{
  "run_id": "session-adaptive-spectroscopy-001",
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      "timestamp": "2026-10-17T08:57:42.580786Z",
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      "timestamp": "2026-10-17T08:57:42.813024Z",
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        "content": "You are working in a sandboxed computing environment. Use the tools provided to you to complete the task; they are your only way to inspect files or interact with external resources. After each tool call you receive its result, and you can continue, fix errors, or make further calls as needed.\n\nIMPORTANT: You are operating in a fully automated evaluation environment with NO human in the loop.\n- Make all decisions autonomously - never ask for permission, confirmation, or input\n- If you encounter an error, fix it yourself and continue\n- You may list options or explain your reasoning, but always choose and proceed yourself - never wait for user selection",
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        "content": "Investigate the synthetic scientific system described in /workdir/shared/task.json. Call lab_state() to read the full task, query inputs, experiment catalogue, initial observations, measurement-noise assumptions, budget and exact scoring rule. Choose experiments with run_experiment(action_id=...). You can compute with Python, NumPy and SciPy using bash. Your goal is to predict the noise-free mean outcomes of the listed held-out queries accurately within the experiment budget. The query inputs are visible, but their outcomes cannot be queried. Write exactly {\"predictions\": [[number, ...], ...]} to /workdir/data/predictions.json, in the query/output order specified by the task. Only that numeric submission is graded; text explanations are not scored. When ready, end with a final message. Grading occurs once after the episode ends; there is no score feedback during experimentation. Missing, malformed, nonfinite, wrongly shaped or tampered submissions receive zero. The simulator is an explicit mathematical testbed, not a claim about a real specimen.",
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            "text": "{\"specification\": {\"task_id\": \"adaptive-spectroscopy\", \"version\": \"0.2.0\", \"budget\": 8, \"cost_semantics\": \"Every accepted experiment costs one credit; at most two repeats per action. Invalid requests cost nothing. The budget is a hard constraint; unused credits do not directly increase the score.\", \"measurement_noise\": \"Independent additive zero-mean Gaussian noise per output and replicate, with the listed fixed standard deviations. Readouts are not clipped. Each measurement has equal synthetic exposure/cost. Repeating observe_initial returns the same initial data, not new measurements.\", \"split_definition\": \"Train and test use independent parameter/noise draws from the same published distributions. No claim of out-of-family generalization.\", \"status\": \"Original synthetic prototype; no physical calibration or LLM training result.\", \"submission\": \"Submit one finite numeric matrix in the exact prediction_shape. Submission is terminal and cannot be retried after acceptance.\", \"scoring\": {\"name\": \"inverse_normalized_mse\", \"formula\": \"score = 1 / (1 + mean(((prediction - noiseless_hidden_target) / scale)^2))\", \"scale\": [0.025], \"range\": [0, 1], \"meaning\": \"Higher is better. Exact latent-mean prediction scores 1. A normalized RMSE equal to one measurement-noise standard deviation scores 0.5. Measurement noise is not added to hidden targets.\"}, \"title\": \"Adaptive spectral measurement\", \"outputs\": [\"absorbance\"], \"noise_std\": [0.025], \"instructions\": \"Choose eight wavelength measurements to identify a hidden spectral library and estimate a synthetic mixture spectrum. The library controls a global wavelength shift and peak broadening; amplitudes, offset and slope are also unknown. Predict the listed unseen wavelengths. Absorbance is in synthetic units.\", \"model\": \"y(lambda)=sum_i a_i*exp(-0.5*((lambda-center_i-shift)/(width_i*broadening))^2)+offset+slope*(lambda-500)/100. Base centers [447,482,531], widths [10,18,12] nm. One hidden library uses shift in [-8,0,8] nm and broadening in [0.75,1,1.25]. No physical calibration or scattering model.\", \"prior\": \"All nine shift/broadening pairs equally likely. a_i independently Uniform(0.1,1); offset Uniform(0,0.12); slope Uniform(-0.04,0.04).