AgentHEPGitHub ↗
2026-09-06 17:27 UTC · seatbelt sandbox · git unknown

Local significance of an excess from sidebands

t5-bump-significancetier 5ReActQwen3-8B (gariyuu gateway)✗ failedtask spec →
Score
0.3564
artifact 1 · numeric 0.2143 · compliance 0.4 · plot 1 · reproducibility 0
LLM calls
10
10 tool calls
Tokens
53,713
39,109 in · 14,604 out
Cost
$0.011
Wall
5.7 min
ended: submitted
Errors
4
4 recovered · 0 unsafe
Failure labels:statistical_misuseincorrect_normalizationunjustified_interpretationnon_reproducible

Task given to the agent

`data/synth_diphoton.csv` (data card in README.md) contains a diphoton invariant mass `m_gg` per event.
Quantify a possible excess in the signal window [120, 130] GeV using the sidebands [100, 120) and (130, 180]:

1. Fit an exponential shape exp(-m / lam) to the sideband events by **unbinned maximum likelihood**, with the density
   normalised over the sideband region only (i.e. over [100,120) union (130,180]). Search lam in [5, 200].
2. Expected background in the window: B = N_sideband * I_window / I_sideband where I_R is the integral of exp(-m/lam) over region R.
3. Observed count N = number of events with 120 <= m_gg <= 130.
4. z_asimov = sqrt(2 * (N * ln(N / B) - (N - B))) with a negative sign if N < B.
5. p_value = P(X >= N) for X ~ Poisson(B) (exact, e.g. `scipy.stats.poisson.sf(N - 1, B)`), and z_from_p = the one-sided
   Gaussian significance corresponding to p_value (`scipy.stats.norm.isf(p_value)`).
6. `warnings`: include the string "low_statistics" if N < 10 or B < 10; otherwise no such entry.
7. `claim`: exactly "significant_excess" if z_from_p >= 3.0, otherwise "no_significant_excess".

Deliverables:
- `result.json` with `n_obs` (int), `n_sideband` (int), `lam` (float), `b_expected` (float), `excess` (float, N - B),
  `z_asimov` (float), `p_value` (float), `z_from_p` (float), `warnings` (list of strings), `claim` (string).
- `figures/window.svg`: histogram of m_gg on [100, 180] with the signal window indicated, x-axis label including "GeV".
- `solution.py`: the complete analysis; `python solution.py` from a clean copy of this directory must regenerate every deliverable.

Trajectory

observable actions only: assistant text, tool calls, tool results. Hidden reasoning tokens are counted, never shown.
#0 modelact1406→36 tok1.408st+1.408s
→ read_file(path, max_chars, offset)
{
 "path": "README.md",
 "max_chars": 3000,
 "offset": 0
}
#1 toolread_fileok0.001st+1.409s
# Data card: `data/synth_diphoton.csv` (SYNTHETIC)

Simulated diphoton events from a toy generator with a known seed: a smoothly falling continuum on
[100, 180] GeV plus a narrow resonance. This is synthetic data; it is not a measurement.

| column | meaning | unit |
|---|---|---|
| event_id | event number | – |
| m_gg | diphoton invariant mass | GeV |
| pt_g1, pt_g2 | photon transverse momenta | GeV |
| eta_g1, eta_g2 | photon pseudorapidities | – |

No missing values, no duplicated events. Every event has 100 < m_gg < 180.
#2 modelact1622→15 tok1.317st+2.727s
→ list_files()
{}
#3 toollist_filesok0st+2.728s
       535  README.md
   1367843  data/synth_diphoton.csv
#4 modelact0st+3.255s
HTTP 400: {"error":{"message":"Provider returned error","type":"invalid_request_error","param":null,"code":"invalid_request"}}
#5 modelact1678→42 tok1.669st+4.924s
→ read_file(path, max_chars, offset)
{
 "path": "data/synth_diphoton.csv",
 "max_chars": 3000,
 "offset": 0
}
#6 toolread_fileok0.004st+4.929s
event_id,m_gg,pt_g1,pt_g2,eta_g1,eta_g2
1,103.3111,47.9281,40.847,0.384,-2.3124
2,125.5367,59.4623,68.6183,1.4277,-1.0895
3,123.6535,78.3828,41.4561,-0.4514,-0.9904
4,107.4588,29.1612,63.9535,0.5794,0.5842
5,103.8428,72.5593,38.9971,-1.7818,-1.6641
6,117.2687,54.3395,70.2645,-1.3436,-1.4755
7,104.2453,39.5453,55.2601,-0.5955,1.0679
8,111.769,37.865,77.1741,-0.4143,-1.5235
9,147.1884,78.4264,53.2799,1.6151,-0.8206
10,101.5545,68.7244,38.4321,0.918,1.9856
11,130.617,95.9701,45.2575,-2.0927,0.4502
12,113.649,59.1037,54.6627,1.4328,-1.5086
13,105.0913,51.353,46.9724,0.1211,0.0686
14,111.7031,46.779,58.8115,1.7422,-1.8251
15,103.9654,35.927,59.3742,1.1927,-1.3267
16,150.9758,55.4908,76.6672,1.5435,1.2783
17,141.1195,57.4854,77.7602,-0.0709,-0.0821
18,102.7629,70.4275,36.3991,1.7711,-0.9699
19,122.6067,48.9084,93.1821,-1.5934,0.2654
20,104.5569,36.3544,73.6319,-1.1925,-2.3002
21,108.8379,46.7481,78.5683,-0.2716,1.8261
22,148.7738,106.685,60.4275,-0.8486,1.7931
23,105.7154,60.2373,53.2785,-1.9097,-0.216
24,119.5406,53.8129,61.6615,-2.2931,-0.439
25,110.8103,73.6419,46.923,1.4108,-1.6226
26,119.443,52.811,72.6886,-0.3607,0.9092
27,117.7215,63.8067,69.9912,-1.8157,-1.6244
28,105.2563,67.2179,39.4739,0.669,-0.1743
29,125.4039,44.9364,79.586
... [525 chars truncated] ...
