{
  "problem": "min/cubes_in_cube",
  "page": "https://erich-friedman.github.io/packing/cubincub/",
  "n": 12,
  "dimension": 3,
  "s": 2.93151,
  "s_plus": "2.93151+",
  "s_full": 2.9315185094797,
  "previous_record": 2.9327717687048653,
  "previous_record_by": "Haowei Lin, July 2026 (Tencent-Hunyuan/Hyra-results, cubincub_n12.json)",
  "improvement": 0.0012532592,
  "found_by": "Yohei Nakajima",
  "date": "2026-10-08",
  "method": "soft-to-rigid homotopy (balls hardened into cubes under inward pressure), then SLSQP tightening with per-pair separating planes",
  "clearance": {
    "min_pair_gap_target": 1e-06,
    "wall_gap_target": 1e-06
  },
  "coords_note": "full-precision coordinates; s_full rounded up at the 13th decimal; reported value truncated to 5dp (x.xxxxx+)",
  "format": "[x, y, z, qw, qx, qy, qz] per piece: unit cube (edge 1) centred at (x, y, z), rotated by the scalar-first unit quaternion q; container [0, s_full]^3",
  "pieces": [
    [
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      0.5838886868807781,
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      -0.3988408220488987
    ],
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      -1.2564110072831059e-16,
      4.177826011452137e-16
    ],
    [
      0.5000010000000003,
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    ],
    [
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      0.4560511351275036,
      -0.5403863020286541,
      -0.45604723940148045,
      0.5403896021973412
    ],
    [
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    ],
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      -1.9389493161765827e-16,
      -1.0
    ],
    [
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    ],
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      -1.701330443461534e-16
    ],
    [
      1.6870691741447312,
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    ],
    [
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    ],
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      0.5,
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      0.5
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      0.5000010000000005,
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      0.7071067811865476,
      -0.7071067811865475,
      2.1753737637419648e-17,
      1.0211918387586666e-16
    ]
  ]
}