{"abstract":"The same pair appears twice when candidates list both orders.","category":"Collision detection broadphase","checks":8,"contract":"solve(fixtures, candidates): fixture [id, body, category bits, mask bits, group, sensor, body type]. A candidate [a,b] is accepted unless: same body; neither body is dynamic; both are sensors. Group rule: equal nonzero groups override masks (positive always collide, negative never); otherwise require (catA & maskB) and (catB & maskA). Return sorted unique [min,max] accepted pairs.","contract_signature":"fixtures, candidates","evaluation_group":"w2-collision_detection_broadphase-fixture-pair-filter","failed_approach":"Sorting the output without normalizing still keeps both orientations.","family":"w2-collision_detection_broadphase-fixture-pair-filter-pair-normalization","id":"FA-87531","implementations":{"attempt":{"sha256":"b3483894414e0a8a828f9a04645d1558fdcc19af089ac9942254c863abbd9d42","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(fixtures, candidates):\n    fx = {f[0]: f for f in fixtures}\n    out = set()\n    for a, b in candidates:\n        fa, fb = fx[a], fx[b]\n        if fa[1] == fb[1]:\n            continue\n        if fa[6] != 'dynamic' and fb[6] != 'dynamic':\n            continue\n        ga, gb = fa[4], fb[4]\n        if ga == gb and ga != 0:\n            ok = ga > 0\n        else:\n            ok = (fa[2] & fb[3]) != 0 and (fb[2] & fa[3]) != 0\n        if not ok:\n            continue\n        if fa[5] and fb[5]:\n            continue\n        out.add((b, a))\n    return [list(p) for p in sorted(out)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[[[[[1, 4, 8, 3, 0, False, 'dynamic'], [2, 4, 8, 12, 1, True, 'static'], [3, 4, 4, 15, -2, True, 'kinematic'], [4, 3, 1, 7, 1, False, 'dynamic'], [5, 2, 1, 12, 2, False, 'kinematic']], [[5, 1], [2, 5], [5, 4], [4, 5]]], [[1, 5]]], [[[[1, 2, 4, 12, 0, True, 'static'], [2, 1, 2, 6, 1, True, 'dynamic'], [3, 4, 4, 15, 0, True, 'static'], [4, 2, 8, 15, 0, False, 'kinematic'], [5, 2, 2, 3, 0, False, 'kinematic'], [6, 1, 8, 15, -1, False, 'dynamic']], [[2, 1], [2, 3], [2, 4], [4, 1], [1, 4], [3, 1]]], []], [[[[1, 4, 4, 6, 0, False, 'static'], [2, 2, 1, 1, 0, False, 'dynamic'], [3, 1, 8, 12, 1, False, 'dynamic']], [[3, 2], [1, 3], [2, 3], [1, 3], [2, 3]]], []], [[[[1, 2, 2, 12, 1, False, 'dynamic'], [2, 1, 4, 3, 2, False, 'dynamic'], [3, 4, 8, 15, 0, False, 'dynamic']], [[1, 2], [1, 2], [3, 2], [2, 3], [3, 2], [3, 2]]], [[1, 2]]], [[[[1, 4, 2, 12, 0, False, 'dynamic'], [2, 3, 8, 15, 0, False, 'kinematic'], [3, 1, 2, 12, 2, True, 'dynamic'], [4, 2, 2, 15, -1, True, 'kinematic'], [5, 3, 1, 7, -1, False, 'static']], [[4, 1], [1, 2], [1, 2], [1, 2], [4, 3], [2, 1], [3, 4], [4, 5], [5, 3], [2, 3]]], [[1, 2], [2, 3]]], [[[[1, 4, 4, 7, 0, False, 'kinematic'], [2, 2, 4, 15, -2, False, 'kinematic'], [3, 3, 1, 6, 0, False, 'dynamic']], [[1, 2], [1, 3], [3, 1], [3, 1], [2, 1], [2, 1], [1, 3]]], [[1, 3]]], [[[[1, 3, 1, 12, -1, True, 'kinematic'], [2, 4, 4, 15, 1, False, 'dynamic'], [3, 1, 8, 6, 1, False, 'dynamic'], [4, 3, 1, 15, 0, False, 'kinematic'], [5, 3, 4, 15, 0, False, 'dynamic'], [6, 1, 1, 3, -2, True, 'kinematic']], [[5, 6], [3, 1], [2, 4], [2, 4], [5, 1], [2, 5], [1, 4], [2, 1], [6, 3]]], [[1, 2], [2, 4], [2, 5]]], [[[[1, 3, 1, 15, -1, False, 'dynamic'], [2, 4, 