\", \"initial_queries\": [{\"wavelength\": 400.0}, {\"wavelength\": 650.0}], \"prediction_queries\": [{\"wavelength\": 421.0}, {\"wavelength\": 437.0}, {\"wavelength\": 453.0}, {\"wavelength\": 469.0}, {\"wavelength\": 487.0}, {\"wavelength\": 501.0}, {\"wavelength\": 517.0}, {\"wavelength\": 533.0}, {\"wavelength\": 549.0}, {\"wavelength\": 577.0}, {\"wavelength\": 613.0}, {\"wavelength\": 637.0}], \"experiments\": [{\"id\": \"measure-405\", \"label\": \"Measure 405 nm\", \"query\": {\"wavelength\": 405.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-410\", \"label\": \"Measure 410 nm\", \"query\": {\"wavelength\": 410.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-415\", \"label\": \"Measure 415 nm\", \"query\": {\"wavelength\": 415.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-420\", \"label\": \"Measure 420 nm\", \"query\": {\"wavelength\": 420.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-425\", \"label\": \"Measure 425 nm\", \"query\": {\"wavelength\": 425.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-430\", \"label\": \"Measure 430 nm\", \"query\": {\"wavelength\": 430.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-435\", \"label\": \"Measure 435 nm\", \"query\": {\"wavelength\": 435.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-440\", \"label\": \"Measure 440 nm\", \"query\": {\"wavelength\": 440.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-445\", \"label\": \"Measure 445 nm\", \"query\": {\"wavelength\": 445.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-450\", \"label\": \"Measure 450 nm\", \"query\": {\"wavelength\": 450.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-455\", \"label\": \"Measure 455 nm\", \"query\": {\"wavelength\": 455.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-460\", \"label\": \"Measure 460 nm\", \"query\": {\"wavelength\": 460.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-465\", \"label\": \"Measure 465 nm\", \"query\": {\"wavelength\": 465.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-470\", \"label\": \"Measure 470 nm\", \"query\": {\"wavelength\": 470.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-475\", \"label\": \"Measure 475 nm\", \"query\": {\"wavelength\": 475.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-480\", \"label\": \"Measure 480 nm\", \"query\": {\"wavelength\": 480.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-485\", \"label\": \"Measure 485 nm\", \"query\": {\"wavelength\": 485.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-490\", \"label\": \"Measure 490 nm\", \"query\": {\"wavelength\": 490.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-495\", \"label\": \"Measure 495 nm\", \"query\": {\"wavelength\": 495.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-500\", \"label\": \"Measure 500 nm\", \"query\": {\"wavelength\": 500.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-505\", \"label\": \"Measure 505 nm\", \"query\": {\"wavelength\": 505.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-510\", \"label\": \"Measure 510 nm\", \"query\": {\"wavelength\": 510.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-515\", \"label\": \"Measure 515 nm\", \"query\": {\"wavelength\": 515.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-520\", \"label\": \"Measure 520 nm\", \"query\": {\"wavelength\": 520.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-525\", \"label\": \"Measure 525 nm\", \"query\": {\"wavelength\": 525.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-530\", \"label\": \"Measure 530 nm\", \"query\": {\"wavelength\": 530.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-535\", \"label\": \"Measure 535 nm\", \"query\": {\"wavelength\": 535.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-540\", \"label\": \"Measure 540 nm\", \"query\": {\"wavelength\": 540.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-545\", \"label\": \"Measure 545 nm\", \"query\": {\"wavelength\": 545.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-550\", \"label\": \"Measure 550 nm\", \"query\": {\"wavelength\": 550.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-555\", \"label\": \"Measure 555 nm\", \"query\": {\"wavelength\": 555.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-560\", \"label\": \"Measure 560 nm\", \"query\": {\"wavelength\": 560.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-565\", \"label\": \"Measure 565 nm\", \"query\": {\"wavelength\": 565.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-570\", \"label\": \"Measure 570 nm\", \"query\": {\"wavelength\": 570.