
        "constant": true,
        "expected_sum": 6666,
        "matches_expected": true
      },
      {
        "shape": "2x8",
        "starts": 40,
        "distinct_sums": [
          8888
        ],
        "constant": true,
        "expected_sum": 8888,
        "matches_expected": true
      },
      {
        "shape": "8x2",
        "starts": 40,
        "distinct_sums": [
          8888
        ],
        "constant": true,
        "expected_sum": 8888,
        "matches_expected": true
      }
    ],
    "cyclic_controls": [
      {
        "shape": "2x4",
        "starts": 256,
        "distinct_sums": [
          4444
        ],
        "constant": true,
        "expected_sum": 4444,
        "matches_expected": true
      },
      {
        "shape": "2x8",
        "starts": 256,
        "distinct_sums": [
          8888
        ],
        "constant": true,
        "expected_sum": 8888,
        "matches_expected": true
      },
      {
        "shape": "2x2",
        "starts": 256,
        "distinct_sums": [
          2198,
          2206,
          2214,
          2222,
          2230,
          2238,
          2246
        ],
        "constant": false,
        "expected_sum": null,
        "matches_expected": false
      }
    ],
    "concentric_squares": [
      {
        "rows_columns_1_based": [
          1,
          16
        ],
        "shape": "16x16",
        "sum": 142208,
        "expected_multiplier_of_8888": 16,
        "matches_expected": true
      },
      {
        "rows_columns_1_based": [
          3,
          14
        ],
        "shape": "12x12",
        "sum": 79992,
        "expected_multiplier_of_8888": 9,
        "matches_expected": true
      },
      {
        "rows_columns_1_based": [
          5,
          12
        ],
        "shape": "8x8",
        "sum": 35552,
        "expected_multiplier_of_8888": 4,
        "matches_expected": true
      },
      {
        "rows_columns_1_based": [
          7,
          10
        ],
        "shape": "4x4",
        "sum": 8888,
        "expected_multiplier_of_8888": 1,
        "matches_expected": true
      }
    ]
  },
  "printed_erratum": {
    "position_1_based": [
      3,
      5
    ],
    "as_printed": "3*3^2*31",
    "printed_value": 837,
    "corrected_factorization": "2*3^2*31",
    "corrected_value": 558,
    "why_correction_is_bounded": [
      "The 16-cell row must sum to the independently repeated magic constant 8888.",
      "All 255 remaining cells are canonical sorted prime-power strings; the corrected expression is canonical while the printed one is not."
    ]
  },
  "checks": {
    "shape": true,
    "permutation_428_through_683": true,
    "all_rows_8888": true,
    "all_columns_8888": true,
    "all_broken_diagonals_8888": true,
    "corrected_transcription_matches_evaluated_table": true,
    "only_correction_is_canonical": true,
    "printed_r03c05_is_the_known_erratum": true,
    "matrix_forces_r03c05_to_558": true,
    "all_aligned_ladder_claims": true,
    "cyclic_2x4_and_2x8": true,
    "cyclic_2x2_is_not_constant": true,
    "concentric_squares": true,
    "binary_xor_formula": true,
    "all_bit_planes_xor_separable": true,
    "complementary_four_dimensional_binary_subspaces": true
  },
  "conclusion": {
    "resolved": "The four numbers have a reproducible natural referent: block sums in the separately published 16x16 factorization magic square.",
    "not_resolved": [
      "No author-selected letter extraction, cipher key, or plaintext follows from the square.",
      "The relation of the square to the 154-letter Page 23 matrix is not established.",
      "The tweet's parent context was not preserved, so the table association is not an explicit author statement."
    ]
  }
}