4, 6, 2, False, 'static'], [3, 2, 8, 15, 0, False, 'dynamic'], [4, 4, 8, 7, 2, False, 'dynamic']], [[1, 3], [2, 3], [4, 3]]], [[1, 3]]]], [[[[[1, 2, 2, 7, 1, False, 'kinematic'], [2, 4, 2, 3, -2, False, 'dynamic'], [3, 3, 1, 6, 1, False, 'kinematic'], [4, 2, 8, 3, 2, False, 'static'], [5, 4, 4, 1, 0, False, 'dynamic'], [6, 1, 4, 7, 2, False, 'kinematic']], [[5, 4], [2, 6], [1, 4], [1, 3], [3, 6], [5, 3], [1, 3], [3, 4], [4, 1]]], [[3, 5]]], [[[[1, 3, 8, 6, 1, False, 'dynamic'], [2, 2, 8, 3, 1, False, 'dynamic'], [3, 1, 1, 3, 2, False, 'dynamic'], [4, 3, 2, 3, 1, False, 'static'], [5, 2, 8, 3, 2, False, 'dynamic']], [[5, 2], [4, 5], [1, 2], [2, 1], [1, 5], [3, 1], [4, 5], [4, 3], [3, 4]]], [[1, 2], [3, 4]]], [[[[1, 4, 1, 6, 0, False, 'dynamic'], [2, 2, 1, 15, 1, False, 'dynamic'], [3, 4, 1, 1, -1, False, 'dynamic'], [4, 3, 4, 15, 0, False, 'kinematic']], [[3, 1], [1, 4], [3, 1]]], [[1, 4]]], [[[[1, 4, 2, 1, 1, False, 'static'], [2, 4, 4, 12, 2, True, 'dynamic'], [3, 3, 1, 12, 0, False, 'kinematic'], [4, 3, 4, 3, -1, False, 'dynamic'], [5, 2, 2, 12, -2, False, 'kinematic'], [6, 2, 4, 15, 2, False, 'kinematic'], [7, 1, 4, 12, 0, False, 'dynamic']], [[6, 2], [5, 6], [7, 4], [7, 3], [3, 1]]], [[2, 6]]], [[[[1, 2, 2, 15, -2, False, 'dynamic'], [2, 2, 4, 1, -1, False, 'dynamic'], [3, 2, 2, 1, -2, True, 'dynamic'], [4, 3, 4, 15, -2, False, 'kinematic'], [5, 3, 8, 6, -1, False, 'dynamic']], [[1, 4], [3, 2], [2, 1], [2, 1], [2, 4], [1, 3], [3, 5], [1, 3], [4, 2], [2, 1]]], []], [[[[1, 4, 4, 15, -1, False, 'dynamic'], [2, 2, 8, 3, 1, False, 'kinematic'], [3, 1, 1, 6, 0, False, 'static'], [4, 2, 4, 15, 0, False, 'kinematic'], [5, 4, 8, 7, 2, False, 'static'], [6, 3, 8, 15, 0, True, 'kinematic'], [7, 4, 4, 1, 1, False, 'kinematic']], [[1, 4], [2, 7], [7, 1], [6, 7], [1, 2], [1, 6], [7, 3]]], [[1, 4], [1, 6]]], [[[[1, 3, 1, 15, 0, False, 'dynamic'], [2, 1, 1, 6, -2, True, 'kinematic']], [[1, 2], [2, 1], [1, 2], [2, 1], [1, 2], [2, 1], [2, 1]]], []], [[[[1, 2, 4, 15, 1, False, 'kinematic'], [2, 1, 4, 6, -1, False, 'kinematic'], [3, 3, 4, 3, 2, True, 'kinematic'], [4, 4, 1, 7, 1, False, 'static']], [[1, 3], [1, 2], [2, 4], [1, 2], [4, 1], [1, 3]]], []]], [[[[[1, 3, 2, 3, -2, False, 'static'], [2, 4, 1, 12, 0, True, 'dynamic'], [3, 4, 4, 12, 0, False, 'static'], [4, 1, 2, 3, -1, False, 'dynamic'], [5, 2, 4, 1, -2, False, 'dynamic'], [6, 2, 4, 12, 2, True, 'dynamic'], [7, 4, 4, 1, -2, False, 'kinematic']], [[3, 2], [2, 3], [3, 2], [4, 5], [2, 5]]], [[2, 5]]], [[[[1, 1, 4, 15, 1, True, 'dynamic'], [2, 3, 2, 7, -2, False, 'kinematic'], [3, 4, 8, 15, 0, False, 'static'], [4, 2, 2, 12, 1, False, 'dynamic']], [[2, 3], [3, 4], [2, 1], [4, 2], [4, 1], [1, 4], [3, 4], [3, 4], [2, 1]]], [[1, 2], [1, 4], [3, 4]]], [[[[1, 3, 8, 15, -2, False, 'kinematic'], [2, 3, 2, 7, -2, False, 'kinematic'], [3, 3, 2, 15, 2, True, 'static'], [4, 2, 2, 3, -2, False, 'dynamic'], [5, 1, 1, 6, -1, False, 'dynamic'], [6, 4, 2, 3, 0, False, 'static']], [[2, 4], [6, 5], [5, 6]]], [[5, 6]]], [[[[1, 2, 1, 7, 0, False, 'kinematic'], [2, 2, 4, 7, 0, False, 'dynamic']], [[1, 2], [2, 1], [1, 2]]], []], [[[[1, 1, 2, 7, 0, False, 'dynamic'], [2, 4, 1, 1, 0, False, 'dynamic'], [3, 2, 4, 6, -2, False, 'static']], [[1, 2], [1, 3], [1, 2], [2, 3], [3, 1]]], [[1, 3]]], [[[[1, 2, 8, 1, 1, False, 'kinematic'], [2, 1, 1, 7, 2, False, 