{
  "seed": 3301031,
  "simulations": 99999,
  "short_gap_threshold": 10,
  "scope": "Same eight substantial LP2 sections: 86 repeat events, 12,939 eligible edges, 78 consecutive-event gaps. Section boundaries not crossed.",
  "definitions": {
    "short": "Count gaps <=10 between consecutive repeat-event LEFT-rune positions, pooled over sections. A gap of 10 means event starts ten rune positions apart.",
    "long": "Maximum number of consecutive eligible edges with no repeat event, over all eight sections. Includes leading/trailing section intervals; excludes the bounding events. Not a printed-page or word distance.",
    "overlap": "Count consecutive-event distances equal to 1, corresponding to AAA. A run AAAA contributes two overlapping-event gaps."
  },
  "null": "Uniformly choose each section observed number of distinct eligible edges, independently by section. Same simulated configuration used for all three tests. Event labels only; rune identities, event spacing and page-level event counts are not preserved.",
  "correction": "Three predeclared one-sided upper-tail Monte Carlo comparisons, each with Bonferroni factor 3. No normal approximation and no selected threshold sweep.",
  "measurements": [
    {
      "statistic": "consecutive_event_gaps_at_most_10",
      "observed": 4,
      "simulation_mean": 5.354443544435444,
      "central_95_percent": [
        2.0,
        10.0
      ],
      "at_or_above": 80022,
      "raw_upper_tail": 0.80023,
      "three_test_bonferroni": 1.0
    },
    {
      "statistic": "longest_empty_edge_stretch",
      "observed": 661,
      "simulation_mean": 664.5112851128512,
      "central_95_percent": [
        465.0,
        985.0
      ],
      "at_or_above": 44634,
      "raw_upper_tail": 0.44635,
      "three_test_bonferroni": 1.0
    },
    {
      "statistic": "overlapping_doubles",
      "observed": 0,
      "simulation_mean": 0.5506955069550695,
      "central_95_percent": [
        0.0,
        2.0
      ],
      "at_or_above": 99999,
      "raw_upper_tail": 1.0,
      "three_test_bonferroni": 1.0
    }
  ],
  "analytic_means": {
    "short_gaps": 5.351747963248245,
    "overlaps": 0.5520103521442756
  },
  "sections": [
    {
      "section": 0,
      "runes": 729,
      "eligible_edges": 728,
      "event_count": 4,
      "event_positions": [
        121,
        206,
        455,
        652
      ],
      "observed_statistics": [
        0,
        248,
        0
      ],
      "analytic_expected_short_gaps": 0.16179669592846085,
      "analytic_expected_overlaps": 0.016483516483516484
    },
    {
      "section": 1,
      "runes": 1145,
      "eligible_edges": 1144,
      "event_count": 6,
      "event_positions": [
        52,
        179,
        202,
        249,
        308,
        861
      ],
      "observed_statistics": [
        0,
        552,
        0
      ],
      "analytic_expected_short_gaps": 0.25712359650477484,
      "analytic_expected_overlaps": 0.026223776223776224
    },
    {
      "section": 2,
      "runes": 1729,
      "eligible_edges": 1728,
      "event_count": 9,
      "event_positions": [
        106,
        141,
        151,
        317,
        366,
        470,
        705,
        865,
        1265
      ],
      "observed_statistics": [
        1,
        462,
        0
      ],
      "analytic_expected_short_gaps": 0.4080744493950448,
      "analytic_expected_overlaps": 0.041666666666666664
    },
    {
      "section": 4,
      "runes": 1894,
      "eligible_edges": 1893,
      "event_count": 10,
      "event_positions": [
        239,
        776,
        967,
        994,
        1059,
        1100,
        1161,
        1462,
        1648,
        1863
      ],
      "observed_statistics": [
        0,
        536,
        0
      ],
      "analytic_expected_short_gaps": 0.46537274745371393,
      "analytic_expected_overlaps": 0.04754358161648178
    },
    {
      "section": 5,
      "runes": 1021,
      "eligible_edges": 1020,
      "event_count": 11,
      "event_positions": [
        127,
        264,
        271,
        318,
        329,
        463,
        513,
        574,
        717,
        816,
        858
      ],
      "observed_statistics": [
        1,
        161,
        0
      ],
      "analytic_expected_short_gaps": 1.0319142772204302,
      "analytic_expected_overlaps": 0.10784313725490197
    },
    {
      "section": 6,
      "runes": 1524,
      "eligible_edges": 1523,
      "event_count": 13,
      "event_positions": [
        14,
        83,
        89,
        122,
        228,
        590,
        616,
        642,
        704,
        853,
        1041,
        1341,
        1415
      ],
      "observed_statistics": [