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-575\", \"label\": \"Measure 575 nm\", \"query\": {\"wavelength\": 575.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-580\", \"label\": \"Measure 580 nm\", \"query\": {\"wavelength\": 580.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-585\", \"label\": \"Measure 585 nm\", \"query\": {\"wavelength\": 585.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-590\", \"label\": \"Measure 590 nm\", \"query\": {\"wavelength\": 590.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-595\", \"label\": \"Measure 595 nm\", \"query\": {\"wavelength\": 595.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-600\", \"label\": \"Measure 600 nm\", \"query\": {\"wavelength\": 600.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-605\", \"label\": \"Measure 605 nm\", \"query\": {\"wavelength\": 605.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-610\", \"label\": \"Measure 610 nm\", \"query\": {\"wavelength\": 610.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-615\", \"label\": \"Measure 615 nm\", \"query\": {\"wavelength\": 615.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-620\", \"label\": \"Measure 620 nm\", \"query\": {\"wavelength\": 620.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-625\", \"label\": \"Measure 625 nm\", \"query\": {\"wavelength\": 625.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-630\", \"label\": \"Measure 630 nm\", \"query\": {\"wavelength\": 630.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-635\", \"label\": \"Measure 635 nm\", \"query\": {\"wavelength\": 635.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-640\", \"label\": \"Measure 640 nm\", \"query\": {\"wavelength\": 640.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-645\", \"label\": \"Measure 645 nm\", \"query\": {\"wavelength\": 645.0}, \"cost\": 1, \"max_replicates\": 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\"additionalProperties\": false}, \"prediction_shape\": [12, 1]}, \"initial_observations\": [{\"query\": {\"wavelength\": 400.0}, \"values\": [-0.06972948619223732], \"noise_std\": [0.025]}, {\"query\": {\"wavelength\": 650.0}, \"values\": [0.05293275693195518], \"noise_std\": [0.025]}], \"transcript\": {\"task_id\": \"adaptive-spectroscopy\", \"version\": \"0.2.0\", \"events\": [{\"type\": \"initial\", \"observations\": [{\"query\": {\"wavelength\": 400.0}, \"values\": [-0.06972948619223732], \"noise_std\": [0.025]}, {\"query\": {\"wavelength\": 650.0}, \"values\": [0.05293275693195518], \"noise_std\": [0.025]}]}]}, \"closed\": false}",
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      "timestamp": "2026-10-17T08:58:05.383162Z",
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            "text": "{\"specification\": {\"task_id\": \"adaptive-spectroscopy\", \"version\": \"0.2.0\", \"budget\": 8, \"cost_semantics\": \"Every accepted experiment costs one credit; at most two repeats per action. Invalid requests cost nothing. The budget is a hard constraint; unused credits do not directly increase the score.\", \"measurement_noise\": \"Independent additive zero-mean Gaussian noise per output and replicate, with the listed fixed standard deviations. Readouts are not clipped. Each measurement has equal synthetic exposure/cost. Repeating observe_initial returns the same initial data, not new measurements.\", \"split_definition\": \"Train and test use independent parameter/noise draws from the same published distributions. No claim of out-of-family generalization.\", \"status\": \"Original synthetic prototype; no physical calibration or LLM training result.\", \"submission\": \"Submit one finite numeric matrix in the exact prediction_shape. Submission is terminal and cannot be retried after acceptance.\", \"scoring\": {\"name\": \"inverse_normalized_mse\", \"formula\": \"score = 1 / (1 + mean(((prediction - noiseless_hidden_target) / scale)^2))\", \"scale\": [0.025], \"range\": [0, 1], \"meaning\": \"Higher is better. Exact latent-mean prediction scores 1. A normalized RMSE equal to one measurement-noise standard deviation scores 0.5. Measurement noise is not added to hidden targets.\"}, \"title\": \"Adaptive spectral measurement\", \"outputs\": [\"absorbance\"], \"noise_std\": [0.025], \"instructions\": \"Choose eight wavelength measurements to identify a hidden spectral library and estimate a synthetic mixture spectrum. The library controls a global wavelength shift and peak broadening; amplitudes, offset and slope are also unknown. Predict the listed unseen wavelengths. Absorbance is in synthetic units.