{
 "problem": "min/cubes_in_cube",
 "page": "https://erich-friedman.github.io/packing/cubincub/",
 "n": 13,
 "dimension": 3,
 "s": 2.95614,
 "s_plus": "2.95614+",
 "s_full": 2.956148820837,
 "previous_record": "2.956+ (display value)",
 "previous_record_by": "Erich Friedman, 1998",
 "improvement": null,
 "found_by": "@BuilderOfAgents (soft-to-rigid method by Yohei Nakajima)",
 "date": "2026-10-09",
 "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": [
  [
   0.500001000000002,
   2.456147820836879,
   2.4146831381572733,
   0.500000000000001,
   -0.49999999999999817,
   -0.4999999999999985,
   -0.5000000000000026
  ],
  [
   1.41741418706108,
   2.456147820836879,
   1.280050096109885,
   1.3971049329457096e-15,
   0.9703616609062629,
   -1.509812144647054e-16,
   0.24165729255132976
  ],
  [
   1.41741418706108,
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   1.676098724726988,
   0.17087751028622278,
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   0.6861493106302623
  ],
  [
   1.4174141870610764,
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   0.6861493106302622,
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   0.17087751028621284,
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  ],
  [
   0.5000010000000014,
   2.451115524806469,
   0.5000010000000008,
   0.7071067811865472,
   -5.0586616693037916e-17,
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   6.518224041480208e-16
  ],
  [
   0.5000010000000011,
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   2.4561478208368754,
   0.7071067811865472,
   5.700649679106068e-16,
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   1.6053514432740606e-15
  ],
  [
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  ],
  [
   2.456147820836874,
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   2.2336701774313922e-17,
   1.4199516915136409e-15,
   1.0,
   5.273562905234564e-16
  ],
  [
   0.5000010000000018,
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   0.5662147795713846,
   0.7071067811865475,
   -6.44217795998904e-17,
   -1.5256651270668808e-16,
   -0.7071067811865477
  ],
  [
   2.456147820836866,
   2.4561478208368763,
   2.4484702875670186,
   1.4023025511463251e-14,
   2.0794954996919306e-14,
   -1.0827750533256622e-14,
   1.0
  ],
  [
   1.4174141870610795,
   1.2800500961098895,
   0.5000010000000017,
   0.6861493106302594,
   0.1708775102862269,
   -0.6861493106302599,
   0.17087751028622672
  ],
  [
   2.456147820836874,
   0.5000010000000051,
   0.5510383052806632,
   4.725153217277742e-16,
   -0.7071067811865476,
   5.380539429938093e-16,
   0.7071067811865475
  ],
  [
   2.4561478208368723,
   1.478074410418441,
   1.47807441041844,
   0.9889755195753916,
   -0.14807910615810768,
   -2.616150471958636e-16,
   1.2534952369048763e-15
  ]
 ],
 "status": "matches the current entry to its displayed precision; not claimed as an improvement",
 "contact_side": 2.956145157584923
}