{
  "benchmark": "single_sku_40hq_stratified",
  "date": "2026-10-16",
  "first_published": "2026-06-20",
  "seed": 20260619,
  "cases": 10000,
  "container": "40HQ_exact_12032x2352x2698",
  "space_lwh_mm": [
    12032,
    2352,
    2698
  ],
  "strata": [
    "small_dense",
    "medium_carton",
    "large_carton",
    "flat_panel",
    "tall_column",
    "long_case",
    "near_divisor",
    "awkward_remainder",
    "mixed_scale",
    "realistic_carton"
  ],
  "packcli_used": "D:\\Z3-worktrees\\t1-d2support-20261017\\SP3\\Pack\\x64\\Release\\PackCli.exe",
  "packcli_cases": 10000,
  "case_count_per_stratum": 1000,
  "dimension_policy": "Normal generated cartons use box_l >= box_w >= box_h. The tall_column stratum is an upright-product exception where box_h may be larger than box_l and box_w.",
  "normal_l_ge_w_ge_h_cases": 9000,
  "tall_upright_exception_cases": 1000,
  "box_width_gt_length_cases": 0,
  "box_height_gt_length_cases": 1000,
  "main_orientation_policy": "all_six_axis_aligned_orientations",
  "upright_baseline_policy": "upright_only_lwh_wlh_height_fixed",
  "all_six_one_cut_better_than_upright_cases": 8923,
  "all_six_one_cut_same_as_upright_cases": 1077,
  "all_six_one_cut_worse_than_upright_cases": 0,
  "avg_all_six_one_cut_gain_vs_upright_boxes": 64.846,
  "avg_all_six_one_cut_improvement_pct_vs_upright": 12.517,
  "median_all_six_one_cut_improvement_pct_vs_upright": 6.667,
  "p95_all_six_one_cut_improvement_pct_vs_upright": 46.269,
  "wins_vs_one_cut": 7873,
  "ties_vs_one_cut": 2127,
  "losses_vs_one_cut": 0,
  "avg_improvement_pct_vs_one_cut": 2.656,
  "median_improvement_pct_vs_one_cut": 1.937,
  "p90_improvement_pct_vs_one_cut": 6.25,
  "p95_improvement_pct_vs_one_cut": 8.0,
  "max_improvement_pct_vs_one_cut": 26.389,
  "avg_box_gain_vs_one_cut": 29.922,
  "wins_vs_single_grid": 9134,
  "ties_vs_single_grid": 866,
  "losses_vs_single_grid": 0,
  "avg_improvement_pct_vs_single_grid": 9.81,
  "median_improvement_pct_vs_single_grid": 8.096,
  "p95_improvement_pct_vs_single_grid": 25.0,
  "wins_vs_depth2": 5105,
  "ties_vs_depth2": 4895,
  "losses_vs_depth2": 0,
  "avg_improvement_pct_vs_depth2": 0.432,
  "median_improvement_pct_vs_depth2": 0.078,
  "p95_improvement_pct_vs_depth2": 1.791,
  "avg_t1_fill_pct": 93.486,
  "median_t1_fill_pct": 95.847,
  "p95_t1_fill_pct": 99.387,
  "by_stratum": [
    {
      "stratum": "small_dense",
      "cases": 1000,
      "wins_vs_one_cut": 980,
      "ties_vs_one_cut": 20,
      "losses_vs_one_cut": 0,
      "avg_improvement_pct_vs_one_cut": 1.741,
      "median_improvement_pct_vs_one_cut": 1.538,
      "p95_improvement_pct_vs_one_cut": 4.001,
      "avg_t1_fill_pct": 99.002
    },
    {
      "stratum": "medium_carton",
      "cases": 1000,
      "wins_vs_one_cut": 868,
      "ties_vs_one_cut": 132,
      "losses_vs_one_cut": 0,
      "avg_improvement_pct_vs_one_cut": 2.724,
      "median_improvement_pct_vs_one_cut": 2.304,
      "p95_improvement_pct_vs_one_cut": 6.923,
      "avg_t1_fill_pct": 95.888
    },
    {
      "stratum": "large_carton",
      "cases": 1000,
      "wins_vs_one_cut": 591,
      "ties_vs_one_cut": 409,
      "losses_vs_one_cut": 0,
      "avg_improvement_pct_vs_one_cut": 3.475,
      "median_improvement_pct_vs_one_cut": 1.81,
      "p95_improvement_pct_vs_one_cut": 13.333,
      "avg_t1_fill_pct": 86.308