\", \"model\": \"y(lambda)=sum_i a_i*exp(-0.5*((lambda-center_i-shift)/(width_i*broadening))^2)+offset+slope*(lambda-500)/100. Base centers [447,482,531], widths [10,18,12] nm. One hidden library uses shift in [-8,0,8] nm and broadening in [0.75,1,1.25]. No physical calibration or scattering model.\", \"prior\": \"All nine shift/broadening pairs equally likely. a_i independently Uniform(0.1,1); offset Uniform(0,0.12); slope Uniform(-0.04,0.04).\", \"initial_queries\": [{\"wavelength\": 400.0}, {\"wavelength\": 650.0}], \"prediction_queries\": [{\"wavelength\": 421.0}, {\"wavelength\": 437.0}, {\"wavelength\": 453.0}, {\"wavelength\": 469.0}, {\"wavelength\": 487.0}, {\"wavelength\": 501.0}, {\"wavelength\": 517.0}, {\"wavelength\": 533.0}, {\"wavelength\": 549.0}, {\"wavelength\": 577.0}, {\"wavelength\": 613.0}, {\"wavelength\": 637.0}], \"experiments\": [{\"id\": \"measure-405\", \"label\": \"Measure 405 nm\", \"query\": {\"wavelength\": 405.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-410\", \"label\": \"Measure 410 nm\", \"query\": {\"wavelength\": 410.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-415\", \"label\": \"Measure 415 nm\", \"query\": {\"wavelength\": 415.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-420\", \"label\": \"Measure 420 nm\", \"query\": {\"wavelength\": 420.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-425\", \"label\": \"Measure 425 nm\", \"query\": {\"wavelength\": 425.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-430\", \"label\": \"Measure 430 nm\", \"query\": {\"wavelength\": 430.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-435\", \"label\": \"Measure 435 nm\", \"query\": {\"wavelength\": 435.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-440\", \"label\": \"Measure 440 nm\", \"query\": {\"wavelength\": 440.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-445\", \"label\": \"Measure 445 nm\", \"query\": {\"wavelength\": 445.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-450\", \"label\": \"Measure 450 nm\", \"query\": {\"wavelength\": 450.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-455\", \"label\": \"Measure 455 nm\", \"query\": {\"wavelength\": 455.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-460\", \"label\": \"Measure 460 nm\", \"query\": {\"wavelength\": 460.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-465\", \"label\": \"Measure 465 nm\", \"query\": {\"wavelength\": 465.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-470\", \"label\": \"Measure 470 nm\", \"query\": {\"wavelength\": 470.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-475\", \"label\": \"Measure 475 nm\", \"query\": {\"wavelength\": 475.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-480\", \"label\": \"Measure 480 nm\", \"query\": {\"wavelength\": 480.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-485\", \"label\": \"Measure 485 nm\", \"query\": {\"wavelength\": 485.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-490\", \"label\": \"Measure 490 nm\", \"query\": {\"wavelength\": 490.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-495\", \"label\": \"Measure 495 nm\", \"query\": {\"wavelength\": 495.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-500\", \"label\": \"Measure 500 nm\", \"query\": {\"wavelength\": 500.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-505\", \"label\": \"Measure 505 nm\", \"query\": {\"wavelength\": 505.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-510\", \"label\": \"Measure 510 nm\", \"query\": {\"wavelength\": 510.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-515\", \"label\": \"Measure 515 nm\", \"query\": {\"wavelength\": 515.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-520\", \"label\": \"Measure 520 nm\", \"query\": {\"wavelength\": 520.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-525\", \"label\": \"Measure 525 nm\", \"query\": {\"wavelength\": 525.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-530\", \"label\": \"Measure 530 nm\", \"query\": {\"wavelength\": 530.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-535\", \"label\": \"Measure 535 nm\", \"query\": {\"wavelength\": 535.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-540\", \"label\": \"Measure 540 nm\", \"query\": {\"wavelength\": 540.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-545\", \"label\": \"Measure 545 nm\", \"query\": {\"wavelength\": 545.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-550\", \"label\": \"Measure 550 nm\", \"query\": {\"wavelength\": 550.