{"abstract":"Bucket distribution differs from the contract and collisions cluster.","category":"Collision detection broadphase","checks":8,"contract":"solve(frames, n): particle hash table of n buckets reused across frames without clearing; a bucket whose stamp is older than the frame is lazily reset on first insert. Cell = floor(x), floor(y); bucket = ((ix*73856093 mod 2^32) xor (iy*19349663 mod 2^32)) mod n. A particle pairs with earlier particles in the same bucket only if they share the exact cell. Per frame return [sorted [min,max] pairs, buckets stamped this frame].","contract_signature":"frames, n","evaluation_group":"w2-collision_detection_broadphase-timestamped-spatial-hash","failed_approach":"Bitwise or loses information and collides more.","family":"w2-collision_detection_broadphase-timestamped-spatial-hash-hash-combine-operator","id":"FA-87751","implementations":{"attempt":{"sha256":"1fef92f3e1fccb004299465dcf4fe420c07c7caa96ec3a8415e3a3a348f6ff16","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(frames, n):\n    table = [[-1, []] for _ in range(n)]\n    result = []\n    for f, pts in enumerate(frames):\n        pairs = []\n        for pid, x, y in pts:\n            ix, iy = math.floor(x), math.floor(y)\n            h = (((ix * 73856093) & 0xFFFFFFFF) | ((iy * 19349663) & 0xFFFFFFFF)) % n\n            slot = table[h]\n            if slot[0] != f:\n                slot[0] = f\n                slot[1] = []\n            for qid, qx, qy in slot[1]:\n                if (qx, qy) == (ix, iy):\n                    pairs.append([min(pid, qid), max(pid, qid)])\n            slot[1].append((pid, ix, iy))\n        result.append([sorted(pairs), sum(1 for s in table if s[0] == f)])\n    return result\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[[[[[[10, 1.5, -1.0], [14, 0.5, -3.0], [7, -1.5, 3.0], [12, 2.0, 3.0]], [[16, 0.5, 0.5], [7, -1.0, 1.5], [14, -2.0, -0.5]], [[8, -1.5, 3.0], [17, 1.0, -1.0], [2, 0.5, -2.5], [1, -3.0, 1.0], [19, -1.0, -1.0]], [[11, 3.0, 2.0], [17, -0.5, 2.5], [14, 2.0, -1.5]]], 3], [[[], 3], [[], 2], [[], 3], [[], 1]]], [[[[[17, -1.0, -1.0], [13, 3.0, -3.0], [16, 3.0, 0.5], [2, 0.0, 2.5]]], 11], [[[], 4]]], [[[[[14, 0.5, -2.0], [3, 3.0, 1.5], [10, 2.0, 2.5]], [[4, 1.5, 2.0], [13, -2.0, 3.0]]], 5], [[[], 3], [[], 2]]], [[[[[16, 3.0, 0.5], [19, 0.0, -1.0], [13, -1.5, 0.5], [3, 1.5, -1.5], [17, 2.5, -0.5], [2, 0.0, 0.5]]], 5], [[[], 4]]], [[[[[7, -1.5, 3.0], [9, 1.0, 0.0], [6, -1.5, -0.5], [15, -2.0, -1.5], [12, 1.0, -0.5]], [[19, 3.0, -3.0], [7, -2.0, 3.0], [9, 1.5, 2.0], [3, 3.0, 2.0]], [[15, 0.0, 3.0], [19, 2.5, -3.0], [2, 1.0, 1.0], [9, -0.5, -0.5], [17, 1.0, 0.5]]], 3], [[[], 2], [[], 3], [[], 3]]], [[[[[15, -1.0, -2.0], [3, 3.0, 1.0], [2, 