{"abstract":"Cube utilization is overstated by one basis point on fractional values.","category":"Warehouse slotting and bin packing","checks":8,"contract":"slot [width, depth, height], unit [w, d, h]. Upright units may only rotate in the horizontal plane; others may take any of the 6 axis orientations. Vertical layers = height // unit height, capped at max_stack when max_stack > 0 (0 = unlimited). Units = best over orientations of (W//a)*(D//b)*layers. Utilization in basis points = floor(units*unit volume*10000/slot volume).","contract_signature":"slot, unit, max_stack, upright","evaluation_group":"w2-warehouse-slotting-slot-cube-fit","failed_approach":"Flooring to whole percent before scaling discards the basis-point precision.","family":"w2-warehouse-slotting-slot-cube-fit-utilization-precision","id":"FA-95081","implementations":{"attempt":{"sha256":"241ab7d3b070655277087c18fdf0738a16285ffd7de1d026d37eaf007ce82ada","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport itertools\nN = 1\nobservations = []\ndef solve(slot, unit, max_stack, upright):\n    SW, SD, SH = slot\n    uw, ud, uh = unit\n    if upright:\n        orients = [(uw, ud, uh), (ud, uw, uh)]\n    else:\n        orients = sorted(set(itertools.permutations(unit)))\n    best = 0\n    for a, b, c in orients:\n        layers = SH // c\n        if max_stack:\n            layers = min(layers, max_stack)\n        best = max(best, (SW // a) * (SD // b) * layers)\n    bp = best * uw * ud * uh * 100 // (SW * SD * SH) * 100\n    return [best, bp]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['stack cap', [[48, 40, 30], [12, 10, 10], 2, True], [32, 6666]], ['laydown helps', [[40, 40, 12], [10, 10, 20], 0, False], [8, 8333]], ['upright plane rotation', [[48, 40, 30], [12, 10, 10], 0, True], [48, 10000]], ['unlimited zero', [[20, 20, 40], [10, 10, 10], 0, True], [16, 10000]], ['upright blocked', [[40, 40, 12], [10, 10, 20], 0, True], [0, 0]], ['generated mix 7', [[48, 40, 60], [12, 15, 12], 5, True], [45, 8437]], ['generated mix 15', [[40, 60, 30], [25, 6, 4], 5, False], [100, 8333]], ['generated mix 23', [[100, 30, 45], [12, 15, 12], 3, True], [48, 7680]]], [['generated mix 21', [[40, 48, 45], [10, 10, 10], 2, True], [32, 3703]], ['generated mix 8', [[60, 48, 60], [25, 10, 12], 5, False], [48, 8333]], ['upright blocked', [[40, 40, 12], [10, 10, 20], 0, True], [0, 0]], ['fraction bp', [[100, 30, 45], [25, 15, 7], 0, True], [48, 9333]], ['stack cap', [[48, 40, 30], [12, 10, 10], 2, True], [32, 6666]], ['generated mix 10', [[48, 60, 45], [25, 20, 10], 0, True], [16, 6172]], ['generated mix 18', [[40, 48, 20], [25, 20, 10], 3, False], [4, 5208]], ['generated mix 27', [[60, 60, 45], [8, 20, 7], 3, False], [112, 7743]]], [['generated mix 56', [[48, 30, 45], [12, 15, 10], 3, True], [24, 6666]], ['generated mix 15', [[40, 60, 30], [25, 6, 4], 5, False], [100, 8333]], ['upright plane rotation', [[48, 40, 30], [12, 10, 10], 0, True], [48, 10000]], ['laydown helps', [[40, 40, 12], [10, 10, 20], 0, False], [8, 8333]], ['unlimited zero', [[20, 20, 40], [10, 10, 10], 0, True], [16, 10000]], ['generated mix 21', [[40, 48, 45], [10, 10, 10], 2, True], [32, 3703]], ['generated mix 29', [[100, 48, 20], [8, 20, 12], 1, True], [30, 6000]], ['generated mix 37', [[40, 48, 20], [8, 6, 7], 1, False], [40, 3500]]], [['generated mix 4', [[60, 30, 45], [25, 15, 12], 0, True], [12, 6666]], ['generated mix 20', [[48, 60, 60], [25, 10, 4], 3, True], [24, 1388]], ['upright blocked', [[40, 40, 12], [10, 10, 20], 0, True], [0, 0]], ['fraction bp', [[100, 30, 45], [25, 15, 7], 0, True], [48, 9333]], ['stack cap', [[48, 40, 30], [12, 10, 10], 2, True], [32, 6666]], ['generated mix 33', [[40, 40, 60], [25, 15, 35], 0, True], [2, 2734]], ['generated mix 41', [[60, 30, 20], [8, 6, 7], 0, True], [70, 6533]], ['generated mix 49', [[100, 60, 60], [25, 20, 7], 5, False], [96, 9333]]], [['generated mix 26', [[40, 40, 45], [5, 6, 35], 0, False], [56, 8166]], ['generated mix 25', [[100, 60, 45], [8, 