'static'], [3, 3, 2, 15, 2, True, 'kinematic'], [4, 3, 4, 7, -1, False, 'kinematic'], [5, 3, 4, 6, 1, False, 'dynamic'], [6, 1, 4, 15, 0, False, 'dynamic']], [[4, 5], [3, 6], [4, 6], [4, 1], [5, 3], [1, 3]]], [[3, 6], [4, 6]]], [[[[1, 2, 2, 1, 0, False, 'dynamic'], [2, 4, 2, 12, 0, False, 'dynamic'], [3, 4, 1, 15, 1, False, 'static'], [4, 2, 8, 12, 0, False, 'dynamic'], [5, 4, 2, 6, 2, False, 'dynamic']], [[5, 3], [3, 1], [3, 1], [2, 3], [3, 4], [1, 2], [1, 5], [5, 4]]], [[1, 3]]], [[[[1, 3, 1, 7, -1, False, 'dynamic'], [2, 1, 8, 12, 0, True, 'kinematic']], [[1, 2], [2, 1], [1, 2], [1, 2], [2, 1], [2, 1], [2, 1], [2, 1], [1, 2]]], []]], [[[[[1, 2, 1, 7, -1, False, 'dynamic'], [2, 2, 2, 6, 0, False, 'dynamic'], [3, 2, 1, 6, 2, False, 'kinematic'], [4, 2, 1, 6, 0, False, 'dynamic'], [5, 4, 4, 7, 1, True, 'static'], [6, 3, 2, 1, 2, False, 'static']], [[6, 4], [1, 4], [6, 5], [4, 5]]], [[4, 5], [4, 6]]], [[[[1, 1, 4, 12, 0, False, 'static'], [2, 3, 2, 12, 2, True, 'dynamic'], [3, 3, 1, 1, -1, True, 'dynamic'], [4, 4, 1, 15, 2, False, 'dynamic'], [5, 1, 4, 15, 0, False, 'static']], [[1, 3], [2, 4], [5, 3], [4, 1], [5, 2]]], [[2, 4], [2, 5]]], [[[[1, 3, 4, 15, 0, False, 'dynamic'], [2, 1, 2, 15, 0, False, 'dynamic'], [3, 3, 2, 3, -2, False, 'dynamic'], [4, 4, 4, 6, -1, False, 'kinematic'], [5, 3, 2, 15, 0, False, 'kinematic']], [[3, 2], [4, 3], [2, 4], [4, 2], [4, 1], [2, 4], [2, 5], [5, 3]]], [[1, 4], [2, 3], [2, 4], [2, 5]]], [[[[1, 1, 1, 15, -1, True, 'kinematic'], [2, 1, 8, 3, 1, False, 'kinematic']], [[1, 2], [2, 1], [2, 1]]], []], [[[[1, 1, 8, 6, -2, True, 'dynamic'], [2, 3, 2, 7, 0, False, 'kinematic'], [3, 1, 2, 15, -2, False, 'dynamic'], [4, 1, 1, 15, 0, False, 'kinematic']], [[2, 3], [4, 2], [4, 3], [1, 4], [2, 3], [2, 1], [1, 4], [4, 2], [2, 1]]], [[2, 3]]], [[[[1, 2, 8, 3, 2, False, 'kinematic'], [2, 2, 1, 1, -2, False, 'dynamic'], [3, 3, 2, 15, 0, True, 'dynamic'], [4, 1, 2, 3, 0, False, 'dynamic'], [5, 2, 2, 15, 1, False, 'kinematic'], [6, 4, 8, 3, 0, False, 'kinematic'], [7, 2, 1, 12, -1, False, 'dynamic'], [8, 4, 8, 1, 1, False, 'kinematic'], [9, 1, 2, 6, -1, False, 'dynamic']], [[3, 2], [6, 3], [5, 6], [1, 2], [6, 9], [6, 7]]], [[3, 6], [6, 7]]], [[[[1, 1, 8, 15, 1, False, 'dynamic'], [2, 1, 4, 6, -1, False, 'kinematic'], [3, 2, 2, 15, 2, False, 'static'], [4, 3, 1, 15, -1, False, 'dynamic'], [5, 3, 2, 7, 0, False, 'kinematic'], [6, 4, 4, 12, 1, False, 'kinematic']], [[2, 4], [1, 2], [3, 2], [5, 3], [6, 3], [4, 3], [5, 4], [4, 5], [1, 4], [1, 4]]], [[1, 4], [3, 4]]], [[[[1, 2, 1, 6, 0, False, 'dynamic'], [2, 4, 2, 3, -1, True, 'dynamic'], [3, 3, 1, 3, 0, False, 'static'], [4, 4, 8, 6, 2, False, 'kinematic'], [5, 1, 2, 6, -1, False, 'kinematic'], [6, 1, 1, 12, -1, False, 'dynamic'], [7, 3, 8, 3, -1, True, 'dynamic']], [[5, 7], [5, 2], [5, 4], [7, 2]]], []]], [[[[[1, 3, 1, 7, 1, False, 'static'], [2, 4, 2, 1, -1, True, 'kinematic'], [3, 1, 1, 12, 0, False, 'kinematic'], [4, 4, 4, 15, -2, True, 'dynamic'], [5, 4, 2, 7, 0, False, 'kinematic']], [[3, 1], [3, 2], [5, 3], [2, 3], [2, 3], [1, 3], [1, 3], [1, 3], [4, 5], [4, 2]]], []], [[[[1, 2, 1, 12, 0, True, 'dynamic'], [2, 1, 8, 15, 0, False, 'dynamic'], [3, 1, 1, 7, -2, False, 'kinematic'], [4, 2, 4, 15, -1, True, 'dynamic']], [[4, 3], [3, 2], [2, 1], [4, 2], [3, 1]]], [[1, 2], [2, 4], [3, 4]]], [[[[1, 