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-555\", \"label\": \"Measure 555 nm\", \"query\": {\"wavelength\": 555.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-560\", \"label\": \"Measure 560 nm\", \"query\": {\"wavelength\": 560.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-565\", \"label\": \"Measure 565 nm\", \"query\": {\"wavelength\": 565.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-570\", \"label\": \"Measure 570 nm\", \"query\": {\"wavelength\": 570.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-575\", \"label\": \"Measure 575 nm\", \"query\": {\"wavelength\": 575.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-580\", \"label\": \"Measure 580 nm\", \"query\": {\"wavelength\": 580.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-585\", \"label\": \"Measure 585 nm\", \"query\": {\"wavelength\": 585.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-590\", \"label\": \"Measure 590 nm\", \"query\": {\"wavelength\": 590.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-595\", \"label\": \"Measure 595 nm\", \"query\": {\"wavelength\": 595.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-600\", \"label\": \"Measure 600 nm\", \"query\": {\"wavelength\": 600.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-605\", \"label\": \"Measure 605 nm\", \"query\": {\"wavelength\": 605.0}, \"cost\": 1, \"max_replicates\": 2}, {\"id\": \"measure-610\", \"label\": 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            "text": "{\"stdout\":\"observations [(400.0, -0.06972948619223732), (650.0, 0.05293275693195518)]\\nlibrary posterior [((-8, 0.75), np.float64(0.118394)), ((-8, 1.0), np.float64(0.114819)), ((-8, 1.25), np.float64(0.069216)), ((0, 0.75), np.float64(0.118401)), ((0, 1.0), np.float64(0.118162)), ((0, 1.25), np.float64(0.107838)), ((8, 0.75), np.float64(0.118402)), ((8, 1.0), np.float64(0.118382)), ((8, 1.25), np.float64(0.116387))]\\nmean predictions [0.030704373700320645, 0.3329048299716566, 0.5431729807238187, 0.48308631522390744, 0.5036655850753776, 0.3579965023499531, 0.3851922104872863, 0.5047933070683817, 0.23384689175179021, 0.03678370770376312, 0.04406035104477921, 0.051378609144892874]\\nprediction sd [0.06823472864879829, 0.2658706647474386, 0.25818040974218087, 0.23348510820388726, 0.24454769952702554, 0.20602975962280282, 0.22109372381005826, 0.24170954416708362, 0.1928440074085918, 0.012553221006479463, 0.011479808701261977, 0.012819626593760186]\\ntop actions [(465, 0.012041164120858398), (500, 0.011932733650961739), (495, 0.011872720774159504), (470, 0.011589881899236454), (490, 0.011584887667030518), (505, 0.011489627765592118), (460, 0.011108626329107925), (485, 0.011049280821453525), (475, 0.010911486209624302), (480, 0.010644837898866397), (510, 0.010310248456093752), (455, 0.010089347431853218)]\\nposterior mean normalized risk 59.16212124311369\\n\",\"exit_code\":0}",
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          "stdout": "observations [(400.0, -0.06972948619223732), (650.0, 0.05293275693195518)]\nlibrary posterior [((-8, 0.75), np.float64(0.118394)), ((-8, 1.0), np.float64(0.114819)), ((-8, 1.25), np.float64(0.069216)), ((0, 0.75), np.float64(0.118401)), ((0, 1.0), np.float64(0.118162)), ((0, 1.25), np.float64(0.107838)), ((8, 0.75), np.float64(0.118402)), ((8, 1.0), np.float64(0.118382)), ((8, 1.25), np.float64(0.116387))]\nmean predictions [0.030704373700320645, 0.3329048299716566, 0.5431729807238187, 0.48308631522390744, 0.5036655850753776, 0.3579965023499531, 0.3851922104872863, 0.5047933070683817, 0.23384689175179021, 0.03678370770376312, 0.04406035104477921, 0.051378609144892874]\nprediction sd [0.06823472864879829, 0.2658706647474386, 0.25818040974218087, 0.23348510820388726, 0.24454769952702554, 0.20602975962280282, 0.22109372381005826, 0.24170954416708362, 0.1928440074085918, 0.012553221006479463, 0.011479808701261977, 0.012819626593760186]\ntop actions [(465, 0.012041164120858398), (500, 0.011932733650961739), (495, 0.011872720774159504), (470, 0.011589881899236454), (490, 0.011584887667030518), (505, 0.011489627765592118), (460, 0.011108626329107925), (485, 0.011049280821453525), (475, 0.010911486209624302), (480, 0.010644837898866397), (510, 0.010310248456093752), (455, 0.010089347431853218)]\nposterior mean normalized risk 59.16212124311369\n",