10, 12], 1, False], [72, 2560]], ['upright plane rotation', [[48, 40, 30], [12, 10, 10], 0, True], [48, 10000]], ['laydown helps', [[40, 40, 12], [10, 10, 20], 0, False], [8, 8333]], ['unlimited zero', [[20, 20, 40], [10, 10, 10], 0, True], [16, 10000]], ['generated mix 44', [[40, 60, 30], [12, 10, 10], 0, True], [60, 10000]], ['generated mix 52', [[40, 48, 45], [10, 20, 35], 2, True], [8, 6481]], ['generated mix 60', [[40, 48, 20], [8, 6, 12], 1, False], [40, 6000]]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"c59b797e7dc2f67bd8de9c4f741a964e8be069e8ee8160b2cc43e77c0355613a","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport itertools\nN = 1\nobservations = []\ndef solve(slot, unit, max_stack, upright):\n    SW, SD, SH = slot\n    uw, ud, uh = unit\n    if upright:\n        orients = [(uw, ud, uh), (ud, uw, uh)]\n    else:\n        orients = sorted(set(itertools.permutations(unit)))\n    best = 0\n    for a, b, c in orients:\n        layers = SH // c\n        if max_stack:\n            layers = min(layers, max_stack)\n        best = max(best, (SW // a) * (SD // b) * layers)\n    bp = round(best * uw * ud * uh * 10000 / (SW * SD * SH))\n    return [best, bp]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['stack cap', [[48, 40, 30], [12, 10, 10], 2, True], [32, 6666]], ['laydown helps', [[40, 40, 12], [10, 10, 20], 0, False], [8, 8333]], ['upright plane rotation', [[48, 40, 30], [12, 10, 10], 0, True], [48, 10000]], ['unlimited zero', [[20, 20, 40], [10, 10, 10], 0, True], [16, 10000]], ['upright blocked', [[40, 40, 12], [10, 10, 20], 0, True], [0, 0]], ['generated mix 7', [[48, 40, 60], [12, 15, 12], 5, True], [45, 8437]], ['generated mix 15', [[40, 60, 30], [25, 6, 4], 5, False], [100, 8333]], ['generated mix 23', [[100, 30, 45], [12, 15, 12], 3, True], [48, 7680]]], [['generated mix 21', [[40, 48, 45], [10, 10, 10], 2, True], [32, 3703]], ['generated mix 8', [[60, 48, 60], [25, 10, 12], 5, False], [48, 8333]], ['upright blocked', [[40, 40, 12], [10, 10, 20], 0, True], [0, 0]], ['fraction bp', [[100, 30, 45], [25, 15, 7], 0, True], [48, 9333]], ['stack cap', [[48, 40, 30], [12, 10, 10], 2, True], [32, 6666]], ['generated mix 10', [[48, 60, 45], [25, 20, 10], 0, True], [16, 6172]], ['generated mix 18', [[40, 48, 20], [25, 20, 10], 3, False], [4, 5208]], ['generated mix 27', [[60, 60, 45], [8, 20, 7], 3, False], [112, 7743]]], [['generated mix 56', [[48, 30, 45], [12, 15, 10], 3, True], [24, 6666]], ['generated mix 15', [[40, 60, 30], [25, 6, 4], 5, False], [100, 8333]], ['upright plane rotation', [[48, 40, 30], [12, 10, 10], 0, True], [48, 10000]], ['laydown helps', [[40, 40, 12], [10, 10, 20], 0, False], [8, 8333]], ['unlimited zero', [[20, 20, 40], [10, 10, 10], 0, True], [16, 10000]], ['generated mix 21', [[40, 48, 45], [10, 10, 10], 2, True], [32, 3703]], ['generated mix 29', [[100, 48, 20], [8, 20, 12], 1, True], [30, 6000]], ['generated mix 37', [[40, 48, 20], [8, 6, 7], 1, False], [40, 3500]]], [['generated mix 4', [[60, 30, 45], [25, 15, 12], 0, True], [12, 6666]], ['generated mix 20', [[48, 60, 60], [25, 10, 4], 3, True], [24, 1388]], ['upright blocked', [[40, 40, 12], [10, 10, 20], 0, True], [0, 0]], ['fraction bp', [[100, 30, 45], [25, 15, 7], 0, True], [48, 9333]], ['stack cap', [[48, 40, 30], [12, 10, 10], 2, True], [32, 6666]], ['generated mix 33', [[40, 40, 60], [25, 15, 35], 0, True], [2, 2734]], ['generated mix 41', [[60, 30, 20], [8, 6, 7], 0, True], [70, 6533]], ['generated mix 49', [[100, 60, 60], [25, 20, 7], 5, False], [96, 9333]]], [['generated mix 26', [[40, 40, 45], [5, 6, 35], 0, False], [56, 8166]], ['generated mix 25', [[100, 60, 45], [8, 10, 12], 1, False], [72, 2560]], ['upright plane rotation', [[48, 40, 30], [12, 10, 10], 0, True], [48, 10000]], ['laydown helps', [[40, 40, 12], [10, 10, 20], 0, False], [8, 8333]], ['unlimited zero', [[20, 20, 40], [10, 10, 10], 0, True], [16, 10000]], ['generated mix 44', [[40, 60, 30], [12, 10, 10], 0, True], [60, 10000]], ['generated mix 52', [[40, 48, 45], [10, 20, 35], 2, True], [8, 6481]], ['generated mix 60', [[40, 48, 20], [8, 6, 12], 1, False], [40, 6000]]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"Uniform unit, single orientation per slot; no mixed orientation packing. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-warehouse-slotting-slot-cube-fit-utilization-precision","generated_at":"2026-09-29T14:52:10.451706+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Slot sizing converts product cube into units per location for slotting and replenishment.","root_cause":"Utilization basis points are rounded to nearest instead of floored as the contract requires.","sha256":"ae2a74dc2fa87a40365fcc0d06418a865b2cd3d4baca985f07080c8d842e56a4","title":"Slot fit: utilization rounded instead of floored · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":43.514,"exit_code":1,"observations":[{"actual":[32,6600],"check":"stack cap","expected":[32,6666],"passed":false},{"actual":[8,8300],"check":"laydown helps","expected":[8,8333],"passed":false},{"actual":[48,10000],"check":"upright plane rotation","expected":[48,10000],"passed":true},{"actual":[16,10000],"check":"unlimited zero","expected":[16,10000],"passed":true},{"actual":[0,0],"check":"upright blocked","expected":[0,0],"passed":true},{"actual":[45,8400],"check":"generated mix 7","expected":[45,8437],"passed":false},{"actual":[100,8300],"check":"generated mix 15","expected":[100,8333],"passed":false},{"actual":[48,7600],"check":"generated mix 23","expected":[48,7680],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"stack cap\", \"actual\": [32, 6600], \"expected\": [32, 6666], \"passed\": false}, {\"check\": \"laydown helps\", \"actual\": [8, 8300], \"expected\": [8, 8333], \"passed\": false}, {\"check\": \"upright plane rotation\", \"actual\": [48, 10000], \"expected\": [48, 10000], \"passed\": true}, {\"check\": \"unlimited zero\", \"actual\": [16, 10000], \"expected\": [16, 10000], \"passed\": true}, {\"check\": \"upright blocked\", \"actual\": [0, 0], \"expected\": [0, 0], \"passed\": true}, {\"check\": \"generated mix 7\", \"actual\": [45, 8400], \"expected\": [45, 8437], \"passed\": false}, {\"check\": \"generated mix 15\", \"actual\": [100, 8300], \"expected\": [100, 8333], \"passed\": false}, {\"check\": \"generated mix 23\", \"actual\": [48, 7600], \"expected\": [48, 7680], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.778,"exit_code":1,"observations":[{"actual":[32,6667],"check":"stack cap","expected":[32,6666],"passed":false},{"actual":[8,8333],"check":"laydown helps","expected":[8,8333],"passed":true},{"actual":[48,10000],"check":"upright plane rotation","expected":[48,10000],"passed":true},{"actual":[16,10000],"check":"unlimited zero","expected":[16,10000],"passed":true},{"actual":[0,0],"check":"upright blocked","expected":[0,0],"passed":true},{"actual":[45,8438],"check":"generated mix 7","expected":[45,8437],"passed":false},{"actual":[100,8333],"check":"generated mix 15","expected":[100,8333],"passed":true},{"actual":[48,7680],"check":"generated mix 23","expected":[48,7680],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"stack cap\", \"actual\": [32, 6667], \"expected\": [32, 6666], \"passed\": false}, {\"check\": \"laydown helps\", \"actual\": [8, 8333], \"expected\": [8, 8333], \"passed\": true}, {\"check\": \"upright plane rotation\", \"actual\": [48, 10000], \"expected\": [48, 10000], \"passed\": true}, {\"check\": \"unlimited zero\", \"actual\": [16, 10000], \"expected\": [16, 10000], \"passed\": true}, {\"check\": \"upright blocked\", \"actual\": [0, 0], \"expected\": [0, 0], \"passed\": true}, {\"check\": \"generated mix 7\", \"actual\": [45, 8438], \"expected\": [45, 8437], \"passed\": false}, {\"check\": \"generated mix 15\", \"actual\": [100, 8333], \"expected\": [100, 8333], \"passed\": true}, {\"check\": \"generated mix 23\", \"actual\": [48, 7680], \"expected\": [48, 7680], \"passed\": true}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}