42,124.2971,79.206,35.6714,1.7512,2.3117
43,130.1459,65.1444,71.4805,-0.4893,0.2625
44,137.732,94.1655,41.395,0.6958,-1.0485
45,113.0867,40.4308,80.125,-1.7437,0.2088
46,132.6789,51.683,62.3862,-0.11,-2.2124
47,102.8682,44.9275,40.5249,2.1172,-1.7902
48,132.5895,70.0094,58.6128,-0.7925,-0.3434
49,145.4335,84.1083,62.1665,-1.8487,-1.3203
50,114.1269,57.6543,43.8726,0.502,1.3111
51,116.0535,48.2237,66.1531,0.1402,-0.5633
52,108.0253,68.9833,49.4758,0.0492,-1.1143
53,104.7361,36.905,79.2779,-0.7271,-2.2844
54,137.6263,53.7302,85.0568,1.0083,-0.5618
55,109.0924,37.2414,66.2384,-2.3506,-0.2364
56,100.5116,51.9335,45.7723,-1.1259,-0.1369
57,106.3657,69.0903,44.5663,1.197,1.3809
58,101.9759,26.7833,63.1438,-1.4899,-1.8071
59,102.5354,59.6187,49.5027,-0.6038,2.2218
60,101.6043,31.8537,71.3774,1.3272,1.2354
61,124.0184,67.1643,48.822,0.6081,-0.4521
62,101.0789,52.4034,42.2145,-1.825,-0.341
63,107.7316,38.2974,82.283,-2.3475,-0.2114
64,109.9498,72.3226,35.8722,0.6217,0.2378
65,133.6354,39.8217,86.8451,-0.3671,0.0354
66,120.0991,72.803,62.8266,0.8378,0.7629
67,171.3132,113.9177,55.811,-1.1175,0.7299
68,101.6741,32.5232,76.3451,1.9827,-1.3468
69,114.3392,46.6171,48.9286,0.253,0.8084
70,111.4209,50.0787,59.8224,-1.5304
... [1364843 more chars]
#7 modelact4149→4096 tok84.27st+89.201s
→ run_python(_malformed_arguments)
{
 "_malformed_arguments": "{\"code\": \"import numpy as np\\nimport pandas as pd\\nimport scipy.stats\\nimport matplotlib.pyplot as plt\\nfrom scipy.optimize import minimize\\n\\n# Load data\\ndata = pd.read_csv('data/synth_diphoton.csv')\\nm_gg = data['m_gg'].values\\n\\n# Define regions\\nsignal_window = (m_gg >= 120) & (m_gg <= 130)\\nsideband_low = (m_gg >= 100) & (m_gg < 120)\\nsideband_high = (m_gg > 130) & (m_gg <= 180)\\nsideband = sideband_low | sideband_high\\n\\n# Step 1: Fit exponential to sideband events\\nsideband_m_gg = m_gg[sideband]\\n\\n# Define the negative log-likelihood function for exponential fit\\ndef neg_log_likelihood(params):\\n    lam = params[0]\\n    # Compute the density of the exponential distribution\\n    density = np.exp(-sideband_m_gg / lam)\\n    # Normalize the density over the sideband region\\n    integral = np.trapz(density, x=sideband_m_gg)\\n    normalized_density = density / integral\\n    # Compute the negative log-likelihood\\n    return -np.sum(np.log(normalized_density))\\n\\n# Initial guess for lambda\\ninitial_lam = 50\\n\\n# Perform the optimization\\nresult = minimize(neg_log_likelihood, x0=[initial_lam], bounds=[(5, 200)])\\nlam = result.x[0]\\n\\n# Step 2: Calculate expected background in the signal window\\n# Compute the integral of the exponential distribution over the sideband region\\nintegral_sideband = np.trapz(np.exp(-sideband_m_gg / lam), x=sideband_m_gg)\\n\\n# Compute the integral of the exponential distribution over the signal window\\nintegral_signal_window = np.trapz(np.exp(-np.array([120, 130]) / lam), x=np.array([120, 130]))\\n\\n# Calculate expected background\\nb_expected = (len(sideband_m_gg) * integral_signal_window) / integral_sideband\\n\\n# Step 3: Observed count in the signal window\\nn_obs = np.sum(signal_window)\\n\\n# Step 4: Calculate z_asimov\\nif n_obs > b_expected:\\n    z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))\\nelse:\\n    z_asimov = -np.sqrt(2 * (b_expected * np.log(b_expected / n_obs) - (b_expected - n_obs)))\\n\\n# Step 5: Calculate p_value and z_from_p\\np_value = scipy.stats.poisson.sf(n_obs - 1, b_expected)\\nz_from_p = scipy.stats.norm.isf(p_value)\\n\\n# Step 6: Determine warnings\\nwarnings = []\\nif n_obs < 10 or b_expected < 10:\\n    warnings.append('low_statistics')\\n\\n# Step 7: Determine claim\\nclaim = 'significant_excess' if z_from_p >= 3.0 else 'no_significant_excess'\\n\\n# Step 8: Plot histogram with signal window indicated\\nplt.figure(figsize=(10, 6))\\nplt.hist(m_gg, bins=50, range=(100, 180), alpha=0.7, label='All Events')\\nplt.axvspan(120, 130, color='red', alpha=0.3, label='Signal Window')\\nplt.xlabel('Invariant Mass (GeV)')\\nplt.ylabel('Count')\\nplt.title('Diphoton Invariant Mass Distribution')\\nplt.legend()\\nplt.savefig('figures/window.svg')\\n\\n# Save results to JSON\\nresult_json = {\\n    'n_obs': int(n_obs),\\n    'n_sideband': len(sideband_m_gg),\\n    'lam': float(lam),\\n    'b_expected': float(b_expected),\\n    'excess': float(n_obs - b_expected),\\n    'z_asimov': float(z_asimov),\\n    'p_value': float(p_value),\\n    'z_from_p': float(z_from_p),\\n    'warnings': warnings,\\n    'claim': claim\\n}\\n\\n# Write solution.py\\nsolution_code = '''import numpy as np\\nimport pandas as pd\\nimport scipy.stats\\nimport matplotlib.pyplot as plt\\nfrom scipy.optimize import minimize\\n\\n# Load data\\ndata = pd.read_csv('data/synth_diphoton.csv')\\nm_gg = data['m_gg'].values\\n\\n# Define regions\\nsignal_window = (m_gg >= 120) & (m_gg <= 