2.5, -3.0], [1, -1.0, -1.0]], [[3, 3.0, -2.5], [16, -2.5, 1.0], [7, 0.0, 0.5], [1, 0.0, -2.0], [12, 0.5, -3.0], [2, 3.0, -3.0]], [[17, 2.0, -2.0], [2, -0.5, -1.0], [8, -0.5, -2.5], [12, -1.0, -1.0], [7, 0.5, 1.5], [9, 0.5, 2.0]], [[14, 1.5, 3.0], [18, 0.5, 1.5], [12, -1.0, -2.5], [16, 0.5, -3.0]]], 7], [[[], 3], [[[2, 3]], 3], [[[2, 12]], 5], [[], 3]]], [[[[[5, 2.5, 1.5], [14, 0.0, 1.5], [15, 0.0, -1.5], [13, -2.0, -1.0], [16, 1.5, 1.5], [9, 1.5, 0.5]], [[11, 1.5, -3.0], [12, -2.0, -1.0], [9, -3.0, -1.0], [2, 2.5, -1.0]]], 7], [[[], 4], [[], 3]]], [[[[[12, 1.5, 1.0], [2, 1.0, 1.0]]], 3], [[[[2, 12]], 1]]]], [[[[[[18, 0.5, 2.0], [11, 0.0, 0.5]], [[19, -0.5, -2.0], [7, -0.5, 0.5], [9, 1.5, -0.5]]], 3], [[[], 2], [[], 1]]], [[[[[3, 0.0, 1.0], [10, -2.5, 0.5]]], 3], [[[], 2]]], [[[[[4, 1.5, 0.0], [6, 0.0, -0.5]], [[18, -1.5, 2.5], [11, -1.0, -1.0], [9, 2.5, 3.0], [12, 1.0, 2.0], [17, 0.5, -1.0]]], 3], [[[], 1], [[], 3]]], [[[[[4, 2.0, 1.5], [7, -0.5, 2.0]], [[2, 0.0, 1.0], [13, 1.5, 0.0], [14, -3.0, 1.0]]], 7], [[[], 2], [[], 3]]], [[[[[6, -1.5, -3.0], [3, 0.0, 2.0]], [[11, 3.0, 2.0], [17, 2.0, 1.5], [12, 0.5, -1.5], [14, 1.5, 0.5], [1, 1.0, -3.0]]], 11], [[[], 2], [[], 5]]], [[[[[11, 3.0, -2.0], [6, 1.5, 2.0], [4, -2.5, -1.5]], [[17, -1.5, 2.5], [4, 2.0, 0.0], [5, 3.0, 0.0], [1, 0.5, -2.5], [7, -1.0, 2.5], [14, 0.5, -2.0]], [[18, -1.0, 3.0], [13, -0.5, -3.0], [11, 1.5, 2.5], [12, 2.0, 0.5], [4, 1.0, -3.0]], [[8, -3.0, 0.0], [18, -1.0, -2.0], [5, -0.5, 2.0], [16, -1.5, 1.5]]], 3], [[[], 2], [[], 2], [[], 3], [[], 3]]], [[[[[13, -1.5, 1.0], [8, 2.0, -2.5], [1, 1.5, -2.5], [3, 1.0, -3.0]], [[2, -1.5, -3.0], [16, -2.5, 2.5], [19, -2.0, 1.5]], [[8, 3.0, -1.5], [2, -2.0, -2.5], [4, -0.5, -1.5], [18, 2.5, 3.0], [10, 1.5, -0.5], [16, -2.5, -2.0]]], 11], [[[[1, 3]], 3], [[], 2], [[], 6]]], [[[[[5, 1.5, -1.0], [6, 3.0, 2.5], [16, 0.0, 0.0], [17, -1.0, 2.0], [18, -1.5, -3.0]], [[15, -1.0, 3.0], [2, -2.0, 3.0], [19, -1.0, -2.5], [16, 3.0, 1.0], [5, 3.0, 0.5]]], 3], [[[], 3], [[], 2]]]], [[[[[[1, -1.5, 0.0], [15, 0.5, -1.0], [2, 2.5, 0.5]], [[13, -3.0, -0.5], [5, 2.0, -1.5]], [[6, 1.5, 1.5], [7, 2.5, 3.0]]], 7], [[[], 3], [[], 1], [[], 2]]], [[[[[13, 1.5, 2.5], [3, 2.0, -0.5], [11, -3.0, -2.0], [8, 3.0, -3.0]], [[13, 2.5, 1.5], [18, 0.0, -1.5], [4, 1.0, -1.5], [6, 2.5, 2.5], [9, 0.0, -2.5]]], 7], [[[], 4], [[], 4]]], [[[[[14, 1.5, 1.0], [13, -3.0, -0.5], [5, 0.0, 0.5]], [[11, -1.0, 0.0], [4, -0.5, 0.0], [19, 3.0, 2.5], [15, 2.0, -1.0]]], 11], [[[], 2], [[[4, 11]], 3]]], [[[[[14, -0.5, -0.5], [7, 3.0, 1.5], [12, 1.5, -0.5], [2, 1.0, 3.0], [18, -1.5, -2.5], [1, -3.0, -1.5]]], 11], [[[], 5]]], [[[[[7, 2.0, -0.5], [16, 2.5, -3.0], [11, -1.0, -3.0]]], 7], [[[], 3]]], [[[[[2, 2.0, 0.5], [5, -0.5, 