3, 2, 6, 0, False, 'static'], [2, 2, 1, 15, 0, True, 'kinematic']], [[2, 1], [2, 1], [2, 1], [2, 1], [1, 2], [2, 1], [2, 1]]], []], [[[[1, 1, 4, 15, 1, True, 'dynamic'], [2, 4, 8, 15, 1, False, 'static'], [3, 4, 2, 15, 0, False, 'dynamic'], [4, 2, 1, 7, 0, False, 'static']], [[1, 2], [2, 3], [2, 4], [2, 3], [2, 3], [3, 1], [2, 3], [1, 4], [3, 2], [2, 3]]], [[1, 2], [1, 3], [1, 4]]], [[[[1, 2, 8, 1, 0, False, 'dynamic'], [2, 1, 8, 3, 2, False, 'static'], [3, 3, 2, 3, 2, False, 'dynamic'], [4, 2, 4, 6, -2, False, 'kinematic'], [5, 2, 4, 7, 1, False, 'kinematic'], [6, 4, 8, 15, -1, False, 'dynamic']], [[3, 5], [1, 5], [6, 1], [4, 2], [3, 2], [4, 1], [3, 1]]], [[2, 3]]], [[[[1, 3, 2, 15, 1, False, 'static'], [2, 2, 1, 15, -1, False, 'static'], [3, 4, 8, 15, -2, False, 'dynamic'], [4, 4, 1, 3, 0, False, 'dynamic'], [5, 1, 4, 3, 0, False, 'kinematic'], [6, 4, 4, 7, 2, False, 'dynamic'], [7, 4, 8, 15, 1, True, 'kinematic'], [8, 2, 1, 3, -2, False, 'dynamic'], [9, 2, 4, 1, -1, False, 'static'], [10, 1, 8, 15, 1, False, 'static']], [[8, 2], [10, 9], [5, 3], [2, 4], [6, 5], [3, 7], [7, 9], [6, 5], [10, 5]]], [[2, 4]]], [[[[1, 3, 1, 15, 1, False, 'dynamic'], [2, 4, 8, 6, 0, False, 'static'], [3, 3, 2, 6, 2, True, 'kinematic'], [4, 4, 1, 1, 0, True, 'kinematic'], [5, 1, 2, 15, 0, False, 'dynamic'], [6, 1, 2, 15, 0, False, 'kinematic'], [7, 2, 4, 3, 0, False, 'static']], [[1, 7], [3, 1], [3, 1], [2, 4], [6, 5], [1, 5], [1, 3]]], [[1, 5], [1, 7]]], [[[[1, 1, 1, 12, 0, True, 'static'], [2, 3, 1, 6, 0, False, 'dynamic'], [3, 3, 2, 12, 0, False, 'static'], [4, 1, 8, 7, 0, False, 'dynamic'], [5, 1, 4, 12, -2, True, 'kinematic'], [6, 4, 8, 7, 1, False, 'kinematic'], [7, 2, 4, 6, 2, False, 'dynamic'], [8, 4, 4, 15, 2, False, 'dynamic'], [9, 2, 8, 6, -2, False, 'kinematic'], [10, 2, 8, 1, 0, True, 'static']], [[10, 8], [2, 3], [7, 3]]], [[3, 7]]]]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"case %d\" % i, 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":"b4c1a92bca7b0ee815153489ffd5b4537081d4ba64104c28d2a750a107307ad9","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(fixtures, candidates):\n    fx = {f[0]: f for f in fixtures}\n    out = set()\n    for a, b in candidates:\n        fa, fb = fx[a], fx[b]\n        if fa[1] == fb[1]:\n            continue\n        if fa[6] != 'dynamic' and fb[6] != 'dynamic':\n            continue\n        ga, gb = fa[4], fb[4]\n        if ga == gb and ga != 0:\n            ok = ga > 0\n        else:\n            ok = (fa[2] & fb[3]) != 0 and (fb[2] & fa[3]) != 0\n        if not ok:\n            continue\n        if fa[5] and fb[5]:\n            continue\n        out.add((a, b))\n    return [list(p) for p in sorted(out)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[[[[[1, 4, 8, 3, 0, False, 'dynamic'], [2, 4, 8, 12, 1, True, 'static'], [3, 4, 4, 15, -2, True, 'kinematic'], [4, 3, 1, 7, 1, False, 'dynamic'], [5, 2, 1, 12, 2, False, 'kinematic']], [[5, 1], [2, 5], [5, 4], [4, 5]]], [[1, 5]]], [[[[1, 2, 4, 12, 0, True, 'static'], [2, 1, 2, 6, 1, True, 'dynamic'], [3, 4, 4, 15, 0, True, 'static'], [4, 2, 8, 15, 0, False, 'kinematic'], [5, 2, 2, 3, 0, False, 'kinematic'], [6, 1, 8, 15, -1, False, 'dynamic']], [[2, 1], [2, 3], [2, 4], [4, 1], [1, 4], [3, 1]]], []], [[[[1, 4, 4, 6, 0, False, 'static'], [2, 2, 1, 1, 0, False, 'dynamic'], [3, 