        1,
        361,
        0
      ],
      "analytic_expected_short_gaps": 0.9886454320378033,
      "analytic_expected_overlaps": 0.10242941562705186
    },
    {
      "section": 7,
      "runes": 1589,
      "eligible_edges": 1588,
      "event_count": 12,
      "event_positions": [
        60,
        90,
        144,
        257,
        333,
        579,
        586,
        648,
        674,
        724,
        882,
        1544
      ],
      "observed_statistics": [
        1,
        661,
        0
      ],
      "analytic_expected_short_gaps": 0.8057389153553487,
      "analytic_expected_overlaps": 0.08312342569269521
    },
    {
      "section": 8,
      "runes": 3316,
      "eligible_edges": 3315,
      "event_count": 21,
      "event_positions": [
        276,
        499,
        525,
        867,
        928,
        971,
        1109,
        1120,
        1201,
        1313,
        1462,
        1548,
        1703,
        1958,
        2018,
        2204,
        2474,
        2733,
        3027,
        3163,
        3298
      ],
      "observed_statistics": [
        0,
        341,
        0
      ],
      "analytic_expected_short_gaps": 1.233081849352669,
      "analytic_expected_overlaps": 0.12669683257918551
    }
  ],
  "consecutive_event_gaps": [
    {
      "section": 0,
      "left_event": 121,
      "right_event": 206,
      "distance": 85
    },
    {
      "section": 0,
      "left_event": 206,
      "right_event": 455,
      "distance": 249
    },
    {
      "section": 0,
      "left_event": 455,
      "right_event": 652,
      "distance": 197
    },
    {
      "section": 1,
      "left_event": 52,
      "right_event": 179,
      "distance": 127
    },
    {
      "section": 1,
      "left_event": 179,
      "right_event": 202,
      "distance": 23
    },
    {
      "section": 1,
      "left_event": 202,
      "right_event": 249,
      "distance": 47
    },
    {
      "section": 1,
      "left_event": 249,
      "right_event": 308,
      "distance": 59
    },
    {
      "section": 1,
      "left_event": 308,
      "right_event": 861,
      "distance": 553
    },
    {
      "section": 2,
      "left_event": 106,
      "right_event": 141,
      "distance": 35
    },
    {
      "section": 2,
      "left_event": 141,
      "right_event": 151,
      "distance": 10
    },
    {
      "section": 2,
      "left_event": 151,
      "right_event": 317,
      "distance": 166
    },
    {
      "section": 2,
      "left_event": 317,
      "right_event": 366,
      "distance": 49
    },
    {
      "section": 2,
      "left_event": 366,
      "right_event": 470,
      "distance": 104
    },
    {
      "section": 2,
      "left_event": 470,
      "right_event": 705,
      "distance": 235
    },
    {
      "section": 2,
      "left_event": 705,
      "right_event": 865,
      "distance": 160
    },
    {
      "section": 2,
      "left_event": 865,
      "right_event": 1265,
      "distance": 400
    },
    {
      "section": 4,
      "left_event": 239,
      "right_event": 776,
      "distance": 537
    },
    {
      "section": 4,
      "left_event": 776,
      "right_event": 967,
      "distance": 191
    },
    {
      "section": 4,
      "left_event": 967,
      "right_event": 994,
      "distance": 27
    },
    {
      "section": 4,
      "left_event": 994,
      "right_event": 1059,
      "distance": 65
    },
    {
      "section": 4,
      "left_event": 1059,
      "right_event": 1100,
      "distance": 41
    },
    {
      "section": 4,
      "left_event": 1100,
      "right_event": 1161,
      "distance": 61
    },
    {
      "section": 4,
      "left_event": 1161,
      "right_event": 1462,
      "distance": 301
    },
    {
      "section": 4,
      "left_event": 1462,
      "right_event": 1648,
      "distance": 186
    },
    {
      "section": 4,
      "left_event": 1648,
      "right_event": 1863,
      "distance": 215
    },
    {
      "section": 5,
      "left_event": 127,
      "right_event": 264,
      "distance": 137
    },
    {
      "section": 5,
      "left_event": 264,
      "right_event": 271,
      "distance": 7
    },
    {
      "section": 5,
      "left_event": 271,
      "right_event": 318,
      "distance": 47
    },
    {
      "section": 5,
      "left_event": 318,
      "right_event": 329,
      "distance": 11
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    {
      "section": 5,
      "left_event": 329,
      "right_event": 463,
      "distance": 134
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    {
      "section": 5,
      "left_event": 463,
      "right_event": 513,
      "distance": 50
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    {
      "section": 5,