2.5], [16, -2.0, -1.5], [1, 0.0, -2.0]], [[4, -1.0, 3.0], [5, -1.0, -3.0], [3, 2.0, -2.0], [11, 0.5, -2.5], [9, 1.5, 3.0]]], 3], [[[], 2], [[], 3]]], [[[[[18, 1.0, 3.0], [15, 3.0, -1.0]]], 11], [[[], 2]]], [[[[[16, -2.0, -2.0], [14, -1.0, -3.0], [18, 2.5, 2.0], [1, -3.0, -0.5], [15, 2.0, 0.5]], [[16, 0.5, 2.5], [17, -0.5, -0.5]]], 7], [[[], 4], [[], 2]]]], [[[[[[12, -2.5, 2.0], [3, -1.5, -3.0], [15, 0.5, 1.0], [11, 2.5, -1.0]], [[8, 0.5, 0.0], [2, -1.5, -2.0]]], 7], [[[], 3], [[], 2]]], [[[[[15, -2.5, 2.0], [17, 3.0, 2.5], [3, 0.0, -2.0], [1, -2.5, 1.5]], [[5, 1.0, -2.5], [15, 2.0, -2.0], [11, 0.5, -1.5]], [[6, 0.5, -1.0], [5, 1.5, 2.0], [12, 1.0, -3.0], [8, -2.0, 1.5], [14, -2.5, -2.0]], [[8, -0.5, -2.5], [9, -1.0, -0.5]]], 7], [[[], 3], [[], 2], [[], 4], [[], 2]]], [[[[[2, 0.0, 0.5], [4, -3.0, -2.5], [9, -2.0, 1.5], [1, -3.0, 1.0]], [[3, 0.0, -0.5], [5, 3.0, 1.0]]], 7], [[[], 3], [[], 2]]], [[[[[17, -1.5, -2.5], [18, 0.5, 0.0], [15, -0.5, -2.5], [12, -1.0, 0.0]], [[13, 2.0, -2.5], [17, 2.5, -1.0]], [[13, 1.0, -3.0], [16, 0.5, 2.0]]], 3], [[[], 3], [[], 2], [[], 2]]], [[[[[12, -0.5, -2.5], [1, -2.5, 1.5], [11, 2.5, 3.0], [5, 0.5, 3.0], [8, -2.0, 3.0], [18, -3.0, -0.5]], [[4, 1.0, -0.5], [17, 1.5, -1.0], [7, -1.5, 2.5], [10, -1.5, 0.5]], [[8, 3.0, 0.5], [5, 2.0, 1.5], [16, -0.5, 2.0]]], 3], [[[], 2], [[[4, 17]], 2], [[], 2]]], [[[[[9, 2.5, -0.5], [10, -0.5, -3.0], [6, 0.5, 3.0], [15, 3.0, -2.0], [13, -3.0, -0.5], [5, -3.0, -3.0]]], 11], [[[], 5]]], [[[[[12, -0.5, 0.5], [13, -2.0, -1.0], [10, -3.0, 0.5], [6, -3.0, 3.0]], [[2, -2.0, 0.0], [3, 3.0, 3.0], [7, 0.0, 2.5], [16, 2.0, 1.0], [19, -3.0, 1.0], [4, 3.0, -0.5]]], 11], [[[], 4], [[], 4]]], [[[[[15, -1.5, 3.0], [3, -3.0, 1.0], [8, -0.5, 3.0], [11, -1.5, 3.0], [1, 0.0, 3.0], [13, -1.5, 0.0]], [[6, 3.0, 0.0], [5, 1.5, 0.5], [11, -2.0, -0.5], [9, -0.5, 1.5]]], 5], [[[[11, 15]], 3], [[], 3]]]], [[[[[[18, 0.0, 1.5], [6, -1.5, -1.0]], [[13, 2.0, 3.0], [19, 3.0, -1.5], [14, 3.0, 0.0]]], 5], [[[], 2], [[], 1]]], [[[[[13, 1.0, -0.5], [1, -2.0, 1.0], [2, 2.0, 0.5], [14, 2.0, 3.0]], [[1, 2.5, -0.5], [10, 3.0, 1.5], [18, 1.0, 0.5], [15, 0.5, -2.5], [8, 2.0, -0.5], [6, -2.0, 1.0]]], 3], [[[], 3], [[[1, 8]], 3]]], [[[[[10, -3.0, 1.0], [14, -1.5, -0.5]], [[16, 1.0, 3.0], [1, 2.0, 0.0], [5, -1.5, -2.5]], [[1, 1.5, -3.0], [14, -1.5, 1.5], [5, -1.5, -2.0], [10, 2.5, -0.5]], [[18, 0.5, -0.5], [7, 2.5, 0.0]]], 11], [[[], 2], [[], 3], [[], 3], [[], 2]]], [[[[[5, -1.5, 2.5], [14, 3.0, -2.5], [1, -2.5, -1.0], [2, -2.0, 1.0], [6, 2.5, 0.5]]], 11], [[[], 4]]], [[[[[15, -1.0, -1.0], [6, 0.0, -2.0], [8, 0.5, 2.5], [14, 2.5, -0.5], [11, 2.5, -2.0], [9, -0.5, 3.0]], [[6, 1.0, -1.0], [18, 3.0, 0.0], [11, -0.5, -2.5], [15, 1.5, -1.0]], [[16, 