1, 8, 12, 1, False, 'dynamic']], [[3, 2], [1, 3], [2, 3], [1, 3], [2, 3]]], []], [[[[1, 2, 2, 12, 1, False, 'dynamic'], [2, 1, 4, 3, 2, False, 'dynamic'], [3, 4, 8, 15, 0, False, 'dynamic']], [[1, 2], [1, 2], [3, 2], [2, 3], [3, 2], [3, 2]]], [[1, 2]]], [[[[1, 4, 2, 12, 0, False, 'dynamic'], [2, 3, 8, 15, 0, False, 'kinematic'], [3, 1, 2, 12, 2, True, 'dynamic'], [4, 2, 2, 15, -1, True, 'kinematic'], [5, 3, 1, 7, -1, False, 'static']], [[4, 1], [1, 2], [1, 2], [1, 2], [4, 3], [2, 1], [3, 4], [4, 5], [5, 3], [2, 3]]], [[1, 2], [2, 3]]], [[[[1, 4, 4, 7, 0, False, 'kinematic'], [2, 2, 4, 15, -2, False, 'kinematic'], [3, 3, 1, 6, 0, False, 'dynamic']], [[1, 2], [1, 3], [3, 1], [3, 1], [2, 1], [2, 1], [1, 3]]], [[1, 3]]], [[[[1, 3, 1, 12, -1, True, 'kinematic'], [2, 4, 4, 15, 1, False, 'dynamic'], [3, 1, 8, 6, 1, False, 'dynamic'], [4, 3, 1, 15, 0, False, 'kinematic'], [5, 3, 4, 15, 0, False, 'dynamic'], [6, 1, 1, 3, -2, True, 'kinematic']], [[5, 6], [3, 1], [2, 4], [2, 4], [5, 1], [2, 5], [1, 4], [2, 1], [6, 3]]], [[1, 2], [2, 4], [2, 5]]], [[[[1, 3, 1, 15, -1, False, 'dynamic'], [2, 4, 4, 6, 2, False, 'static'], [3, 2, 8, 15, 0, False, 'dynamic'], [4, 4, 8, 7, 2, False, 'dynamic']], [[1, 3], [2, 3], [4, 3]]], [[1, 3]]]], [[[[[1, 2, 2, 7, 1, False, 'kinematic'], [2, 4, 2, 3, -2, False, 'dynamic'], [3, 3, 1, 6, 1, False, 'kinematic'], [4, 2, 8, 3, 2, False, 'static'], [5, 4, 4, 1, 0, False, 'dynamic'], [6, 1, 4, 7, 2, False, 'kinematic']], [[5, 4], [2, 6], [1, 4], [1, 3], [3, 6], [5, 3], [1, 3], [3, 4], [4, 1]]], [[3, 5]]], [[[[1, 3, 8, 6, 1, False, 'dynamic'], [2, 2, 8, 3, 1, False, 'dynamic'], [3, 1, 1, 3, 2, False, 'dynamic'], [4, 3, 2, 3, 1, False, 'static'], [5, 2, 8, 3, 2, False, 'dynamic']], [[5, 2], [4, 5], [1, 2], [2, 1], [1, 5], [3, 1], [4, 5], [4, 3], [3, 4]]], [[1, 2], [3, 4]]], [[[[1, 4, 1, 6, 0, False, 'dynamic'], [2, 2, 1, 15, 1, False, 'dynamic'], [3, 4, 1, 1, -1, False, 'dynamic'], [4, 3, 4, 15, 0, False, 'kinematic']], [[3, 1], [1, 4], [3, 1]]], [[1, 4]]], [[[[1, 4, 2, 1, 1, False, 'static'], [2, 4, 4, 12, 2, True, 'dynamic'], [3, 3, 1, 12, 0, False, 'kinematic'], [4, 3, 4, 3, -1, False, 'dynamic'], [5, 2, 2, 12, -2, False, 'kinematic'], [6, 2, 4, 15, 2, False, 'kinematic'], [7, 1, 4, 12, 0, False, 'dynamic']], [[6, 2], [5, 6], [7, 4], [7, 3], [3, 1]]], [[2, 6]]], [[[[1, 2, 2, 15, -2, False, 'dynamic'], [2, 2, 4, 1, -1, False, 'dynamic'], [3, 2, 2, 1, -2, True, 'dynamic'], [4, 3, 4, 15, -2, False, 'kinematic'], [5, 3, 8, 6, -1, False, 'dynamic']], [[1, 4], [3, 2], [2, 1], [2, 1], [2, 4], [1, 3], [3, 5], [1, 3], [4, 2], [2, 1]]], []], [[[[1, 4, 4, 15, -1, False, 'dynamic'], [2, 2, 8, 3, 1, False, 'kinematic'], [3, 1, 1, 6, 0, False, 'static'], [4, 2, 4, 15, 0, False, 'kinematic'], [5, 4, 8, 7, 2, False, 'static'], [6, 3, 8, 15, 0, True, 'kinematic'], [7, 4, 4, 1, 1, False, 'kinematic']], [[1, 4], [2, 7], [7, 1], [6, 7], [1, 2], [1, 6], [7, 3]]], [[1, 4], [1, 6]]], [[[[1, 3, 1, 15, 0, False, 'dynamic'], [2, 1, 1, 6, -2, True, 'kinematic']], [[1, 2], [2, 1], [1, 2], [2, 1], [1, 2], [2, 1], [2, 1]]], []], [[[[1, 2, 4, 15, 1, False, 'kinematic'], [2, 1, 4, 6, -1, False, 'kinematic'], [3, 3, 4, 3, 2, True, 'kinematic'], [4, 4, 1, 7, 1, False, 'static']], [[1, 3], [1, 2], [2, 4], [1, 2], [4, 1], [1, 3]]], []]], [[[[[1, 3, 2, 3, -2, False, 'static'], [2, 