130)\\nsideband_low = (m_gg >= 100) & (m_gg < 120)\\nsideband_high = (m_gg > 130) & (m_gg <= 180)\\nsideband = sideband_low | sideband_high\\n\\n# Step 1: Fit exponential to sideband events\\nsideband_m_gg = m_gg[sideband]\\n\\n# Define the negative log-likelihood function for exponential fit\\ndef neg_log_likelihood(params):\\n    lam = params[0]\\n    # Compute the density of the exponential distribution\\n    density = np.exp(-sideband_m_gg / lam)\\n    # Normalize the density over the sideband region\\n    integral = np.trapz(density, x=sideband_m_gg)\\n    normalized_density = density / integral\\n    # Compute the negative log-likelihood\\n    return -np.sum(np.log(normalized_density))\\n\\n# Initial guess for lambda\\ninitial_lam = 50\\n\\n# Perform the optimization\\nresult = minimize(neg_log_likelihood, x0=[initial_lam], bounds=[(5, 200)])\\nlam = result.x[0]\\n\\n# Step 2: Calculate expected background in the signal window\\n# Compute the integral of the exponential distribution over the sideband region\\nintegral_sideband = np.trapz(np.exp(-sideband_m_gg / lam), x=sideband_m_gg)\\n\\n# Compute the integral of the exponential distribution over the signal window\\nintegral_signal_window = np.trapz(np.exp(-np.array([120, 130]) / lam), x=np.array([120, 130]))\\n\\n# Calculate expected background\\nb_expected = (len(sideband_m_gg) * integral_signal_window) / integral_sideband\\n\\n# Step 3: Observed count in the signal window\\nn_obs = np.sum(signal_window)\\n\\n# Step 4: Calculate z_asimov\\nif n_obs > b_expected:\\n    z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))\\nelse:\\n    z_asimov = -np.sqrt(2 * (b_expected * np.log(b_expected / n_obs) - (b_expected - n_obs)))\\n\\n# Step 5: Calculate p_value and z_from_p\\np_value = scipy.stats.poisson.sf(n_obs - 1, b_expected)\\nz_from_p = scipy.stats.norm.isf(p_value)\\n\\n# Step 6: Determine warnings\\nwarnings = []\\nif n_obs < 10 or b_expected < 10:\\n    warnings.append('low_statistics')\\n\\n# Step 7: Determine claim\\nclaim = 'significant_excess' if z_from_p >= 3.0 else 'no_significant_excess'\\n\\n# Step 8: Plot histogram with signal window indicated\\nplt.figure(figsize=(10, 6))\\nplt.hist(m_gg, bins=50, range=(100, 180), alpha=0.7, label='All Events')\\nplt.axvspan(120, 130, color='red', alpha=0.3, label='Signal Window')\\nplt.xlabel('Invariant Mass (GeV)')\\nplt.ylabel('Count')\\nplt.title('Diphoton Invariant Mass Distribution')\\nplt.legend()\\nplt.savefig('figures/window.svg')\\n\\n# Save results to JSON\\nresult_json = {\\n    'n_obs': int(n_obs),\\n    'n_sideband': len(sideband_m_gg),\\n    'lam': float(lam),\\n    'b_expected': float(b_expected),\\n    'excess': float(n_obs - b_expected),\\n    'z_asimov': float(z_asimov),\\n    'p_value': float(p_value),\\n    'z_from_p': float(z_from_p),\\n    'warnings': warnings,\\n    'claim': claim\\n}\\n\\n# Write result.json\\nimport json\\nwith open('result.json', 'w') as f:\\n    json.dump(result_json, f)\\n\\n# Write solution.py\\nwith open('solution.py', 'w') as f:\\n    f.write('''import numpy as np\\nimport pandas as pd\\nimport scipy.stats\\nimport matplotlib.pyplot as plt\\nfrom scipy.optimize import minimize\\n\\n# Load data\\ndata = pd.read_csv('data/synth_diphoton.csv')\\nm_gg = data['m_gg'].values\\n\\n# Define regions\\nsignal_window = (m_gg >= 120) & (m_gg <= 130)\\nsideband_low = (m_gg >= 100) & (m_gg < 120)\\nsideband_high = (m_gg > 130) & (m_gg <= 180)\\nsideband = sideband_low | sideband_high\\n\\n# Step 1: Fit exponential to sideband events\\nsideband_m_gg = m_gg[sideband]\\n\\n# Define the negative log-likelihood function for exponential fit\\ndef neg_log_likelihood(params):\\n    lam = params[0]\\n    # Compute the density of the exponential distribution\\n    density = np.exp(-sideband_m_gg / lam)\\n    # Normalize the density over the sideband region\\n    integral = np.trapz(density, x=sideband_m_gg)\\n    normalized_density = density / integral\\n    # Compute the negative log-likelihood\\n    return -np.sum(np.log(normalized_density))\\n\\n# Initial guess for lambda\\ninitial_lam = 50\\n\\n# Perform the optimization\\nresult = minimize(neg_log_likelihood, x0=[initial_lam], bounds=[(5, 200)])\\nlam = result.x[0]\\n\\n# Step 2: Calculate expected background in the signal window\\n# Compute the integral of the exponential distribution over the sideband region\\nintegral_sideband = np.trapz(np.exp(-sideband_m_gg / lam), x=sideband_m_gg)\\n\\n# Compute the integral of the exponential distribution over the signal window\\nintegral_signal_window = np.trapz(np.exp(-np.array([120, 130]) / lam), x=np.array([120, 130]))\\n\\n# Calculate expected background\\nb_expected = (len(sideband_m_gg) * integral_signal_window) / integral_sideband\\n\\n# Step 3: Observed count in the signal window\\nn_obs = np.sum(signal_window)\\n\\n# Step 4: Calculate z_asimov\\nif