0.0, -0.5], [1, -1.5, -0.5], [13, 2.0, 3.0], [8, 1.5, 3.0], [19, 1.0, 2.5], [18, -3.0, 3.0]], [[17, -0.5, -2.5], [7, 1.0, 2.5], [6, 0.5, -3.0]]], 3], [[[], 3], [[[6, 15]], 2], [[], 3], [[], 2]]], [[[[[9, -1.5, 2.0], [13, 2.0, -1.5], [3, -2.0, 0.0], [8, 3.0, -1.0], [15, -2.0, 2.0], [12, -2.5, -1.5]], [[15, 1.5, -2.0], [2, -3.0, 3.0], [14, 1.0, -1.0], [1, -3.0, 3.0], [10, 3.0, -1.5]], [[13, 0.5, 0.5], [17, 3.0, 2.0], [3, 1.0, 2.5], [6, 0.5, 0.5], [1, 0.5, 0.0]], [[12, -1.5, -2.5], [15, 2.5, 0.0]]], 11], [[[[9, 15]], 3], [[[1, 2]], 4], [[[1, 6], [1, 13], [6, 13]], 3], [[], 2]]], [[[[[4, 2.0, 2.5], [7, -1.5, 2.0], [18, 3.0, 3.0]], [[2, -2.0, 0.5], [19, 2.5, -1.0], [8, -2.5, -3.0], [1, -3.0, -0.5], [7, -3.0, 0.0]], [[16, 1.5, -0.5], [7, 0.5, -1.0], [6, -1.5, 1.5], [3, -0.5, -1.5], [10, 1.0, -1.0]]], 7], [[[], 3], [[], 4], [[[10, 16]], 3]]], [[[[[15, 0.5, 0.5], [1, 3.0, 0.0], [3, -2.0, 2.0], [10, 0.0, -1.5], [18, 0.5, -2.0], [17, -0.5, 2.5]], [[17, -2.5, -2.0], [16, -0.5, -1.5], [4, 1.0, -1.0], [14, -0.5, -2.0]], [[6, -2.5, -1.0], [14, 3.0, 2.0], [18, -2.5, 3.0], [13, -3.0, -1.0]]], 5], [[[[10, 18]], 2], [[[14, 16]], 2], [[[6, 13]], 2]]]]]\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":"bf186ed89663dacdab1baf7b29cbaec7c004ea60ffc33d8ed9b0ae99c93c0862","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(frames, n):\n    table = [[-1, []] for _ in range(n)]\n    result = []\n    for f, pts in enumerate(frames):\n        pairs = []\n        for pid, x, y in pts:\n            ix, iy = math.floor(x), math.floor(y)\n            h = (((ix * 73856093) & 0xFFFFFFFF) + ((iy * 19349663) & 0xFFFFFFFF)) % n\n            slot = table[h]\n            if slot[0] != f:\n                slot[0] = f\n                slot[1] = []\n            for qid, qx, qy in slot[1]:\n                if (qx, qy) == (ix, iy):\n                    pairs.append([min(pid, qid), max(pid, qid)])\n            slot[1].append((pid, ix, iy))\n        result.append([sorted(pairs), sum(1 for s in table if s[0] == f)])\n    return result\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[[[[[[10, 1.5, -1.0], [14, 0.5, -3.0], [7, -1.5, 3.0], [12, 2.0, 3.0]], [[16, 0.5, 0.5], [7, -1.0, 1.5], [14, -2.0, -0.5]], [[8, -1.5, 3.0], [17, 1.0, -1.0], [2, 0.5, -2.5], [1, -3.0, 1.0], [19, -1.0, -1.0]], [[11, 3.0, 2.0], [17, -0.5, 2.5], [14, 2.0, -1.5]]], 3], [[[], 3], [[], 2], [[], 3], [[], 1]]], [[[[[17, -1.0, -1.0], [13, 3.0, -3.0], [16, 3.0, 0.5], [2, 0.0, 2.5]]], 11], [[[], 4]]], [[[[[14, 0.5, -2.0], [3, 3.0, 1.5], [10, 2.0, 2.5]], [[4, 1.5, 2.0], [13, -2.0, 3.0]]], 5], [[[], 3], [[], 2]]], [[[[[16, 3.0, 0.5], [19, 0.0, -1.0], [13, -1.5, 0.5], [3, 1.5, -1.5], [17, 2.5, -0.5], [2, 0.0, 0.5]]], 5], [[[], 4]]], [[[[[7, -1.5, 3.0], [9, 