4, 1, 12, 0, True, 'dynamic'], [3, 4, 4, 12, 0, False, 'static'], [4, 1, 2, 3, -1, False, 'dynamic'], [5, 2, 4, 1, -2, False, 'dynamic'], [6, 2, 4, 12, 2, True, 'dynamic'], [7, 4, 4, 1, -2, False, 'kinematic']], [[3, 2], [2, 3], [3, 2], [4, 5], [2, 5]]], [[2, 5]]], [[[[1, 1, 4, 15, 1, True, 'dynamic'], [2, 3, 2, 7, -2, False, 'kinematic'], [3, 4, 8, 15, 0, False, 'static'], [4, 2, 2, 12, 1, False, 'dynamic']], [[2, 3], [3, 4], [2, 1], [4, 2], [4, 1], [1, 4], [3, 4], [3, 4], [2, 1]]], [[1, 2], [1, 4], [3, 4]]], [[[[1, 3, 8, 15, -2, False, 'kinematic'], [2, 3, 2, 7, -2, False, 'kinematic'], [3, 3, 2, 15, 2, True, 'static'], [4, 2, 2, 3, -2, False, 'dynamic'], [5, 1, 1, 6, -1, False, 'dynamic'], [6, 4, 2, 3, 0, False, 'static']], [[2, 4], [6, 5], [5, 6]]], [[5, 6]]], [[[[1, 2, 1, 7, 0, False, 'kinematic'], [2, 2, 4, 7, 0, False, 'dynamic']], [[1, 2], [2, 1], [1, 2]]], []], [[[[1, 1, 2, 7, 0, False, 'dynamic'], [2, 4, 1, 1, 0, False, 'dynamic'], [3, 2, 4, 6, -2, False, 'static']], [[1, 2], [1, 3], [1, 2], [2, 3], [3, 1]]], [[1, 3]]], [[[[1, 2, 8, 1, 1, False, 'kinematic'], [2, 1, 1, 7, 2, False, 'static'], [3, 3, 2, 15, 2, True, 'kinematic'], [4, 3, 4, 7, -1, False, 'kinematic'], [5, 3, 4, 6, 1, False, 'dynamic'], [6, 1, 4, 15, 0, False, 'dynamic']], [[4, 5], [3, 6], [4, 6], [4, 1], [5, 3], [1, 3]]], [[3, 6], [4, 6]]], [[[[1, 2, 2, 1, 0, False, 'dynamic'], [2, 4, 2, 12, 0, False, 'dynamic'], [3, 4, 1, 15, 1, False, 'static'], [4, 2, 8, 12, 0, False, 'dynamic'], [5, 4, 2, 6, 2, False, 'dynamic']], [[5, 3], [3, 1], [3, 1], [2, 3], [3, 4], [1, 2], [1, 5], [5, 4]]], [[1, 3]]], [[[[1, 3, 1, 7, -1, False, 'dynamic'], [2, 1, 8, 12, 0, True, 'kinematic']], [[1, 2], [2, 1], [1, 2], [1, 2], [2, 1], [2, 1], [2, 1], [2, 1], [1, 2]]], []]], [[[[[1, 2, 1, 7, -1, False, 'dynamic'], [2, 2, 2, 6, 0, False, 'dynamic'], [3, 2, 1, 6, 2, False, 'kinematic'], [4, 2, 1, 6, 0, False, 'dynamic'], [5, 4, 4, 7, 1, True, 'static'], [6, 3, 2, 1, 2, False, 'static']], [[6, 4], [1, 4], [6, 5], [4, 5]]], [[4, 5], [4, 6]]], [[[[1, 1, 4, 12, 0, False, 'static'], [2, 3, 2, 12, 2, True, 'dynamic'], [3, 3, 1, 1, -1, True, 'dynamic'], [4, 4, 1, 15, 2, False, 'dynamic'], [5, 1, 4, 15, 0, False, 'static']], [[1, 3], [2, 4], [5, 3], [4, 1], [5, 2]]], [[2, 4], [2, 5]]], [[[[1, 3, 4, 15, 0, False, 'dynamic'], [2, 1, 2, 15, 0, False, 'dynamic'], [3, 3, 2, 3, -2, False, 'dynamic'], [4, 4, 4, 6, -1, False, 'kinematic'], [5, 3, 2, 15, 0, False, 'kinematic']], [[3, 2], [4, 3], [2, 4], [4, 2], [4, 1], [2, 4], [2, 5], [5, 3]]], [[1, 4], [2, 3], [2, 4], [2, 5]]], [[[[1, 1, 1, 15, -1, True, 'kinematic'], [2, 1, 8, 3, 1, False, 'kinematic']], [[1, 2], [2, 1], [2, 1]]], []], [[[[1, 1, 8, 6, -2, True, 'dynamic'], [2, 3, 2, 7, 0, False, 'kinematic'], [3, 1, 2, 15, -2, False, 'dynamic'], [4, 1, 1, 15, 0, False, 'kinematic']], [[2, 3], [4, 2], [4, 3], [1, 4], [2, 3], [2, 1], [1, 4], [4, 2], [2, 1]]], [[2, 3]]], [[[[1, 2, 8, 3, 2, False, 'kinematic'], [2, 2, 1, 1, -2, False, 'dynamic'], [3, 3, 2, 15, 0, True, 'dynamic'], [4, 1, 2, 3, 0, False, 'dynamic'], [5, 2, 2, 15, 1, False, 'kinematic'], [6, 4, 8, 3, 0, False, 'kinematic'], [7, 2, 1, 12, -1, False, 'dynamic'], [8, 4, 8, 1, 1, False, 'kinematic'], [9, 1, 2, 6, -1, False, 'dynamic']], [[3, 2], [6, 3], [5, 6], [1, 2], [6, 9], [6, 7]]], [[3, 6], [6, 7]]], [[[[1, 1, 8, 15, 