    },
    {
      "stratum": "flat_panel",
      "cases": 1000,
      "wins_vs_one_cut": 900,
      "ties_vs_one_cut": 100,
      "losses_vs_one_cut": 0,
      "avg_improvement_pct_vs_one_cut": 3.371,
      "median_improvement_pct_vs_one_cut": 2.933,
      "p95_improvement_pct_vs_one_cut": 8.173,
      "avg_t1_fill_pct": 94.156
    },
    {
      "stratum": "tall_column",
      "cases": 1000,
      "wins_vs_one_cut": 778,
      "ties_vs_one_cut": 222,
      "losses_vs_one_cut": 0,
      "avg_improvement_pct_vs_one_cut": 3.028,
      "median_improvement_pct_vs_one_cut": 2.264,
      "p95_improvement_pct_vs_one_cut": 8.75,
      "avg_t1_fill_pct": 93.34
    },
    {
      "stratum": "long_case",
      "cases": 1000,
      "wins_vs_one_cut": 488,
      "ties_vs_one_cut": 512,
      "losses_vs_one_cut": 0,
      "avg_improvement_pct_vs_one_cut": 1.703,
      "median_improvement_pct_vs_one_cut": 0.0,
      "p95_improvement_pct_vs_one_cut": 6.667,
      "avg_t1_fill_pct": 86.636
    },
    {
      "stratum": "near_divisor",
      "cases": 1000,
      "wins_vs_one_cut": 749,
      "ties_vs_one_cut": 251,
      "losses_vs_one_cut": 0,
      "avg_improvement_pct_vs_one_cut": 2.014,
      "median_improvement_pct_vs_one_cut": 1.106,
      "p95_improvement_pct_vs_one_cut": 7.774,
      "avg_t1_fill_pct": 96.484
    },
    {
      "stratum": "awkward_remainder",
      "cases": 1000,
      "wins_vs_one_cut": 868,
      "ties_vs_one_cut": 132,
      "losses_vs_one_cut": 0,
      "avg_improvement_pct_vs_one_cut": 3.148,
      "median_improvement_pct_vs_one_cut": 2.824,
      "p95_improvement_pct_vs_one_cut": 7.563,
      "avg_t1_fill_pct": 94.928
    },
    {
      "stratum": "mixed_scale",
      "cases": 1000,
      "wins_vs_one_cut": 776,
      "ties_vs_one_cut": 224,
      "losses_vs_one_cut": 0,
      "avg_improvement_pct_vs_one_cut": 2.59,
      "median_improvement_pct_vs_one_cut": 1.897,
      "p95_improvement_pct_vs_one_cut": 8.312,
      "avg_t1_fill_pct": 91.993
    },
    {
      "stratum": "realistic_carton",
      "cases": 1000,
      "wins_vs_one_cut": 875,
      "ties_vs_one_cut": 125,
      "losses_vs_one_cut": 0,
      "avg_improvement_pct_vs_one_cut": 2.766,
      "median_improvement_pct_vs_one_cut": 2.325,
      "p95_improvement_pct_vs_one_cut": 7.212,
      "avg_t1_fill_pct": 96.126
    }
  ],
  "placed": {
    "headline_depth": 3,
    "solver_command": "PackCli --t1-pack with T1_DEPTH=2 (standard search) and T1_DEPTH=3 (Deeper search)",
    "checker": "t1_layout_checker.py: orientation, grid, containment, overlap, 100% base support, count, volume bound",
    "depth2": {
      "check_pass": 10000,
      "check_fail": 0,
      "plans_with_unsupported_cartons": 0,
      "unsupported_cartons_total": 0,
      "least_support_pct": 100.0,
      "below_count_only_search": 2171,
      "equal_to_count_only_search": 7829,
      "above_count_only_search": 0,
      "vs_one_cut": {
        "wins": 7592,
        "ties": 2405,
        "losses": 3,
        "avg_improvement_pct": 2.052,
        "median_improvement_pct": 1.364,
        "p95_improvement_pct": 6.452,
        "avg_box_gain": 21.683
      },
      "vs_supported_one_cut": {
        "wins": 7600,
        "ties": 2400,
        "losses": 0,
        "avg_improvement_pct": 2.063,
        "median_improvement_pct": 1.375,