1.0, 0.0], [6, -1.5, -0.5], [15, -2.0, -1.5], [12, 1.0, -0.5]], [[19, 3.0, -3.0], [7, -2.0, 3.0], [9, 1.5, 2.0], [3, 3.0, 2.0]], [[15, 0.0, 3.0], [19, 2.5, -3.0], [2, 1.0, 1.0], [9, -0.5, -0.5], [17, 1.0, 0.5]]], 3], [[[], 2], [[], 3], [[], 3]]], [[[[[15, -1.0, -2.0], [3, 3.0, 1.0], [2, 2.5, -3.0], [1, -1.0, -1.0]], [[3, 3.0, -2.5], [16, -2.5, 1.0], [7, 0.0, 0.5], [1, 0.0, -2.0], [12, 0.5, -3.0], [2, 3.0, -3.0]], [[17, 2.0, -2.0], [2, -0.5, -1.0], [8, -0.5, -2.5], [12, -1.0, -1.0], [7, 0.5, 1.5], [9, 0.5, 2.0]], [[14, 1.5, 3.0], [18, 0.5, 1.5], [12, -1.0, -2.5], [16, 0.5, -3.0]]], 7], [[[], 3], [[[2, 3]], 3], [[[2, 12]], 5], [[], 3]]], [[[[[5, 2.5, 1.5], [14, 0.0, 1.5], [15, 0.0, -1.5], [13, -2.0, -1.0], [16, 1.5, 1.5], [9, 1.5, 0.5]], [[11, 1.5, -3.0], [12, -2.0, -1.0], [9, -3.0, -1.0], [2, 2.5, -1.0]]], 7], [[[], 4], [[], 3]]], [[[[[12, 1.5, 1.0], [2, 1.0, 1.0]]], 3], [[[[2, 12]], 1]]]], [[[[[[18, 0.5, 2.0], [11, 0.0, 0.5]], [[19, -0.5, -2.0], [7, -0.5, 0.5], [9, 1.5, -0.5]]], 3], [[[], 2], [[], 1]]], [[[[[3, 0.0, 1.0], [10, -2.5, 0.5]]], 3], [[[], 2]]], [[[[[4, 1.5, 0.0], [6, 0.0, -0.5]], [[18, -1.5, 2.5], [11, -1.0, -1.0], [9, 2.5, 3.0], [12, 1.0, 2.0], [17, 0.5, -1.0]]], 3], [[[], 1], [[], 3]]], [[[[[4, 2.0, 1.5], [7, -0.5, 2.0]], [[2, 0.0, 1.0], [13, 1.5, 0.0], [14, -3.0, 1.0]]], 7], [[[], 2], [[], 3]]], [[[[[6, -1.5, -3.0], [3, 0.0, 2.0]], [[11, 3.0, 2.0], [17, 2.0, 1.5], [12, 0.5, -1.5], [14, 1.5, 0.5], [1, 1.0, -3.0]]], 11], [[[], 2], [[], 5]]], [[[[[11, 3.0, -2.0], [6, 1.5, 2.0], [4, -2.5, -1.5]], [[17, -1.5, 2.5], [4, 2.0, 0.0], [5, 3.0, 0.0], [1, 0.5, -2.5], [7, -1.0, 2.5], [14, 0.5, -2.0]], [[18, -1.0, 3.0], [13, -0.5, -3.0], [11, 1.5, 2.5], [12, 2.0, 0.5], [4, 1.0, -3.0]], [[8, -3.0, 0.0], [18, -1.0, -2.0], [5, -0.5, 2.0], [16, -1.5, 1.5]]], 3], [[[], 2], [[], 2], [[], 3], [[], 3]]], [[[[[13, -1.5, 1.0], [8, 2.0, -2.5], [1, 1.5, -2.5], [3, 1.0, -3.0]], [[2, -1.5, -3.0], [16, -2.5, 2.5], [19, -2.0, 1.5]], [[8, 3.0, -1.5], [2, -2.0, -2.5], [4, -0.5, -1.5], [18, 2.5, 3.0], [10, 1.5, -0.5], [16, -2.5, -2.0]]], 11], [[[[1, 3]], 3], [[], 2], [[], 6]]], [[[[[5, 1.5, -1.0], [6, 3.0, 2.5], [16, 0.0, 0.0], [17, -1.0, 2.0], [18, -1.5, -3.0]], [[15, -1.0, 3.0], [2, -2.0, 3.0], [19, -1.0, -2.5], [16, 3.0, 1.0], [5, 3.0, 0.5]]], 3], [[[], 3], [[], 2]]]], [[[[[[1, -1.5, 0.0], [15, 0.5, -1.0], [2, 2.5, 0.5]], [[13, -3.0, -0.5], [5, 2.0, -1.5]], [[6, 1.5, 1.5], [7, 2.5, 3.0]]], 7], [[[], 3], [[], 1], [[], 2]]], [[[[[13, 1.5, 2.5], [3, 2.0, -0.5], [11, -3.0, -2.0], [8, 3.0, -3.0]], [[13, 2.5, 1.5], [18, 0.0, -1.5], [4, 1.0, -1.5], [6, 2.5, 2.5], [9, 0.0, -2.5]]], 7], [[[], 4], [[], 4]]], [[[[[14, 1.5, 1.0], [13, -3.0, -0.5], [5, 0.0, 0.5]], [[11, -1.0, 0.0], [4, -0.5, 0.0], [19, 