1, False, 'dynamic'], [2, 1, 4, 6, -1, False, 'kinematic'], [3, 2, 2, 15, 2, False, 'static'], [4, 3, 1, 15, -1, False, 'dynamic'], [5, 3, 2, 7, 0, False, 'kinematic'], [6, 4, 4, 12, 1, False, 'kinematic']], [[2, 4], [1, 2], [3, 2], [5, 3], [6, 3], [4, 3], [5, 4], [4, 5], [1, 4], [1, 4]]], [[1, 4], [3, 4]]], [[[[1, 2, 1, 6, 0, False, 'dynamic'], [2, 4, 2, 3, -1, True, 'dynamic'], [3, 3, 1, 3, 0, False, 'static'], [4, 4, 8, 6, 2, False, 'kinematic'], [5, 1, 2, 6, -1, False, 'kinematic'], [6, 1, 1, 12, -1, False, 'dynamic'], [7, 3, 8, 3, -1, True, 'dynamic']], [[5, 7], [5, 2], [5, 4], [7, 2]]], []]], [[[[[1, 3, 1, 7, 1, False, 'static'], [2, 4, 2, 1, -1, True, 'kinematic'], [3, 1, 1, 12, 0, False, 'kinematic'], [4, 4, 4, 15, -2, True, 'dynamic'], [5, 4, 2, 7, 0, False, 'kinematic']], [[3, 1], [3, 2], [5, 3], [2, 3], [2, 3], [1, 3], [1, 3], [1, 3], [4, 5], [4, 2]]], []], [[[[1, 2, 1, 12, 0, True, 'dynamic'], [2, 1, 8, 15, 0, False, 'dynamic'], [3, 1, 1, 7, -2, False, 'kinematic'], [4, 2, 4, 15, -1, True, 'dynamic']], [[4, 3], [3, 2], [2, 1], [4, 2], [3, 1]]], [[1, 2], [2, 4], [3, 4]]], [[[[1, 3, 2, 6, 0, False, 'static'], [2, 2, 1, 15, 0, True, 'kinematic']], [[2, 1], [2, 1], [2, 1], [2, 1], [1, 2], [2, 1], [2, 1]]], []], [[[[1, 1, 4, 15, 1, True, 'dynamic'], [2, 4, 8, 15, 1, False, 'static'], [3, 4, 2, 15, 0, False, 'dynamic'], [4, 2, 1, 7, 0, False, 'static']], [[1, 2], [2, 3], [2, 4], [2, 3], [2, 3], [3, 1], [2, 3], [1, 4], [3, 2], [2, 3]]], [[1, 2], [1, 3], [1, 4]]], [[[[1, 2, 8, 1, 0, False, 'dynamic'], [2, 1, 8, 3, 2, False, 'static'], [3, 3, 2, 3, 2, False, 'dynamic'], [4, 2, 4, 6, -2, False, 'kinematic'], [5, 2, 4, 7, 1, False, 'kinematic'], [6, 4, 8, 15, -1, False, 'dynamic']], [[3, 5], [1, 5], [6, 1], [4, 2], [3, 2], [4, 1], [3, 1]]], [[2, 3]]], [[[[1, 3, 2, 15, 1, False, 'static'], [2, 2, 1, 15, -1, False, 'static'], [3, 4, 8, 15, -2, False, 'dynamic'], [4, 4, 1, 3, 0, False, 'dynamic'], [5, 1, 4, 3, 0, False, 'kinematic'], [6, 4, 4, 7, 2, False, 'dynamic'], [7, 4, 8, 15, 1, True, 'kinematic'], [8, 2, 1, 3, -2, False, 'dynamic'], [9, 2, 4, 1, -1, False, 'static'], [10, 1, 8, 15, 1, False, 'static']], [[8, 2], [10, 9], [5, 3], [2, 4], [6, 5], [3, 7], [7, 9], [6, 5], [10, 5]]], [[2, 4]]], [[[[1, 3, 1, 15, 1, False, 'dynamic'], [2, 4, 8, 6, 0, False, 'static'], [3, 3, 2, 6, 2, True, 'kinematic'], [4, 4, 1, 1, 0, True, 'kinematic'], [5, 1, 2, 15, 0, False, 'dynamic'], [6, 1, 2, 15, 0, False, 'kinematic'], [7, 2, 4, 3, 0, False, 'static']], [[1, 7], [3, 1], [3, 1], [2, 4], [6, 5], [1, 5], [1, 3]]], [[1, 5], [1, 7]]], [[[[1, 1, 1, 12, 0, True, 'static'], [2, 3, 1, 6, 0, False, 'dynamic'], [3, 3, 2, 12, 0, False, 'static'], [4, 1, 8, 7, 0, False, 'dynamic'], [5, 1, 4, 12, -2, True, 'kinematic'], [6, 4, 8, 7, 1, False, 'kinematic'], [7, 2, 4, 6, 2, False, 'dynamic'], [8, 4, 4, 15, 2, False, 'dynamic'], [9, 2, 8, 6, -2, False, 'kinematic'], [10, 2, 8, 1, 0, True, 'static']], [[10, 8], [2, 3], [7, 3]]], [[3, 7]]]]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"case %d\" % i, 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":"A deterministic bounded teaching model with stipulated toy conventions; not a production physics engine or spatial index. 