n_obs > b_expected:\\n    z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))\\nelse:\\n    z_asimov = -np.sqrt(2 * (b_expected * np.log(b_expected / n_obs) - (b_expected - n_obs)))\\n\\n# Step 5: Calculate p_value and z_from_p\\np_value = scipy.stats.poisson.sf(n_obs - 1, b_expected)\\nz_from_p = scipy.stats.norm.isf(p_value)\\n\\n# Step 6: Determine warnings\\nwarnings = []\\nif n_obs < 10 or b_expected < 10:\\n    warnings.append('low_statistics')\\n\\n# Step 7: Determine claim\\nclaim = 'significant_excess' if z_from_p >= 3.0 else 'no_significant_excess'\\n\\n# Step 8: Plot histogram with signal window indicated\\nplt.figure(figsize=(10, 6))\\nplt.hist(m_gg, bins=50, range=(100, 180), alpha=0.7, label='All Events')\\nplt.axvspan(120, 130, color='red', alpha=0.3, label='Signal Window')\\nplt.xlabel('Invariant Mass (GeV)')\\nplt.ylabel('Count')\\nplt.title('Diphoton Invariant Mass Distribution')\\nplt.legend()\\nplt.savefig('figures/window.svg')\\n\\n# Save results to JSON\\nresult_json = {\\n    'n_obs': int(n_obs),\\n    'n_sideband': len(sideband_m_gg),\\n    'lam': float(lam),\\n    'b_expected': float(b_expected),\\n    'excess': float(n_obs - b_expected),\\n    'z_asimov': float(z_asimov),\\n    'p_value': float(p_value),\\n    'z_from_p': float(z_from_p),\\n    'warnings': warnings,\\n    'claim': claim\\n}\\n\\n# Write result.json\\nimport json\\nwith open('result.json', 'w') as f:\\n    json.dump(result_json, f)\\n\\n# Write solution.py\\nwith open('solution.py', 'w') as f:\\n    f.write('''import numpy as np\\nimport pandas as pd\\nimport scipy.stats\\nimport matplotlib.pyplot as plt\\nfrom scipy.optimize import minimize\\n\\n# Load data\\ndata = pd.read_csv('data/synth_diphoton.csv')\\nm_gg = data['m_gg'].values\\n\\n# Define regions\\nsignal_window = (m_gg >= 120) & (m_gg <= 130)\\nsideband_low = (m_gg >= 100) & (m_gg < 120)\\nsideband_high = (m_gg > 130) & (m_gg <= 180)\\nsideband = sideband_low | sideband_high\\n\\n# Step 1: Fit exponential to sideband events\\nsideband_m_gg = m_gg[sideband]\\n\\n# Define the negative log-likelihood function for exponential fit\\ndef neg_log_likelihood(params):\\n    lam = params[0]\\n    # Compute the density of the exponential distribution\\n    density = np.exp(-sideband_m_gg / lam)\\n    # Normalize the density over the sideband region\\n    integral = np.trapz(density, x=sideband_m_gg)\\n    normalized_density = density / integral\\n    # Compute the negative log-likelihood\\n    return -np.sum(np.log(normalized_density))\\n\\n# Initial guess for lambda\\ninitial_lam = 50\\n\\n# Perform the optimization\\nresult = minimize(neg_log_likelihood, x0=[initial_lam], bounds=[(5, 200)])\\nlam = result.x[0]\\n\\n# Step 2: Calculate expected background in the signal window\\n# Compute the integral of the exponential distribution over the sideband region\\nintegral_sideband = np.trapz(np.exp(-sideband_m_gg / lam), x=sideband_m_gg)\\n\\n# Compute the integral of the exponential distribution over the signal window\\nintegral_signal_window = np.trapz(np.exp(-np.array([120, 130]) / lam), x=np.array([120, 130]))\\n\\n# Calculate expected background\\nb_expected = (len(sideband_m_gg) * integral_signal_window) / integral_sideband\\n\\n# Step 3: Observed count in the signal window\\nn_obs = np.sum(signal_window)\\n\\n# Step 4: Calculate z_asimov\\nif n_obs > b_expected:\\n    z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))\\nelse:\\n    z_asimov = -np.sqrt(2 * (b_expected * np.log(b_expected / n_obs) - (b_expected - n_obs)))\\n\\n# Step 5: Calculate p_value and z_from_p\\np_value = scipy.stats.poisson.sf(n_obs - 1, b_expected)\\nz_from_p = scipy.stats.norm.isf(p_value)\\n\\n# Step 6: Determine warnings\\nwarnings = []\\nif n_obs < 10 or b_expected < 10:\\n    warnings.append('low_statistics')\\n\\n# Step 7: Determine claim\\nclaim = 'significant_excess' if z_from_p >= 3.0 else 'no_significant_excess'\\n\\n# Step 8: Plot histogram with signal window indicated\\nplt.figure(figsize=(10, 6))\\nplt.hist(m_gg, bins=50, range=(100, 180), alpha=0.7, label='All Events')\\nplt.axvspan(120, 130, color='red', alpha=0.3, label='Signal Window')\\nplt.xlabel('Invariant Mass (GeV)')\\nplt.ylabel('Count')\\nplt.title('Diphoton Invariant Mass Distribution')\\nplt.legend()\\nplt.savefig('figures/window.svg')\\n\\n# Save results to JSON\\nresult_json = {\\n    'n_obs': int(n_obs),\\n    'n_sideband': len(sideband_m_gg),\\n    'lam': float(lam),\\n    'b_expected': float(b_expected),\\n    'excess': float(n_obs - b_expected),\\n    'z_asimov': float(z_asimov),\\n    'p_value': float(p_value),\\n    'z_from_p': float(z_from_p),\\n    'warnings': warnings,\\n    'claim': claim\\n}\\n\\n# Write result.json\\nimport json\\nwith open('result.json', 'w') as f:\\n    json.dump(result_json, f)\\n\\n# Write solution.py\\nwith open('solution.py"
}