3.0, 2.5], [15, 2.0, -1.0]]], 11], [[[], 2], [[[4, 11]], 3]]], [[[[[14, -0.5, -0.5], [7, 3.0, 1.5], [12, 1.5, -0.5], [2, 1.0, 3.0], [18, -1.5, -2.5], [1, -3.0, -1.5]]], 11], [[[], 5]]], [[[[[7, 2.0, -0.5], [16, 2.5, -3.0], [11, -1.0, -3.0]]], 7], [[[], 3]]], [[[[[2, 2.0, 0.5], [5, -0.5, 2.5], [16, -2.0, -1.5], [1, 0.0, -2.0]], [[4, -1.0, 3.0], [5, -1.0, -3.0], [3, 2.0, -2.0], [11, 0.5, -2.5], [9, 1.5, 3.0]]], 3], [[[], 2], [[], 3]]], [[[[[18, 1.0, 3.0], [15, 3.0, -1.0]]], 11], [[[], 2]]], [[[[[16, -2.0, -2.0], [14, -1.0, -3.0], [18, 2.5, 2.0], [1, -3.0, -0.5], [15, 2.0, 0.5]], [[16, 0.5, 2.5], [17, -0.5, -0.5]]], 7], [[[], 4], [[], 2]]]], [[[[[[12, -2.5, 2.0], [3, -1.5, -3.0], [15, 0.5, 1.0], [11, 2.5, -1.0]], [[8, 0.5, 0.0], [2, -1.5, -2.0]]], 7], [[[], 3], [[], 2]]], [[[[[15, -2.5, 2.0], [17, 3.0, 2.5], [3, 0.0, -2.0], [1, -2.5, 1.5]], [[5, 1.0, -2.5], [15, 2.0, -2.0], [11, 0.5, -1.5]], [[6, 0.5, -1.0], [5, 1.5, 2.0], [12, 1.0, -3.0], [8, -2.0, 1.5], [14, -2.5, -2.0]], [[8, -0.5, -2.5], [9, -1.0, -0.5]]], 7], [[[], 3], [[], 2], [[], 4], [[], 2]]], [[[[[2, 0.0, 0.5], [4, -3.0, -2.5], [9, -2.0, 1.5], [1, -3.0, 1.0]], [[3, 0.0, -0.5], [5, 3.0, 1.0]]], 7], [[[], 3], [[], 2]]], [[[[[17, -1.5, -2.5], [18, 0.5, 0.0], [15, -0.5, -2.5], [12, -1.0, 0.0]], [[13, 2.0, -2.5], [17, 2.5, -1.0]], [[13, 1.0, -3.0], [16, 0.5, 2.0]]], 3], [[[], 3], [[], 2], [[], 2]]], [[[[[12, -0.5, -2.5], [1, -2.5, 1.5], [11, 2.5, 3.0], [5, 0.5, 3.0], [8, -2.0, 3.0], [18, -3.0, -0.5]], [[4, 1.0, -0.5], [17, 1.5, -1.0], [7, -1.5, 2.5], [10, -1.5, 0.5]], [[8, 3.0, 0.5], [5, 2.0, 1.5], [16, -0.5, 2.0]]], 3], [[[], 2], [[[4, 17]], 2], [[], 2]]], [[[[[9, 2.5, -0.5], [10, -0.5, -3.0], [6, 0.5, 3.0], [15, 3.0, -2.0], [13, -3.0, -0.5], [5, -3.0, -3.0]]], 11], [[[], 5]]], [[[[[12, -0.5, 0.5], [13, -2.0, -1.0], [10, -3.0, 0.5], [6, -3.0, 3.0]], [[2, -2.0, 0.0], [3, 3.0, 3.0], [7, 0.0, 2.5], [16, 2.0, 1.0], [19, -3.0, 1.0], [4, 3.0, -0.5]]], 11], [[[], 4], [[], 4]]], [[[[[15, -1.5, 3.0], [3, -3.0, 1.0], [8, -0.5, 3.0], [11, -1.5, 3.0], [1, 0.0, 3.0], [13, -1.5, 0.0]], [[6, 3.0, 0.0], [5, 1.5, 0.5], [11, -2.0, -0.5], [9, -0.5, 1.5]]], 5], [[[[11, 15]], 3], [[], 3]]]], [[[[[[18, 0.0, 1.5], [6, -1.5, -1.0]], [[13, 2.0, 3.0], [19, 3.0, -1.5], [14, 3.0, 0.0]]], 5], [[[], 2], [[], 1]]], [[[[[13, 1.0, -0.5], [1, -2.0, 1.0], [2, 2.0, 0.5], [14, 2.0, 3.0]], [[1, 2.5, -0.5], [10, 3.0, 1.5], [18, 1.0, 0.5], [15, 0.5, -2.5], [8, 2.0, -0.5], [6, -2.0, 1.0]]], 3], [[[], 3], [[[1, 8]], 3]]], [[[[[10, -3.0, 1.0], [14, -1.5, -0.5]], [[16, 1.0, 3.0], [1, 2.0, 0.0], [5, -1.5, -2.5]], [[1, 1.5, -3.0], [14, -1.5, 1.5], [5, -1.5, -2.0], [10, 2.5, -0.5]], [[18, 0.5, -0.5], [7, 2.5, 0.0]]], 11], [[[], 2], [[], 3], [[], 3], [[], 2]]], [[[[[5, -1.5, 