        "p95_improvement_pct": 6.481,
        "avg_box_gain": 21.77
      },
      "vs_single_grid": {
        "wins": 9099,
        "ties": 901,
        "losses": 0,
        "avg_improvement_pct": 9.159,
        "median_improvement_pct": 7.407,
        "p95_improvement_pct": 25.0,
        "avg_box_gain": 79.557
      }
    },
    "depth3": {
      "check_pass": 10000,
      "check_fail": 0,
      "plans_with_unsupported_cartons": 0,
      "unsupported_cartons_total": 0,
      "least_support_pct": 100.0,
      "below_count_only_search": 2875,
      "equal_to_count_only_search": 7124,
      "above_count_only_search": 1,
      "vs_one_cut": {
        "wins": 7816,
        "ties": 2181,
        "losses": 3,
        "avg_improvement_pct": 2.512,
        "median_improvement_pct": 1.818,
        "p95_improvement_pct": 7.653,
        "avg_box_gain": 28.385
      },
      "vs_supported_one_cut": {
        "wins": 7824,
        "ties": 2176,
        "losses": 0,
        "avg_improvement_pct": 2.524,
        "median_improvement_pct": 1.826,
        "p95_improvement_pct": 7.692,
        "avg_box_gain": 28.472
      },
      "vs_single_grid": {
        "wins": 9129,
        "ties": 871,
        "losses": 0,
        "avg_improvement_pct": 9.654,
        "median_improvement_pct": 7.937,
        "p95_improvement_pct": 25.0,
        "avg_box_gain": 86.259
      }
    },
    "deeper_vs_standard": {
      "wins": 5134,
      "ties": 4866,
      "losses": 0,
      "avg_improvement_pct": 0.446,
      "median_improvement_pct": 0.086,
      "p95_improvement_pct": 1.852,
      "avg_box_gain": 6.702
    },
    "avg_fill_pct": 93.357,
    "median_fill_pct": 95.653,
    "by_stratum": [
      {
        "stratum": "small_dense",
        "cases": 1000,
        "wins_vs_one_cut": 980,
        "ties_vs_one_cut": 20,
        "losses_vs_one_cut": 0,
        "avg_improvement_pct_vs_one_cut": 1.651,
        "median_improvement_pct_vs_one_cut": 1.443,
        "p95_improvement_pct_vs_one_cut": 3.898,
        "avg_box_gain_vs_one_cut": 137.165,
        "avg_fill_pct": 98.915,
        "standard_plans_with_unsupported_cartons": 0,
        "deeper_below_count_only_search": 662
      },
      {
        "stratum": "medium_carton",
        "cases": 1000,
        "wins_vs_one_cut": 864,
        "ties_vs_one_cut": 135,
        "losses_vs_one_cut": 1,
        "avg_improvement_pct_vs_one_cut": 2.575,
        "median_improvement_pct_vs_one_cut": 2.146,
        "p95_improvement_pct_vs_one_cut": 6.667,
        "avg_box_gain_vs_one_cut": 19.769,
        "avg_fill_pct": 95.75,
        "standard_plans_with_unsupported_cartons": 0,
        "deeper_below_count_only_search": 329
      },
      {
        "stratum": "large_carton",
        "cases": 1000,
        "wins_vs_one_cut": 585,
        "ties_vs_one_cut": 415,
        "losses_vs_one_cut": 0,
        "avg_improvement_pct_vs_one_cut": 3.268,
        "median_improvement_pct_vs_one_cut": 1.739,
        "p95_improvement_pct_vs_one_cut": 12.5,
        "avg_box_gain_vs_one_cut": 2.453,
        "avg_fill_pct": 86.144,
        "standard_plans_with_unsupported_cartons": 0,
        "deeper_below_count_only_search": 96
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      {
        "stratum": "flat_panel",
        "cases": 1000,
        "wins_vs_one_cut": 895,