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            "text": "{\"stdout\":\"observations [(400.0, -0.06972948619223732), (650.0, 0.05293275693195518)]\\nlibrary posterior [((-8, 0.75), np.float64(0.118394)), ((-8, 1.0), np.float64(0.114819)), ((-8, 1.25), np.float64(0.069216)), ((0, 0.75), np.float64(0.118401)), ((0, 1.0), np.float64(0.118162)), ((0, 1.25), np.float64(0.107838)), ((8, 0.75), np.float64(0.118402)), ((8, 1.0), np.float64(0.118382)), ((8, 1.25), np.float64(0.116387))]\\nmean predictions [0.030704373700320645, 0.3329048299716566, 0.5431729807238187, 0.48308631522390744, 0.5036655850753776, 0.3579965023499531, 0.3851922104872863, 0.5047933070683817, 0.23384689175179021, 0.03678370770376312, 0.04406035104477921, 0.051378609144892874]\\nprediction sd [0.06823472864879829, 0.2658706647474386, 0.25818040974218087, 0.23348510820388726, 0.24454769952702554, 0.20602975962280282, 0.22109372381005826, 0.24170954416708362, 0.1928440074085918, 0.012553221006479463, 0.011479808701261977, 0.012819626593760186]\\ntop actions [(465, 0.012041164120858398), (500, 0.011932733650961739), (495, 0.011872720774159504), (470, 0.011589881899236454), (490, 0.011584887667030518), (505, 0.011489627765592118), (460, 0.011108626329107925), (485, 0.011049280821453525), (475, 0.010911486209624302), (480, 0.010644837898866397), (510, 0.010310248456093752), (455, 0.010089347431853218)]\\nposterior mean normalized risk 59.16212124311369\\n\",\"exit_code\":0}"
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              "arguments": "{\"command\": \"cat > /workdir/data/finalize.py <<'PY'\\nimport numpy as np, json\\nfrom scipy.stats import multivariate_normal, qmc\\nfrom scipy.special import ndtri, logsumexp\\nfrom scipy.optimize import minimize\\nP='/workdir/data/'\\nd=np.load(P+'state.npz');x=d['x'];y=d['y'];sig=.025\\nlo=np.array([.1,.1,.1,0.,-.04]);hi=np.array([1,1,1,.12,.04]);qs=np.array([421,437,453,469,487,501,517,533,549,577,613,637])\\ndef A(w,s,b):\\n w=np.asarray(w)\\n return np.column_stack([np.exp(-.5*((w[:,None]-np.array([447,482,531])-s)/(np.array([10,18,12])*b))**2),np.ones(len(w)),(w-500)/100])\\nrng=np.random.default_rng(20261017); libs=[(s,b) for s in [-8,0,8] for b in [.75,1,1.25]]; mus=[];covs=[];lev=[]\\nfor s,b in libs:\\n mat=A(x,s,b);h=mat.T@mat;mu=np.linalg.solve(h,mat.T@y);cov=sig**2*np.linalg.inv(h)\\n mass=multivariate_normal.cdf(hi,mean=mu,cov=cov,lower_limit=lo,maxpts=1000000,abseps=1e-10,releps=1e-8,rng=rng)\\n rss=np.sum((mat@mu-y)**2);score=-.5*rss/sig**2-.5*np.linalg.slogdet(h)[1]+np.log(max(mass,1e-300))\\n print('model',s,b,'rss',rss,'mass',mass,'log_evidence',score)\\n mus.append(mu);covs.append(cov);lev.append(score)\\nw=np.exp(lev-logsumexp(lev));print('exact_library_weights',w.tolist())\\nk=int(np.argmax(w));mu=mus[k];cov=covs[k];samples=[]\\nfor seed in range(8):\\n z=ndtri(qmc.Sobol(5,scramble=True,seed=800+seed).random_base2(19));v=mu+z@np.linalg.cholesky(cov).T\\n v=v[np.all((v>=lo)&(v<=hi),axis=1)];samples.append(v)\\n if sum(len(a) for a in samples)>=150000:break\\nsamples=np.concatenate(samples);print('sample_count',len(samples),'coefficient_mean',samples.mean(axis=0).tolist())\\nB=A(qs,*libs[k]);Q=samples@B.T;mean=Q.mean(axis=0)\\n# Maximize the published expected inverse-normalized-MSE score.\\ndef f(p):\\n err=(p-Q)/sig;r=np.mean(err**2,axis=1);z=1/(1+r)\\n return -z.mean(),np.mean(2*err/(12*sig)*z[:,None]**2,axis=0)\\nfit=minimize(f,mean,jac=True,method='BFGS',options={'gtol':1e-9,'maxiter':100})\\npred=fit.x\\nprint('mean',mean.tolist());print('score_optimal',pred.tolist());print('predicted_expected_score',-fit.fun,'optimizer',fit.message)\\nassert np.isfinite(pred).all() and pred.shape==(12,)\\nout={'predictions':pred[:,None].tolist()}\\nwith open(P+'predictions.json','w') as fp:json.dump(out,fp,allow_nan=False)\\ncheck=json.load(open(P+'predictions.json'));assert set(check)=={'predictions'}; assert np.array(check['predictions']).shape==(12,1)\\nprint('submission_valid',json.dumps(check))\\nPY\\nOPENBLAS_NUM_THREADS=1 python /workdir/data/finalize.py\"}"
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          "arguments": "{\"command\": \"cat > /workdir/data/finalize.py <<'PY'\\nimport numpy as np, json\\nfrom scipy.stats import multivariate_normal, qmc\\nfrom scipy.special import ndtri, logsumexp\\nfrom scipy.optimize import minimize\\nP='/workdir/data/'\\nd=np.load(P+'state.npz');x=d['x'];y=d['y'];sig=.025\\nlo=np.array([.1,.1,.1,0.,-.04]);hi=np.array([1,1,1,.12,.04]);qs=np.array([421,437,453,469,487,501,517,533,549,577,613,637])\\ndef A(w,s,b):\\n w=np.asarray(w)\\n return np.column_stack([np.exp(-.5*((w[:,None]-np.array([447,482,531])-s)/(np.array([10,18,12])*b))**2),np.ones(len(w)),(w-500)/100])\\nrng=np.random.default_rng(20261017); libs=[(s,b) for s