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-collision_detection_broadphase-fixture-pair-filter-pair-normalization","generated_at":"2026-09-29T14:50:59.677485+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Broadphase stages decide which object pairs ever reach narrowphase; a wrong boundary, ordering or bookkeeping rule silently drops real contacts or floods the solver with false candidates.","root_cause":"out stores (a,b) as given.","sha256":"e5891d0521e852470a381258bbe182c9f793673df74d4e01720cf62174b12d55","title":"Accepted pairs keep candidate orientation · 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":43.74,"exit_code":1,"observations":[{"actual":[[1,5]],"check":"case 0","expected":[[1,5]],"passed":true},{"actual":[],"check":"case 1","expected":[],"passed":true},{"actual":[],"check":"case 2","expected":[],"passed":true},{"actual":[[2,1]],"check":"case 3","expected":[[1,2]],"passed":false},{"actual":[[1,2],[2,1],[3,2]],"check":"case 4","expected":[[1,2],[2,3]],"passed":false},{"actual":[[1,3],[3,1]],"check":"case 5","expected":[[1,3]],"passed":false},{"actual":[[1,2],[4,2],[5,2]],"check":"case 6","expected":[[1,2],[2,4],[2,5]],"passed":false},{"actual":[[3,1]],"check":"case 7","expected":[[1,3]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"case 0\", \"actual\": [[1, 5]], \"expected\": [[1, 5]], \"passed\": true}, {\"check\": \"case 1\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"case 2\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"case 3\", \"actual\": [[2, 1]], \"expected\": [[1, 2]], \"passed\": false}, {\"check\": \"case 4\", \"actual\": [[1, 2], [2, 1], [3, 2]], \"expected\": [[1, 2], [2, 3]], \"passed\": false}, {\"check\": \"case 5\", \"actual\": [[1, 3], [3, 1]], \"expected\": [[1, 3]], \"passed\": false}, {\"check\": \"case 6\", \"actual\": [[1, 2], [4, 2], [5, 2]], \"expected\": [[1, 2], [2, 4], [2, 5]], \"passed\": false}, {\"check\": \"case 7\", \"actual\": [[3, 1]], \"expected\": [[1, 3]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.495,"exit_code":1,"observations":[{"actual":[[5,1]],"check":"case 0","expected":[[1,5]],"passed":false},{"actual":[],"check":"case 1","expected":[],"passed":true},{"actual":[],"check":"case 2","expected":[],"passed":true},{"actual":[[1,2]],"check":"case 3","expected":[[1,2]],"passed":true},{"actual":[[1,2],[2,1],[2,3]],"check":"case 4","expected":[[1,2],[2,3]],"passed":false},{"actual":[[1,3],[3,1]],"check":"case 5","expected":[[1,3]],"passed":false},{"actual":[[2,1],[2,4],[2,5]],"check":"case 6","expected":[[1,2],[2,4],[2,5]],"passed":false},{"actual":[[1,3]],"check":"case 7","expected":[[1,3]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"case 0\", \"actual\": [[5, 1]], \"expected\": [[1, 5]], \"passed\": false}, {\"check\": \"case 1\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"case 2\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"case 3\", \"actual\": [[1, 2]], \"expected\": [[1, 2]], \"passed\": true}, {\"check\": \"case 4\", \"actual\": [[1, 2], [2, 1], [2, 3]], \"expected\": [[1, 2], [2, 3]], \"passed\": false}, {\"check\": \"case 5\", \"actual\": [[1, 3], [3, 1]], \"expected\": [[1, 3]], \"passed\": false}, {\"check\": \"case 6\", \"actual\": [[2, 1], [2, 4], [2, 5]], \"expected\": [[1, 2], [2, 4], [2, 5]], \"passed\": false}, {\"check\": \"case 7\", \"actual\": [[1, 3]], \"expected\": [[1, 3]], \"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."}}