2.5], [14, 3.0, -2.5], [1, -2.5, -1.0], [2, -2.0, 1.0], [6, 2.5, 0.5]]], 11], [[[], 4]]], [[[[[15, -1.0, -1.0], [6, 0.0, -2.0], [8, 0.5, 2.5], [14, 2.5, -0.5], [11, 2.5, -2.0], [9, -0.5, 3.0]], [[6, 1.0, -1.0], [18, 3.0, 0.0], [11, -0.5, -2.5], [15, 1.5, -1.0]], [[16, 0.0, -0.5], [1, -1.5, -0.5], [13, 2.0, 3.0], [8, 1.5, 3.0], [19, 1.0, 2.5], [18, -3.0, 3.0]], [[17, -0.5, -2.5], [7, 1.0, 2.5], [6, 0.5, -3.0]]], 3], [[[], 3], [[[6, 15]], 2], [[], 3], [[], 2]]], [[[[[9, -1.5, 2.0], [13, 2.0, -1.5], [3, -2.0, 0.0], [8, 3.0, -1.0], [15, -2.0, 2.0], [12, -2.5, -1.5]], [[15, 1.5, -2.0], [2, -3.0, 3.0], [14, 1.0, -1.0], [1, -3.0, 3.0], [10, 3.0, -1.5]], [[13, 0.5, 0.5], [17, 3.0, 2.0], [3, 1.0, 2.5], [6, 0.5, 0.5], [1, 0.5, 0.0]], [[12, -1.5, -2.5], [15, 2.5, 0.0]]], 11], [[[[9, 15]], 3], [[[1, 2]], 4], [[[1, 6], [1, 13], [6, 13]], 3], [[], 2]]], [[[[[4, 2.0, 2.5], [7, -1.5, 2.0], [18, 3.0, 3.0]], [[2, -2.0, 0.5], [19, 2.5, -1.0], [8, -2.5, -3.0], [1, -3.0, -0.5], [7, -3.0, 0.0]], [[16, 1.5, -0.5], [7, 0.5, -1.0], [6, -1.5, 1.5], [3, -0.5, -1.5], [10, 1.0, -1.0]]], 7], [[[], 3], [[], 4], [[[10, 16]], 3]]], [[[[[15, 0.5, 0.5], [1, 3.0, 0.0], [3, -2.0, 2.0], [10, 0.0, -1.5], [18, 0.5, -2.0], [17, -0.5, 2.5]], [[17, -2.5, -2.0], [16, -0.5, -1.5], [4, 1.0, -1.0], [14, -0.5, -2.0]], [[6, -2.5, -1.0], [14, 3.0, 2.0], [18, -2.5, 3.0], [13, -3.0, -1.0]]], 5], [[[[10, 18]], 2], [[[14, 16]], 2], [[[6, 13]], 2]]]]]\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-timestamped-spatial-hash-hash-combine-operator","generated_at":"2026-09-29T14:51:01.815587+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":"The products are added instead of xored.","sha256":"9510c947ccddb0443b011672ca481742566daa6336caf671d5fd27fa3b1838c2","title":"Hash combines cell products with addition · 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":41.792,"exit_code":1,"observations":[{"actual":[[[],3],[[],2],[[],3],[[],2]],"check":"case 0","expected":[[[],3],[[],2],[[],3],[[],1]],"passed":false},{"actual":[[[],4]],"check":"case 1","expected":[[[],4]],"passed":true},{"actual":[[[],2],[[],2]],"check":"case 2","expected":[[[],3],[[],2]],"passed":false},{"actual":[[[],5]],"check":"case 3","expected":[[[],4]],"passed":false},{"actual":[[[],3],[[],2],[[],2]],"check":"case 4","expected":[[[],2],[[],3],[[],3]],"passed":false},{"actual":[[[],3],[[[2,3]],3],[[[2,12]],4],[[],3]],"check":"case 5","expected":[[[],3],[[[2,3]],3],[[[2,12]],5],[[],3]],"passed":false},{"actual":[[[],3],[[],3]],"check":"case 6","expected":[[[],4],[[],3]],"passed":false},{"actual":[[[[2,12]],1]],"check":"case 7","expected":[[[[2,12]],1]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"case 0\", \"actual\": [[[], 3], [[], 2], [[], 