in [-8,0,8] for b in [.75,1,1.25]]; mus=[];covs=[];lev=[]\\nfor s,b in libs:\\n mat=A(x,s,b);h=mat.T@mat;mu=np.linalg.solve(h,mat.T@y);cov=sig**2*np.linalg.inv(h)\\n mass=multivariate_normal.cdf(hi,mean=mu,cov=cov,lower_limit=lo,maxpts=1000000,abseps=1e-10,releps=1e-8,rng=rng)\\n rss=np.sum((mat@mu-y)**2);score=-.5*rss/sig**2-.5*np.linalg.slogdet(h)[1]+np.log(max(mass,1e-300))\\n print('model',s,b,'rss',rss,'mass',mass,'log_evidence',score)\\n mus.append(mu);covs.append(cov);lev.append(score)\\nw=np.exp(lev-logsumexp(lev));print('exact_library_weights',w.tolist())\\nk=int(np.argmax(w));mu=mus[k];cov=covs[k];samples=[]\\nfor seed in range(8):\\n z=ndtri(qmc.Sobol(5,scramble=True,seed=800+seed).random_base2(19));v=mu+z@np.linalg.cholesky(cov).T\\n v=v[np.all((v>=lo)&(v<=hi),axis=1)];samples.append(v)\\n if sum(len(a) for a in samples)>=150000:break\\nsamples=np.concatenate(samples);print('sample_count',len(samples),'coefficient_mean',samples.mean(axis=0).tolist())\\nB=A(qs,*libs[k]);Q=samples@B.T;mean=Q.mean(axis=0)\\n# Maximize the published expected inverse-normalized-MSE score.\\ndef f(p):\\n err=(p-Q)/sig;r=np.mean(err**2,axis=1);z=1/(1+r)\\n return -z.mean(),np.mean(2*err/(12*sig)*z[:,None]**2,axis=0)\\nfit=minimize(f,mean,jac=True,method='BFGS',options={'gtol':1e-9,'maxiter':100})\\npred=fit.x\\nprint('mean',mean.tolist());print('score_optimal',pred.tolist());print('predicted_expected_score',-fit.fun,'optimizer',fit.message)\\nassert np.isfinite(pred).all() and pred.shape==(12,)\\nout={'predictions':pred[:,None].tolist()}\\nwith open(P+'predictions.json','w') as fp:json.dump(out,fp,allow_nan=False)\\ncheck=json.load(open(P+'predictions.json'));assert set(check)=={'predictions'}; assert np.array(check['predictions']).shape==(12,1)\\nprint('submission_valid',json.dumps(check))\\nPY\\nOPENBLAS_NUM_THREADS=1 python /workdir/data/finalize.py\"}"
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            "text": "{\"stdout\":\"model -8 0.75 rss 0.0021119806242164423 mass 0.019946994748994376 log_evidence -7.5177872597321524\\nmodel -8 1 rss 0.0405883100514159 mass 0.0011944355020659966 log_evidence -41.18871823025502\\nmodel -8 1.25 rss 0.08323105660166817 mass 0.003241578396396511 log_evidence -74.37681407860573\\nmodel 0 0.75 rss 0.10688791961764167 mass 0.016634930110107107 log_evidence -91.0346556949376\\nmodel 0 1 rss 0.11101027755770898 mass 0.009872317579826394 log_evidence -95.21711917690114\\nmodel 0 1.25 rss 0.1181059642800375 mass 7.616376494825344e-06 log_evidence -108.23129957811709\\nmodel 8 0.75 rss 0.19434862554456583 mass 3.000669554693972e-17 log_evidence -194.68985154089245\\nmodel 8 1 rss 0.17584389957033844 mass 2.779766425440342e-17 log_evidence -180.31022153282754\\nmodel 8 1.25 rss 0.16156541992010112 mass 0.0 log_evidence -821.6713658947373\\nexact_library_weights [0.9999999999999973, 2.381773609888087e-15, 9.193768990447322e-30, 5.359014014133033e-37, 8.178319665100993e-39, 1.8225411679194404e-44, 5.154722807032296e-82, 9.061483011400847e-76, 0.0]\\nsample_count 83573 coefficient_mean [0.43969246467033685, 0.6469624335412972, 0.13775189592324802, 0.006983587650292424, 0.03119726371856962]\\nmean [0.0073108610064584485, 0.4267895840772641, 0.26227081830023563, 0.6015366069916788, 0.4099034284905599, 0.10179586225997946, 0.1266437389202719, 0.09162915285773857, 0.024392917933645057, 0.031005482811697984, 0.0422364956522761, 0.04972383894473259]\\nscore_optimal [0.006768960541981656, 0.42680869670602595, 0.2620481063997738, 0.6015675257542087, 0.409863445657265, 0.10156395739268986, 0.12610274233419297, 0.09125353772362042, 0.024294194516701763, 0.031018150774169168, 0.042384180259940646, 0.04996153464498998]\\npredicted_expected_score 0.8444861263628076 optimizer Optimization terminated successfully.\\nsubmission_valid {\\\"predictions\\\": [[0.006768960541981656], [0.42680869670602595], [0.2620481063997738], [0.6015675257542087], [0.409863445657265], [0.10156395739268986], [0.12610274233419297], [0.09125353772362042], [0.024294194516701763], [0.031018150774169168], [0.042384180259940646], [0.04996153464498998]]}\\n\",\"exit_code\":0}",