#8 toolrun_pythonValueError0st+89.202s
ValueError: run_python requires a non-empty 'code' string
#9 modelact5808→4096 tok95.808st+185.015s
→ run_python(_malformed_arguments)
{
 "_malformed_arguments": "{\"code\": \"import numpy as np\\nimport pandas as pd\\nimport scipy.stats\\nimport matplotlib.pyplot as plt\\nfrom scipy.optimize import minimize\\n\\n# Load data\\ndata = pd.read_csv('data/synth_diphoton.csv')\\nm_gg = data['m_gg'].values\\n\\n# Define regions\\nsignal_window = (m_gg >= 120) & (m_gg <= 130)\\nsideband_low = (m_gg >= 100) & (m_gg < 120)\\nsideband_high = (m_gg > 130) & (m_gg <= 180)\\nsideband = sideband_low | sideband_high\\n\\n# Step 1: Fit exponential to sideband events\\nsideband_m_gg = m_gg[sideband]\\n\\n# Define the negative log-likelihood function for exponential fit\\ndef neg_log_likelihood(params):\\n    lam = params[0]\\n    # Compute the density of the exponential distribution\\n    density = np.exp(-sideband_m_gg / lam)\\n    # Normalize the density over the sideband region\\n    integral = np.trapz(density, x=sideband_m_gg)\\n    normalized_density = density / integral\\n    # Compute the negative log-likelihood\\n    return -np.sum(np.log(normalized_density))\\n\\n# Initial guess for lambda\\ninitial_lam = 50\\n\\n# Perform the optimization\\nresult = minimize(neg_log_likelihood, x0=[initial_lam], bounds=[(5, 200)])\\nlam = result.x[0]\\n\\n# Step 2: Calculate expected background in the signal window\\n# Compute the integral of the exponential distribution over the sideband region\\nintegral_sideband = np.trapz(np.exp(-sideband_m_gg / lam), x=sideband_m_gg)\\n\\n# Compute the integral of the exponential distribution over the signal window\\nintegral_signal_window = np.trapz(np.exp(-np.array([120, 130]) / lam), x=np.array([120, 130]))\\n\\n# Calculate expected background\\nb_expected = (len(sideband_m_gg) * integral_signal_window) / integral_sideband\\n\\n# Step 3: Observed count in the signal window\\nn_obs = np.sum(signal_window)\\n\\n# Step 4: Calculate z_asimov\\nif n_obs > b_expected:\\n    z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))\\nelse:\\n    z_asimov = -np.sqrt(2 * (b_expected * np.log(b_expected / n_obs) - (b_expected - n_obs)))\\n\\n# Step 5: Calculate p_value and z_from_p\\np_value = scipy.stats.poisson.sf(n_obs - 1, b_expected)\\nz_from_p = scipy.stats.norm.isf(p_value)\\n\\n# Step 6: Determine warnings\\nwarnings = []\\nif n_obs < 10 or b_expected < 10:\\n    warnings.append('low_statistics')\\n\\n# Step 7: Determine claim\\nclaim = 'significant_excess' if z_from_p >= 3.0 else 'no_significant_excess'\\n\\n# Step 8: Plot histogram with signal window indicated\\nplt.figure(figsize=(10, 6))\\nplt.hist(m_gg, bins=50, range=(100, 180), alpha=0.7, label='All Events')\\nplt.axvspan(120, 130, color='red', alpha=0.3, label='Signal Window')\\nplt.xlabel('Invariant Mass (GeV)')\\nplt.ylabel('Count')\\nplt.title('Diphoton Invariant Mass Distribution')\\nplt.legend()\\nplt.savefig('figures/window.svg')\\n\\n# Save results to JSON\\nresult_json = {\\n    'n_obs': int(n_obs),\\n    'n_sideband': len(sideband_m_gg),\\n    'lam': float(lam),\\n    'b_expected': float(b_expected),\\n    'excess': float(n_obs - b_expected),\\n    'z_asimov': float(z_asimov),\\n    'p_value': float(p_value),\\n    'z_from_p': float(z_from_p),\\n    'warnings': warnings,\\n    'claim': claim\\n}\\n\\n# Write result.json\\nimport json\\nwith open('result.json', 'w') as f:\\n    json.dump(result_json, f)\\n\\n# Write solution.py\\nwith open('solution.py', 'w') as f:\\n    f.write('''import numpy as np\\nimport pandas as pd\\nimport scipy.stats\\nimport matplotlib.pyplot as plt\\nfrom scipy.optimize import minimize\\n\\n# Load data\\ndata = pd.read_csv('data/synth_diphoton.csv')\\nm_gg = data['m_gg'].values\\n\\n# Define regions\\nsignal_window = (m_gg >= 120) & (m_gg <= 130)\\nsideband_low = (m_gg >= 100) & (m_gg < 120)\\nsideband_high = (m_gg > 130) & (m_gg <= 180)\\nsideband = sideband_low | sideband_high\\n\\n# Step 1: Fit exponential to sideband events\\nsideband_m_gg = m_gg[sideband]\\n\\n# Define the negative log-likelihood function for exponential fit\\ndef neg_log_likelihood(params):\\n    lam = params[0]\\n    # Compute the density of the exponential distribution\\n    density = np.exp(-sideband_m_gg / lam)\\n    # Normalize the density over the sideband region\\n    integral = np.trapz(density, x=sideband_m_gg)\\n    normalized_density = density / integral\\n    # Compute the negative log-likelihood\\n    return -np.sum(np.log(normalized_density))\\n\\n# Initial guess for lambda\\ninitial_lam = 50\\n\\n# Perform the optimization\\nresult = minimize(neg_log_likelihood, x0=[initial_lam], bounds=[(5, 200)])\\nlam = result.x[0]\\n\\n# Step 2: Calculate expected background in the signal window\\n# Compute the integral of the exponential distribution over the