3], [[], 2]], \"expected\": [[[], 3], [[], 2], [[], 3], [[], 1]], \"passed\": false}, {\"check\": \"case 1\", \"actual\": [[[], 4]], \"expected\": [[[], 4]], \"passed\": true}, {\"check\": \"case 2\", \"actual\": [[[], 2], [[], 2]], \"expected\": [[[], 3], [[], 2]], \"passed\": false}, {\"check\": \"case 3\", \"actual\": [[[], 5]], \"expected\": [[[], 4]], \"passed\": false}, {\"check\": \"case 4\", \"actual\": [[[], 3], [[], 2], [[], 2]], \"expected\": [[[], 2], [[], 3], [[], 3]], \"passed\": false}, {\"check\": \"case 5\", \"actual\": [[[], 3], [[[2, 3]], 3], [[[2, 12]], 4], [[], 3]], \"expected\": [[[], 3], [[[2, 3]], 3], [[[2, 12]], 5], [[], 3]], \"passed\": false}, {\"check\": \"case 6\", \"actual\": [[[], 3], [[], 3]], \"expected\": [[[], 4], [[], 3]], \"passed\": false}, {\"check\": \"case 7\", \"actual\": [[[[2, 12]], 1]], \"expected\": [[[[2, 12]], 1]], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.924,"exit_code":1,"observations":[{"actual":[[[],2],[[],3],[[],2],[[],2]],"check":"case 0","expected":[[[],3],[[],2],[[],3],[[],1]],"passed":false},{"actual":[[[],4]],"check":"case 1","expected":[[[],4]],"passed":true},{"actual":[[[],2],[[],1]],"check":"case 2","expected":[[[],3],[[],2]],"passed":false},{"actual":[[[],3]],"check":"case 3","expected":[[[],4]],"passed":false},{"actual":[[[],3],[[],2],[[],3]],"check":"case 4","expected":[[[],2],[[],3],[[],3]],"passed":false},{"actual":[[[],4],[[[2,3]],4],[[[2,12]],4],[[],4]],"check":"case 5","expected":[[[],3],[[[2,3]],3],[[[2,12]],5],[[],3]],"passed":false},{"actual":[[[],4],[[],3]],"check":"case 6","expected":[[[],4],[[],3]],"passed":true},{"actual":[[[[2,12]],1]],"check":"case 7","expected":[[[[2,12]],1]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"case 0\", \"actual\": [[[], 2], [[], 3], [[], 2], [[], 2]], \"expected\": [[[], 3], [[], 2], [[], 3], [[], 1]], \"passed\": false}, {\"check\": \"case 1\", \"actual\": [[[], 4]], \"expected\": [[[], 4]], \"passed\": true}, {\"check\": \"case 2\", \"actual\": [[[], 2], [[], 1]], \"expected\": [[[], 3], [[], 2]], \"passed\": false}, {\"check\": \"case 3\", \"actual\": [[[], 3]], \"expected\": [[[], 4]], \"passed\": false}, {\"check\": \"case 4\", \"actual\": [[[], 3], [[], 2], [[], 3]], \"expected\": [[[], 2], [[], 3], [[], 3]], \"passed\": false}, {\"check\": \"case 5\", \"actual\": [[[], 4], [[[2, 3]], 4], [[[2, 12]], 4], [[], 4]], \"expected\": [[[], 3], [[[2, 3]], 3], [[[2, 12]], 5], [[], 3]], \"passed\": false}, {\"check\": \"case 6\", \"actual\": [[[], 4], [[], 3]], \"expected\": [[[], 4], [[], 3]], \"passed\": true}, {\"check\": \"case 7\", \"actual\": [[[[2, 12]], 1]], \"expected\": [[[[2, 12]], 1]], \"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."}}