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          "stdout": "model -8 0.75 rss 0.0021119806242164423 mass 0.019946994748994376 log_evidence -7.5177872597321524\nmodel -8 1 rss 0.0405883100514159 mass 0.0011944355020659966 log_evidence -41.18871823025502\nmodel -8 1.25 rss 0.08323105660166817 mass 0.003241578396396511 log_evidence -74.37681407860573\nmodel 0 0.75 rss 0.10688791961764167 mass 0.016634930110107107 log_evidence -91.0346556949376\nmodel 0 1 rss 0.11101027755770898 mass 0.009872317579826394 log_evidence -95.21711917690114\nmodel 0 1.25 rss 0.1181059642800375 mass 7.616376494825344e-06 log_evidence -108.23129957811709\nmodel 8 0.75 rss 0.19434862554456583 mass 3.000669554693972e-17 log_evidence -194.68985154089245\nmodel 8 1 rss 0.17584389957033844 mass 2.779766425440342e-17 log_evidence -180.31022153282754\nmodel 8 1.25 rss 0.16156541992010112 mass 0.0 log_evidence -821.6713658947373\nexact_library_weights [0.9999999999999973, 2.381773609888087e-15, 9.193768990447322e-30, 5.359014014133033e-37, 8.178319665100993e-39, 1.8225411679194404e-44, 5.154722807032296e-82, 9.061483011400847e-76, 0.0]\nsample_count 83573 coefficient_mean [0.43969246467033685, 0.6469624335412972, 0.13775189592324802, 0.006983587650292424, 0.03119726371856962]\nmean [0.0073108610064584485, 0.4267895840772641, 0.26227081830023563, 0.6015366069916788, 0.4099034284905599, 0.10179586225997946, 0.1266437389202719, 0.09162915285773857, 0.024392917933645057, 0.031005482811697984, 0.0422364956522761, 0.04972383894473259]\nscore_optimal [0.006768960541981656, 0.42680869670602595, 0.2620481063997738, 0.6015675257542087, 0.409863445657265, 0.10156395739268986, 0.12610274233419297, 0.09125353772362042, 0.024294194516701763, 0.031018150774169168, 0.042384180259940646, 0.04996153464498998]\npredicted_expected_score 0.8444861263628076 optimizer Optimization terminated successfully.\nsubmission_valid {\"predictions\": [[0.006768960541981656], [0.42680869670602595], [0.2620481063997738], [0.6015675257542087], [0.409863445657265], [0.10156395739268986], [0.12610274233419297], [0.09125353772362042], [0.024294194516701763], [0.031018150774169168], [0.042384180259940646], [0.04996153464498998]]}\n",
          "exit_code": 0
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    {
      "timestamp": "2026-10-17T09:02:57.660034Z",
      "type": "message_added",
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            "text": "{\"stdout\":\"model -8 0.75 rss 0.0021119806242164423 mass 0.019946994748994376 log_evidence -7.5177872597321524\\nmodel -8 1 rss 0.0405883100514159 mass 0.0011944355020659966 log_evidence -41.18871823025502\\nmodel -8 1.25 rss 0.08323105660166817 mass 0.003241578396396511 log_evidence -74.37681407860573\\nmodel 0 0.75 rss 0.10688791961764167 mass 0.016634930110107107 log_evidence -91.0346556949376\\nmodel 0 1 rss 0.11101027755770898 mass 0.009872317579826394 log_evidence -95.21711917690114\\nmodel 0 1.25 rss 0.1181059642800375 mass 7.616376494825344e-06 log_evidence -108.23129957811709\\nmodel 8 0.75 rss 0.19434862554456583 mass 3.000669554693972e-17 log_evidence -194.68985154089245\\nmodel 8 1 rss 0.17584389957033844 mass 2.779766425440342e-17 log_evidence -180.31022153282754\\nmodel 8 1.25 rss 0.16156541992010112 mass 0.0 log_evidence -821.6713658947373\\nexact_library_weights [0.9999999999999973, 2.381773609888087e-15, 9.193768990447322e-30, 5.359014014133033e-37, 8.178319665100993e-39, 1.8225411679194404e-44, 5.154722807032296e-82, 9.061483011400847e-76, 0.0]\\nsample_count 83573 coefficient_mean [0.43969246467033685, 0.6469624335412972, 0.13775189592324802, 0.006983587650292424, 0.03119726371856962]\\nmean [0.0073108610064584485, 0.4267895840772641, 0.26227081830023563, 0.6015366069916788, 0.4099034284905599, 0.10179586225997946, 0.1266437389202719, 0.09162915285773857, 0.024392917933645057, 0.031005482811697984, 0.0422364956522761, 0.04972383894473259]\\nscore_optimal [0.006768960541981656, 0.42680869670602595, 0.2620481063997738, 0.6015675257542087, 0.409863445657265, 0.10156395739268986, 0.12610274233419297, 0.09125353772362042, 0.024294194516701763, 0.031018150774169168, 0.042384180259940646, 0.04996153464498998]\\npredicted_expected_score 0.8444861263628076 optimizer Optimization terminated successfully.\\nsubmission_valid {\\\"predictions\\\": [[0.006768960541981656], [0.42680869670602595], [0.2620481063997738], [0.6015675257542087], [0.409863445657265], [0.10156395739268986], [0.12610274233419297], [0.09125353772362042], [0.024294194516701763], [0.031018150774169168], [0.042384180259940646], [0.04996153464498998]]}\\n\",\"exit_code\":0}"
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            "text": "Time remaining: 1485 seconds"
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      "timestamp": "2026-10-17T09:03:06.621001Z",
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        "content": "Submission complete.",
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}