Upload proofs/87825.json with huggingface_hub

Browse files

Files changed (1) hide show

proofs/87825.json +1 -0

proofs/87825.json ADDED Viewed

	@@ -0,0 +1 @@

+ {"schema": 2, "epoch": 87825, "nonce": "9c594d1e7ee8ac4f", "hotkey": "5FRE1kqMJz8ddModcXUsCquuWhB8QHnjYib2iK2VfiFetkC5", "source_hash": "24837b9ae6895829747c5eb448673693fedbeb2e3e62a5ca170051a512053fc0", "weights_hash": "8c94d6e58cc59dda7770ab9ad7aa0be90adc8cbedcd419ef4c539a075d371e1f", "model_id": "router", "total_cost_usd": 0.004945137, "n_calls": 6, "call_log_hash": "1161731e1d9fee2f680873cae3fc9d3bc8766b84e7e23fb170a83b9f43659e57", "measurement": "1449fadb4821cadef93f7eecc8c3b040e2cd244e01a2607ea531e5f7055c38d8", "confined": true, "latency_s": 212.082, "tokens_in": 1354, "tokens_out": 23866, "results": [{"benchmark": "mmlu", "task_id": "mmlu-11319", "answer": "C", "cost_usd": 0.00018292, "chosen_rung": 0, "rungs_used": [0], "distribution": [0.999831, 0.000162, 1e-06, 1e-06, 3e-06, 1e-06, 1e-06]}, {"benchmark": "mmlu", "task_id": "mmlu-1448", "answer": "To find the speed of observer $O'$ relative to observer $O$, we apply the principles of special relativity, specifically the relativity of simultaneity.\n\n### 1. Analysis of the Setup\n* **Frame $S$ (Observer $O$):** Observer $O$ is at rest at the midpoint ($x = 5$ m) between two sources at $x_1 = 0$ m and $x_2 = 10$ m. Because $O$ is equidistant from the sources and observes the flashes simultaneously, the emission events are simultaneous in this frame.\n * Time interval: $\\Delta t = 0$\n * Spatial separation: $\\Delta x = 10$ m\n* **Frame $S'$ (Observer $O'$):** Observer $O'$ moves at speed $v$ parallel to the x-axis. In this frame, the time difference between the flashes is $\\Delta t' = 13 \\text{ ns} = 13 \\times 10^{-9}$ s.\n\n### 2. Lorentz Transformation\nThe relationship between the time intervals in the two frames is given by the Lorentz transformation:\n$$\\Delta t' = \\gamma \\left( \\Delta t - \\frac{v \\Delta x}{c^2} \\right)$$\nSubstituting $\\Delta t = 0$ and taking the magnitude:\n$$|\\Delta t'| = \\gamma \\frac{v \\Delta x}{c^2}$$\nUsing $\\beta = v/c$ and $\\gamma = \\frac{1}{\\sqrt{1-\\beta^2}}$, we rearrange to solve for $\\beta$:\n$$\\frac{|\\Delta t'| c}{\\Delta x} = \\frac{\\beta}{\\sqrt{1-\\beta^2}}$$\n\n### 3. Calculation\nUsing $c \\approx 3 \\times 10^8$ m/s:\n$$\\frac{(13 \\times 10^{-9})(3 \\times 10^8)}{10} = \\frac{3.9}{10} = 0.39$$\nSetting $\\frac{\\beta}{\\sqrt{1-\\beta^2}} = 0.39$ and squaring both sides:\n$$\\frac{\\beta^2}{1-\\beta^2} = 0.1521 \\implies \\beta^2 = 0.1521(1 - \\beta^2)$$\n$$\\beta^2(1 + 0.1521) = 0.1521 \\implies \\beta^2 = \\frac{0.1521}{1.1521} \\approx 0.132$$\n$$\\beta = \\sqrt{0.132} \\approx 0.363$$\n\nThe speed of $O'$ relative to $O$ is approximately $0.36c$.\n\nC", "cost_usd": 0.00140604, "chosen_rung": 0, "rungs_used": [0], "distribution": [0.995668, 0.004295, 5e-06, 5e-06, 1.6e-05, 5e-06, 5e-06]}, {"benchmark": "math", "task_id": "gsm8k-1180", "answer": "Mr. Marcellus purchased 4000 gallons of milk at $3.50 per gallon, for a total cost of $14,000. Since 2/5 of the milk was sour, he returned 1600 gallons. The refund is 1600 \u00d7 $3.50 = $5,600.\n\n5600", "cost_usd": 7.329600000000004e-05, "chosen_rung": 1, "rungs_used": [1], "distribution": [0.001508, 0.99847, 3e-06, 3e-06, 9e-06, 3e-06, 3e-06]}, {"benchmark": "math", "task_id": "gsm8k-1291", "answer": "27", "cost_usd": 2.043300000000004e-05, "chosen_rung": 1, "rungs_used": [1], "distribution": [0.00054, 0.999447, 2e-06, 2e-06, 5e-06, 2e-06, 2e-06]}, {"benchmark": "code", "task_id": "lcb-abc400_b", "answer": "```python\nimport sys\n\ndef solve() -> None:\n data = sys.stdin.read().strip().split()\n if not data:\n return\n N = int(data[0])\n M = int(data[1])\n\n limit = 10**9\n total = 0\n term = 1\n for _ in range(M + 1):\n total += term\n if total > limit:\n print(\"inf\")\n return\n term *= N\n print(total)\n\nif __name__ == \"__main__\":\n solve()\n```", "cost_usd": 0.00025004, "chosen_rung": 1, "rungs_used": [1], "distribution": [3.4e-05, 0.999963, 0.0, 0.0, 1e-06, 0.0, 0.0]}, {"benchmark": "code", "task_id": "lcb-abc388_d", "answer": "import sys\n\ndef main():\n data = list(map(int, sys.stdin.buffer.read().split()))\n if not data:\n return\n\n N = data[0]\n diff = [0] * (N + 2)\n ans = [0] * N\n\n active = 0\n for t in range(1, N + 1):\n active += diff[t]\n x = data[t] + t + active\n\n b = x - N\n if b < 0:\n b = 0\n ans[t - 1] = b\n\n l = t + 1\n if l <= N:\n r = x if x < N else N\n if l <= r:\n diff[l] += 1\n diff[r + 1] -= 1\n\n sys.stdout.write(\" \".join(map(str, ans)))\n\nif __name__ == \"__main__\":\n main()", "cost_usd": 0.0030124079999999994, "chosen_rung": 1, "rungs_used": [1], "distribution": [0.000249, 0.999742, 1e-06, 1e-06, 4e-06, 1e-06, 1e-06]}], "quote": {"measurement": "1449fadb4821cadef93f7eecc8c3b040e2cd244e01a2607ea531e5f7055c38d8", "report_data": "e602aa952aef9846597f81ad61654c2be4e1191024f3f437d1eefe5e01a677a5", "platform_sig": "tdx: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"}}