{
  "arm": "Fugu Ultra",
  "provider": "sakana",
  "benchmark": "postcutoff_pilot_v1",
  "freeze_tag": "postcutoff-pilot-v1-freeze-20260705",
  "note": "Frontier comparator. Single public model; full per-task output included.",
  "tasks": [
    {
      "task_id": "PILOT-N2",
      "task_type": "math",
      "answer": "30907",
      "gold": "30907",
      "correct": true,
      "tokens_in": 9961,
      "tokens_out": 43254,
      "cost_usd": 1.347425,
      "latency_s": 445.62,
      "timed_out": false,
      "solution": "Let \\(x\\) mark the number of \\(1\\times 1\\) square tiles used. We scan the \\(3\\times 10\\) board column by column and keep a bitmask state for which cells in the next column are already occupied by horizontal dominoes.\n\nUsing top-bottom symmetry, combine the 8 masks into these 6 states:\n\\[\nu_0=S_0,\\quad u_1=S_1+S_4,\\quad u_2=S_2,\\quad u_3=S_3+S_6,\\quad u_5=S_5,\\quad u_7=S_7.\n\\]\nEach \\(u_i\\) is a polynomial in \\(x\\), truncated after \\(x^2\\), since we only need exactly two square tiles.\n\nFilling one column gives the transitions:\n\\[\n\\begin{aligned}\nu_0'&=2xu_0+(1+x^2)u_1+x^2u_2+xu_3+xu_5+u_7,\\\\\nu_1'&=(2+2x^2)u_0+xu_1+2xu_2+u_3,\\\\\nu_2'&=x^2u_0+xu_1+u_5,\\\\\nu_3'&=2xu_0+u_1,\\\\\nu_5'&=xu_0+u_2,\\\\\nu_7'&=u_0.\n\\end{aligned}\n\\]\n\nStart with \\(u_0=1\\) and all other states \\(0\\). After 9 columns, writing \\(a+bx+cx^2\\) as \\([a,b,c]\\), the state vector is:\n\\[\n\\begin{array}{c|cccccc}\n &u_0&u_1&u_2&u_3&u_5&u_7\\\\\n\\hline\n9&[0,2554,0]&[418,0,17538]&[0,0,2859]&[0,1902,0]&[0,361,0]&[153,0,5580].\n\\end{array}\n\\]\n\nFor the 10th column, the final tiling must end in state \\(u_0\\). The coefficient of \\(x^2\\) in\n\\[\nu_0'=2xu_0+(1+x^2)u_1+x^2u_2+xu_3+xu_5+u_7\n\\]\nis\n\\[\n2(2554)+(17538+418)+0+1902+361+5580=30907.\n\\]\n\nTherefore, the number of valid tilings is\n\nANSWER: 30907"
    },
    {
      "task_id": "PILOT-K1",
      "task_type": "code",
      "answer": null,
      "gold": "121090",
      "correct": false,
      "tokens_in": 0,
      "tokens_out": 0,
      "cost_usd": 0,
      "latency_s": 0,
      "timed_out": true,
      "solution": ""
    },
    {
      "task_id": "PILOT-Q1",
      "task_type": "simple_qa",
      "answer": "10152",
      "gold": "10152",
      "correct": true,
      "tokens_in": 7968,
      "tokens_out": 2701,
      "cost_usd": 0.12087,
      "latency_s": 48.67,
      "timed_out": false,
      "solution": "The depot ships:\n\n- Monday: 48 crates\n- Tuesday: 54 crates\n- Wednesday: 60 crates\n- Thursday: 66 crates\n- Friday: 72 crates\n\nA full crate has 36 units.\n\nMonday: \\(48 \\times 36 = 1728\\)  \nTuesday: \\(54 \\times 36 = 1944\\)\n\nOn Wednesday, one third of 60 crates is 20 crates. These are half-full, with 18 units each. The other 40 crates are full:\n\n\\[\n40 \\times 36 + 20 \\times 18 = 1440 + 360 = 1800\n\\]\n\nThursday:\n\n\\[\n66 \\times 36 = 2376\n\\]\n\nOn Friday, 8 of the 72 crates are returned unopened, so only 64 crates count:\n\n\\[\n64 \\times 36 = 2304\n\\]\n\nTotal:\n\n\\[\n1728 + 1944 + 1800 + 2376 + 2304 = 10152\n\\]\n\nANSWER: 10152"
    },
    {
      "task_id": "PILOT-R1",
      "task_type": "reasoning",
      "answer": "12",
      "gold": "12",
      "correct": true,
      "tokens_in": 8441,
      "tokens_out": 13429,
      "cost_usd": 0.445075,
      "latency_s": 181.18,
      "timed_out": false,
      "solution": "Let the finishing positions of Ava, Ben, Cleo, Dan, and Eve be \\(a,b,c,d,e\\), respectively.\n\nTheir statements translate to:\n\n- Ava truthful iff \\(b=a+1\\).\n- Ben truthful iff \\(c=5\\).\n- Cleo truthful iff \\(c<a\\).\n- Dan truthful iff \\(e\\ne 1\\).\n- Eve truthful iff \\(d=3\\).\n\nAlso, \\(a<d\\).\n\nThe consistent liar pair is Ben and Eve. Then Ava, Cleo, and Dan tell the truth, while Ben and Eve lie:\n\n\\[\nb=a+1,\\quad c<a,\\quad e\\ne1,\\quad c\\ne5,\\quad d\\ne3,\\quad a<d.\n\\]\n\nSince \\(c<a<b\\), the only possible beginning is:\n\n\\[\nc=1,\\quad a=2,\\quad b=3.\n\\]\n\nThe two liars, Ben and Eve, must be in consecutive positions, so Eve must be 4th. Then Dan is 5th:\n\n\\[\n(c,a,b,e,d)=(1,2,3,4,5).\n\\]\n\nCheck: Ben lies because Cleo is not last, and Eve lies because Dan is not third. Their positions are \\(3\\) and \\(4\\), whose product is\n\n\\[\n3\\cdot4=12.\n\\]\n\nANSWER: 12"
    },
    {
      "task_id": "PILOT-C1",
      "task_type": "code",
      "answer": null,
      "gold": "300062",
      "correct": false,
      "tokens_in": 0,
      "tokens_out": 0,
      "cost_usd": 0,
      "latency_s": 0,
      "timed_out": true,
      "solution": ""
    }
  ]
}