      "left_event": 513,
      "right_event": 574,
      "distance": 61
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    {
      "section": 5,
      "left_event": 574,
      "right_event": 717,
      "distance": 143
    },
    {
      "section": 5,
      "left_event": 717,
      "right_event": 816,
      "distance": 99
    },
    {
      "section": 5,
      "left_event": 816,
      "right_event": 858,
      "distance": 42
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    {
      "section": 6,
      "left_event": 14,
      "right_event": 83,
      "distance": 69
    },
    {
      "section": 6,
      "left_event": 83,
      "right_event": 89,
      "distance": 6
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    {
      "section": 6,
      "left_event": 89,
      "right_event": 122,
      "distance": 33
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    {
      "section": 6,
      "left_event": 122,
      "right_event": 228,
      "distance": 106
    },
    {
      "section": 6,
      "left_event": 228,
      "right_event": 590,
      "distance": 362
    },
    {
      "section": 6,
      "left_event": 590,
      "right_event": 616,
      "distance": 26
    },
    {
      "section": 6,
      "left_event": 616,
      "right_event": 642,
      "distance": 26
    },
    {
      "section": 6,
      "left_event": 642,
      "right_event": 704,
      "distance": 62
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    {
      "section": 6,
      "left_event": 704,
      "right_event": 853,
      "distance": 149
    },
    {
      "section": 6,
      "left_event": 853,
      "right_event": 1041,
      "distance": 188
    },
    {
      "section": 6,
      "left_event": 1041,
      "right_event": 1341,
      "distance": 300
    },
    {
      "section": 6,
      "left_event": 1341,
      "right_event": 1415,
      "distance": 74
    },
    {
      "section": 7,
      "left_event": 60,
      "right_event": 90,
      "distance": 30
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    {
      "section": 7,
      "left_event": 90,
      "right_event": 144,
      "distance": 54
    },
    {
      "section": 7,
      "left_event": 144,
      "right_event": 257,
      "distance": 113
    },
    {
      "section": 7,
      "left_event": 257,
      "right_event": 333,
      "distance": 76
    },
    {
      "section": 7,
      "left_event": 333,
      "right_event": 579,
      "distance": 246
    },
    {
      "section": 7,
      "left_event": 579,
      "right_event": 586,
      "distance": 7
    },
    {
      "section": 7,
      "left_event": 586,
      "right_event": 648,
      "distance": 62
    },
    {
      "section": 7,
      "left_event": 648,
      "right_event": 674,
      "distance": 26
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    {
      "section": 7,
      "left_event": 674,
      "right_event": 724,
      "distance": 50
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    {
      "section": 7,
      "left_event": 724,
      "right_event": 882,
      "distance": 158
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    {
      "section": 7,
      "left_event": 882,
      "right_event": 1544,
      "distance": 662
    },
    {
      "section": 8,
      "left_event": 276,
      "right_event": 499,
      "distance": 223
    },
    {
      "section": 8,
      "left_event": 499,
      "right_event": 525,
      "distance": 26
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    {
      "section": 8,
      "left_event": 525,
      "right_event": 867,
      "distance": 342
    },
    {
      "section": 8,
      "left_event": 867,
      "right_event": 928,
      "distance": 61
    },
    {
      "section": 8,
      "left_event": 928,
      "right_event": 971,
      "distance": 43
    },
    {
      "section": 8,
      "left_event": 971,
      "right_event": 1109,
      "distance": 138
    },
    {
      "section": 8,
      "left_event": 1109,
      "right_event": 1120,
      "distance": 11
    },
    {
      "section": 8,
      "left_event": 1120,
      "right_event": 1201,
      "distance": 81
    },
    {
      "section": 8,
      "left_event": 1201,
      "right_event": 1313,
      "distance": 112
    },
    {
      "section": 8,
      "left_event": 1313,
      "right_event": 1462,
      "distance": 149
    },
    {
      "section": 8,
      "left_event": 1462,
      "right_event": 1548,
      "distance": 86
    },
    {
      "section": 8,
      "left_event": 1548,
      "right_event": 1703,
      "distance": 155
    },
    {
      "section": 8,
      "left_event": 1703,
      "right_event": 1958,
      "distance": 255
    },
    {
      "section": 8,
      "left_event": 1958,
      "right_event": 2018,