        "ties_vs_one_cut": 105,
        "losses_vs_one_cut": 0,
        "avg_improvement_pct_vs_one_cut": 3.215,
        "median_improvement_pct_vs_one_cut": 2.849,
        "p95_improvement_pct_vs_one_cut": 7.812,
        "avg_box_gain_vs_one_cut": 13.911,
        "avg_fill_pct": 94.014,
        "standard_plans_with_unsupported_cartons": 0,
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      {
        "stratum": "tall_column",
        "cases": 1000,
        "wins_vs_one_cut": 768,
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        "avg_improvement_pct_vs_one_cut": 2.842,
        "median_improvement_pct_vs_one_cut": 2.076,
        "p95_improvement_pct_vs_one_cut": 8.187,
        "avg_box_gain_vs_one_cut": 7.95,
        "avg_fill_pct": 93.175,
        "standard_plans_with_unsupported_cartons": 0,
        "deeper_below_count_only_search": 206
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      {
        "stratum": "long_case",
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        "wins_vs_one_cut": 483,
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        "p95_improvement_pct_vs_one_cut": 6.548,
        "avg_box_gain_vs_one_cut": 5.361,
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        "standard_plans_with_unsupported_cartons": 0,
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      {
        "stratum": "near_divisor",
        "cases": 1000,
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        "avg_improvement_pct_vs_one_cut": 1.906,
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        "p95_improvement_pct_vs_one_cut": 7.609,
        "avg_box_gain_vs_one_cut": 14.605,
        "avg_fill_pct": 96.383,
        "standard_plans_with_unsupported_cartons": 0,
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      {
        "stratum": "awkward_remainder",
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        "losses_vs_one_cut": 1,
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        "median_improvement_pct_vs_one_cut": 2.617,
        "p95_improvement_pct_vs_one_cut": 7.323,
        "avg_box_gain_vs_one_cut": 20.009,
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        "standard_plans_with_unsupported_cartons": 0,
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      {
        "stratum": "mixed_scale",
        "cases": 1000,
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        "ties_vs_one_cut": 230,
        "losses_vs_one_cut": 0,
        "avg_improvement_pct_vs_one_cut": 2.45,
        "median_improvement_pct_vs_one_cut": 1.786,
        "p95_improvement_pct_vs_one_cut": 7.922,
        "avg_box_gain_vs_one_cut": 35.958,
        "avg_fill_pct": 91.87,
        "standard_plans_with_unsupported_cartons": 0,
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      {
        "stratum": "realistic_carton",
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        "wins_vs_one_cut": 872,
        "ties_vs_one_cut": 128,
        "losses_vs_one_cut": 0,
        "avg_improvement_pct_vs_one_cut": 2.608,
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        "avg_box_gain_vs_one_cut": 26.673,
        "avg_fill_pct": 95.979,
        "standard_plans_with_unsupported_cartons": 0,
        "deeper_below_count_only_search": 381
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    ]
  }
}