      "distance": 60
    },
    {
      "section": 8,
      "left_event": 2018,
      "right_event": 2204,
      "distance": 186
    },
    {
      "section": 8,
      "left_event": 2204,
      "right_event": 2474,
      "distance": 270
    },
    {
      "section": 8,
      "left_event": 2474,
      "right_event": 2733,
      "distance": 259
    },
    {
      "section": 8,
      "left_event": 2733,
      "right_event": 3027,
      "distance": 294
    },
    {
      "section": 8,
      "left_event": 3027,
      "right_event": 3163,
      "distance": 136
    },
    {
      "section": 8,
      "left_event": 3163,
      "right_event": 3298,
      "distance": 135
    }
  ],
  "longest_empty_intervals": [
    {
      "section": 7,
      "start_edge_inclusive": 883,
      "end_edge_exclusive": 1544,
      "length": 661,
      "touches_section_start": false,
      "touches_section_end": false
    },
    {
      "section": 1,
      "start_edge_inclusive": 309,
      "end_edge_exclusive": 861,
      "length": 552,
      "touches_section_start": false,
      "touches_section_end": false
    },
    {
      "section": 4,
      "start_edge_inclusive": 240,
      "end_edge_exclusive": 776,
      "length": 536,
      "touches_section_start": false,
      "touches_section_end": false
    },
    {
      "section": 2,
      "start_edge_inclusive": 1266,
      "end_edge_exclusive": 1728,
      "length": 462,
      "touches_section_start": false,
      "touches_section_end": true
    },
    {
      "section": 2,
      "start_edge_inclusive": 866,
      "end_edge_exclusive": 1265,
      "length": 399,
      "touches_section_start": false,
      "touches_section_end": false
    },
    {
      "section": 6,
      "start_edge_inclusive": 229,
      "end_edge_exclusive": 590,
      "length": 361,
      "touches_section_start": false,
      "touches_section_end": false
    },
    {
      "section": 8,
      "start_edge_inclusive": 526,
      "end_edge_exclusive": 867,
      "length": 341,
      "touches_section_start": false,
      "touches_section_end": false
    },
    {
      "section": 4,
      "start_edge_inclusive": 1162,
      "end_edge_exclusive": 1462,
      "length": 300,
      "touches_section_start": false,
      "touches_section_end": false
    },
    {
      "section": 6,
      "start_edge_inclusive": 1042,
      "end_edge_exclusive": 1341,
      "length": 299,
      "touches_section_start": false,
      "touches_section_end": false
    },
    {
      "section": 8,
      "start_edge_inclusive": 2734,
      "end_edge_exclusive": 3027,
      "length": 293,
      "touches_section_start": false,
      "touches_section_end": false
    }
  ],
  "calculation_controls": {
    "manual_example": {
      "eligible_edges": 12,
      "event_positions": [
        1,
        2,
        8
      ],
      "statistics": [
        2,
        5,
        1
      ]
    },
    "exhaustive_control": {
      "eligible_edges": 8,
      "event_count": 3,
      "configurations": 56,
      "short_threshold": 2,
      "mean_short_gaps": 1.2857142857142858,
      "mean_overlaps": 0.75,
      "minimum_longest_gap": 2,
      "maximum_longest_gap": 5
    },
    "passed": true
  },
  "artificial_cluster_control": {
    "description": "Place each section events consecutively at its start, retaining all section counts. Deliberately extreme event-label pattern, not encrypted text.",
    "results": [
      {
        "statistic": "consecutive_event_gaps_at_most_10",
        "observed": 78,
        "three_test_bonferroni": 3e-05
      },
      {
        "statistic": "longest_empty_edge_stretch",
        "observed": 3294,
        "three_test_bonferroni": 3e-05
      },
      {
        "statistic": "overlapping_doubles",
        "observed": 78,
        "three_test_bonferroni": 3e-05
      }
    ]
  },
  "event_inventory_crosscheck": true,
  "transcription_sha256": "b0b2e13c3cd35512ee5955a2d9a56c22d7410e283d35dd9c90abbaa7b99279eb",
  "limits": [
    "Retrospective comparison on previously inspected text; no untouched validation set.",
    "Null requires exchangeability of event locations within sections, not a claimed model of encryption.",
    "Longest interval uses edges without equality, not letters without any repetition at any distance.",
    "Only bursts/excesses are tested; unusually regular spacing or a deficit of overlaps is not a separate tested hypothesis.",
    "Correction covers these three checks only, not every historical research decision.",
    "No full new image audit, rune-specific context test, state-reset attribution, key search or plaintext recovery.",
    "A non-detection does not establish independent events; power is limited by 86 events and the fixed statistics."
  ]
}