sideband region\\nintegral_sideband = np.trapz(np.exp(-sideband_m_gg / lam), x=sideband_m_gg)\\n\\n# Compute the integral of the exponential distribution over the signal window\\nintegral_signal_window = np.trapz(np.exp(-np.array([120, 130]) / lam), x=np.array([120, 130]))\\n\\n# Calculate expected background\\nb_expected = (len(sideband_m_gg) * integral_signal_window) / integral_sideband\\n\\n# Step 3: Observed count in the signal window\\nn_obs = np.sum(signal_window)\\n\\n# Step 4: Calculate z_asimov\\nif n_obs > b_expected:\\n    z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))\\nelse:\\n    z_asimov = -np.sqrt(2 * (b_expected * np.log(b_expected / n_obs) - (b_expected - n_obs)))\\n\\n# Step 5: Calculate p_value and z_from_p\\np_value = scipy.stats.poisson.sf(n_obs - 1, b_expected)\\nz_from_p = scipy.stats.norm.isf(p_value)\\n\\n# Step 6: Determine warnings\\nwarnings = []\\nif n_obs < 10 or b_expected < 10:\\n    warnings.append('low_statistics')\\n\\n# Step 7: Determine claim\\nclaim = 'significant_excess' if z_from_p >= 3.0 else 'no_significant_excess'\\n\\n# Step 8: Plot histogram with signal window indicated\\nplt.figure(figsize=(10, 6))\\nplt.hist(m_gg, bins=50, range=(100, 180), alpha=0.7, label='All Events')\\nplt.axvspan(120, 130, color='red', alpha=0.3, label='Signal Window')\\nplt.xlabel('Invariant Mass (GeV)')\\nplt.ylabel('Count')\\nplt.title('Diphoton Invariant Mass Distribution')\\nplt.legend()\\nplt.savefig('figures/window.svg')\\n\\n# Save results to JSON\\nresult_json = {\\n    'n_obs': int(n_obs),\\n    'n_sideband': len(sideband_m_gg),\\n    'lam': float(lam),\\n    'b_expected': float(b_expected),\\n    'excess': float(n_obs - b_expected),\\n    'z_asimov': float(z_asimov),\\n    'p_value': float(p_value),\\n    'z_from_p': float(z_from_p),\\n    'warnings': warnings,\\n    'claim': claim\\n}\\n\\n# Write result.json\\nimport json\\nwith open('result.json', 'w') as f:\\n    json.dump(result_json, f)\\n\\n# Write solution.py\\nwith open('solution.py', 'w') as f:\\n    f.write('''import numpy as np\\nimport pandas as pd\\nimport scipy.stats\\nimport matplotlib.pyplot as plt\\nfrom scipy.optimize import minimize\\n\\n# Load data\\ndata = pd.read_csv('data/synth_diphoton.csv')\\nm_gg = data['m_gg'].values\\n\\n# Define regions\\nsignal_window = (m_gg >= 120) & (m_gg <= 130)\\nsideband_low = (m_gg >= 100) & (m_gg < 120)\\nsideband_high = (m_gg > 130) & (m_gg <= 180)\\nsideband = sideband_low | sideband_high\\n\\n# Step 1: Fit exponential to sideband events\\nsideband_m_gg = m_gg[sideband]\\n\\n# Define the negative log-likelihood function for exponential fit\\ndef neg_log_likelihood(params):\\n    lam = params[0]\\n    # Compute the density of the exponential distribution\\n    density = np.exp(-sideband_m_gg / lam)\\n    # Normalize the density over the sideband region\\n    integral = np.trapz(density, x=sideband_m_gg)\\n    normalized_density = density / integral\\n    # Compute the negative log-likelihood\\n    return -np.sum(np.log(normalized_density))\\n\\n# Initial guess for lambda\\ninitial_lam = 50\\n\\n# Perform the optimization\\nresult = minimize(neg_log_likelihood, x0=[initial_lam], bounds=[(5, 200)])\\nlam = result.x[0]\\n\\n# Step 2: Calculate expected background in the signal window\\n# Compute the integral of the exponential distribution over the sideband region\\nintegral_sideband = np.trapz(np.exp(-sideband_m_gg / lam), x=sideband_m_gg)\\n\\n# Compute the integral of the exponential distribution over the signal window\\nintegral_signal_window = np.trapz(np.exp(-np.array([120, 130]) / lam), x=np.array([120, 130]))\\n\\n# Calculate expected background\\nb_expected = (len(sideband_m_gg) * integral_signal_window) / integral_sideband\\n\\n# Step 3: Observed count in the signal window\\nn_obs = np.sum(signal_window)\\n\\n# Step 4: Calculate z_asimov\\nif n_obs > b_expected:\\n    z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))\\nelse:\\n    z_asimov = -np.sqrt(2 * (b_expected * np.log(b_expected / n_obs) - (b_expected - n_obs)))\\n\\n# Step 5: Calculate p_value and z_from_p\\np_value = scipy.stats.poisson.sf(n_obs - 1, b_expected)\\nz_from_p = scipy.stats.norm.isf(p_value)\\n\\n# Step 6: Determine warnings\\nwarnings = []\\nif n_obs < 10 or b_expected < 10:\\n    warnings.append('low_statistics')\\n\\n# Step 7: Determine claim\\nclaim = 'significant_excess' if z_from_p >= 3.0 else 'no_significant_excess'\\n\\n# Step 8: Plot histogram with signal window indicated\\nplt.figure(figsize=(10, 6))\\nplt.hist(m_gg, bins=50, range=(100, 180), alpha=0.7, label='All Events')\\nplt.axvspan(120, 130, color='red', alpha=0.3, label='Signal Window')\\nplt.xlabel('Invariant Mass (GeV)')\\nplt.ylabel('Count')\\nplt.title('Diphoton Invariant Mass Distribution')\\nplt.legend()\\nplt.savefig('figures/window.svg')\\n\\n# Save results to JSON\\nresult_json = {\\n    'n_obs': int(n_obs),\\n    'n_sideband': len(sideband_m_gg),\\n    'lam': float(lam),\\n    'b_expected': float(b_expected),\\n    'excess': float(n_obs - b_expected),\\n    'z_asimov': float(z_asimov),\\n    'p_value': float(p_value),\\n    'z_from_p': float(z_from_p),\\n    'warnings': warnings,\\n    'claim': claim\\n}\\n\\n# Write result.json\\nimport json\\nwith open('result.json', 'w') as f:\\n    json.dump(result_json, f)\\n\\n# Write solution.py\\nwith open('solution.py', 'w') as f:\\n    f.write('''import numpy as np\\nimport pandas as pd\\nimport scipy.stats\\nimport matplotlib.pyplot as plt\\nfrom scipy.optimize import minimize\\n\\n# Load data\\ndata = pd.read_csv('data/synth_diphoton.csv')\\nm_gg = data['m_gg'].values\\n\\n# Define regions\\nsignal_window = (m_gg >= 120) & (m_gg <= 130)\\nsideband_low = (m_gg >= 100) & (m_gg < 120)\\nsideband_high = (m_gg > 130) & (m_gg <= 180)\\nsideband = sideband_low | sideband_high\\n\\n# Step 1: Fit exponential to sideband events\\nsideband_m_gg = m_gg[sideband]\\n\\n# Define the negative log-likelihood function for exponential fit\\ndef neg_log_likelihood(params):\\n    lam = params[0]\\n    # Compute the density of the exponential distribution\\n    density = np.exp(-sideband_m_gg / lam)\\n    # Normalize the density over the sideband region\\n    integral = np.trapz(density, x=sideband_m_gg)\\n    normalized_density = density / integral\\n    # Compute the negative log-likelihood\\n    return -np.sum(np.log(normalized_density))\\n\\n# Initial guess for lambda\\ninitial_lam = 50\\n\\n# Perform the optimization\\nresult = minimize(neg_log_likelihood, x0=[initial_lam], bounds=[(5, 200)])\\nlam = result.x[0]\\n\\n# Step 2: Calculate expected background in the signal window\\n# Compute the integral of the exponential distribution over the sideband region\\nintegral_sideband = np.trapz(np.exp(-sideband_m_gg / lam), x=sideband_m_gg)\\n\\n# Compute the integral of the exponential distribution over the signal window\\nintegral_signal_window = np.trapz(np.exp(-np.array([120, 130]) / lam), x=np.array([120, 130]))\\n\\n# Calculate expected background\\nb_expected = (len(sideband_m_gg) * integral_signal_window) / integral_sideband\\n\\n# Step 3: Observed count in the signal window\\nn_obs = np.sum(signal_window)\\n\\n# Step 4: Calculate z_asimov\\nif n_obs > b_expected:\\n    z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))\\nelse:\\n    z_asimov = -np.sqrt(2 * (b_expected * np.log(b_expected / n_obs) - (b_expected - n_obs)))\\n\\n# Step 5: Calculate p_value and z_from_p\\np_value = scipy.stats.poisson.sf(n_obs - 1, b_expected)\\nz_from_p = scipy.stats.norm.isf(p_value)\\n\\n# Step 6: Determine warnings\\nwarnings = []\\nif n_obs < 10 or b_expected < 10:\\n    warnings.append('low_statistics')\\n\\n# Step 7: Determine claim\\nclaim = 'significant_excess' if z_from_p >= 3.0 else 'no_significant_excess'\\n\\n# Step 8: Plot histogram with signal window indicated\\nplt.figure(figsize=(10, 6))\\nplt.hist(m_gg, bins=50, range=(100, 180), alpha=0.7, label='All Events')\\nplt.axvspan(120, 130, color='red', alpha=0.3, label='Signal Window')\\nplt.xlabel('Invariant Mass (GeV)')\\nplt.ylabel('Count')\\nplt.title('Diphoton Invariant Mass Distribution')\\nplt.legend()\\nplt.savefig('figures/window.svg')\\n\\n# Save results to JSON\\nresult_json = {\\n    'n_obs': int(n_obs),\\n    'n_sideband': len(sideband_m_gg),\\n    'lam': float(lam),\\n    'b_expected': float(b_expected),\\n    'excess': float(n_obs - b_expected),\\n    'z_asimov': float(z_asimov),\\n    'p_value': float(p_value),\\n    'z_from_p': float(z_from_p),\\n    'warnings': warnings,\\n    'claim': claim\\n"
}
#10 toolrun_pythonValueError0st+185.015s
ValueError: run_python requires a non-empty 'code' string
#11 modelact5806→2064 tok48.021st+233.046s
→ run_python(_malformed_arguments)
{
 "_malformed_arguments": "{\"code\": \"import numpy as np\\nimport pandas as pd\\nimport scipy.stats\\nimport matplotlib.pyplot as plt\\nfrom scipy.optimize import minimize\\n\\n# Load data\\ndata = pd.read_csv('data/synth_diphoton.csv')\\nm_gg = data['m_gg'].values\\n\\n# Define regions\\nsignal_window = (m_gg >= 120) & (m_gg <= 130)\\nsideband_low = (m_gg >= 100) & (m_gg < 120)\\nsideband_high = (m_gg > 130) & (m_gg <= 180)\\nsideband = sideband_low | sideband_high\\n\\n# Step 1: Fit exponential to sideband events\\nsideband_m_gg = m_gg[sideband]\\n\\n# Define the negative log-likelihood function for exponential fit\\ndef neg_log_likelihood(params):\\n    lam = params[0]\\n    # Compute the density of the exponential distribution\\n    density = np.exp(-sideband_m_gg / lam)\\n    # Normalize the density over the sideband region\\n    integral = np.trapz(density, x=sideband_m_gg)\\n    normalized_density = density / integral\\n    # Compute the negative log-likelihood\\n    return -np.sum(np.log(normalized_density))\\n\\n# Initial guess for lambda\\ninitial_lam = 50\\n\\n# Perform the optimization\\nresult = minimize(neg_log_likelihood, x0=[initial_lam], bounds=[(5, 200)])\\nlam = result.x[0]\\n\\n# Step 2: Calculate expected background in the signal window\\n# Compute the integral of the exponential distribution over the sideband region\\nintegral_sideband = np.trapz(np.exp(-sideband_m_gg / lam), x=sideband_m_gg)\\n\\n# Compute the integral of the exponential distribution over the signal window\\nintegral_signal_window = np.trapz(np.exp(-np.array([120, 130]) / lam), x=np.array([120, 130]))\\n\\n# Calculate expected background\\nb_expected = (len(sideband_m_gg) * integral_signal_window) / integral_sideband\\n\\n# Step 3: Observed count in the signal window\\nn_obs = np.sum(signal_window)\\n\\n# Step 4: Calculate z_asimov\\nif n_obs > b_expected:\\n    z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))\\nelse:\\n    z_asimov = -np.sqrt(2 * (b_expected * np.log(b_expected / n_obs) - (b_expected - n_obs)))\\n\\n# Step 5: Calculate p_value and z_from_p\\np_value = scipy.stats.poisson.sf(n_obs - 1, b_expected)\\nz_from_p = scipy.stats.norm.isf(p_value)\\n\\n# Step 6: Determine warnings\\nwarnings = []\\nif n_obs < 10 or b_expected < 10:\\n    warnings.append('low_statistics')\\n\\n# Step 7: Determine claim\\nclaim = 'significant_excess' if z_from_p >= 3.0 else 'no_significant_excess'\\n\\n# Step 8: Plot histogram with signal window indicated\\nplt.figure(figsize=(10, 6))\\nplt.hist(m_gg, bins=50, range=(100, 180), alpha=0.7, label='All Events')\\nplt.axvspan(120, 130, color='red', alpha=0.3, label='Signal Window')\\nplt.xlabel('Invariant Mass (GeV)')\\nplt.ylabel('Count')\\nplt.title('Diphoton Invariant Mass Distribution')\\nplt.legend()\\nplt.savefig('figures/window.svg')\\n\\n# Save results to JSON\\nresult_json = {\\n    'n_obs': int(n_obs),\\n    'n_sideband': len(sideband_m_gg),\\n    'lam': float(lam),\\n    'b_expected': float(b_expected),\\n    'excess': float(n_obs - b_expected),\\n    'z_asimov': float(z_asimov),\\n    'p_value': float(p_value),\\n    'z_from_p': float(z_from_p),\\n    'warnings': warnings,\\n    'claim': claim\\n}\\n\\n# Write result.json\\nimport json\\nwith open('result.json', 'w') as f:\\n    json.dump(result_json, f)\\n\\n# Write solution.py\\nwith open('solution.py', 'w') as f:\\n    f.write('''import numpy as np\\nimport pandas as pd\\nimport scipy.stats\\nimport matplotlib.pyplot as plt\\nfrom scipy.optimize import minimize\\n\\n# Load data\\ndata = pd.read_csv('data/synth_diphoton.csv')\\nm_gg = data['m_gg'].values\\n\\n# Define regions\\nsignal_window = (m_gg >= 120) & (m_gg <= 130)\\nsideband_low = (m_gg >= 100) & (m_gg < 120)\\nsideband_high = (m_gg > 130) & (m_gg <= 180)\\nsideband = sideband_low | sideband_high\\n\\n# Step 1: Fit exponential to sideband events\\nsideband_m_gg = m_gg[sideband]\\n\\n# Define the negative log-likelihood function for exponential fit\\ndef neg_log_likelihood(params):\\n    lam = params[0]\\n    # Compute the density of the exponential distribution\\n    density = np.exp(-sideband_m_gg / lam)\\n    # Normalize the density over the sideband region\\n    integral = np.trapz(density, x=sideband_m_gg)\\n    normalized_density = density / integral\\n    # Compute the negative log-likelihood\\n    return -np.sum(np.log(normalized_density))\\n\\n# Initial guess for lambda\\ninitial_lam = 50\\n\\n# Perform the optimization\\nresult = minimize(neg_log_likelihood, x0=[initial_lam], bounds=[(5, 200)])\\nlam = result.x[0]\\n\\n# Step 2: Calculate expected background in the signal window\\n# Compute the integral of the exponential distribution over the sideband region\\nintegral_sideband = np.trapz(np.exp(-sideband_m_gg / lam), x=sideband_m_gg)\\n\\n# Compute the integral of the exponential distribution over the signal window\\nintegral_signal_window = np.trapz(np.exp(-np.array([120, 130]) / lam), x=np.array([120, 130]))\\n\\n# Calculate expected background\\nb_expected = (len(sideband_m_gg) * integral_signal_window) / integral_sideband\\n\\n# Step 3: Observed count in the signal window\\nn_obs = np.sum(signal_window)\\n\\n# Step 4: Calculate z_asimov\\nif n_obs > b_expected:\\n    z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))\\nelse:\\n    z_asimov = -np.sqrt(2 * (b_expected * np.log(b_expected / n_obs) - (b_expected - n_obs)))\\n\\n# Step 5: Calculate p_value and z_from_p\\np_value = scipy.stats.poisson.sf(n_obs - 1, b_expected)\\nz_from_p = scipy.stats.norm.isf(p_value)\\n\\n# Step 6: Determine warnings\\nwarnings = []\\nif n_obs < 10 or b_expected < 10:\\n    warnings.append('low_statistics')\\n\\n# Step 7: Determine claim\\nclaim = 'significant_excess' if z_from_p >= 3.0 else 'no_significant_excess'\\n\\n# Step 8: Plot histogram with signal window indicated\\nplt.figure(figsize=(10, 6))\\nplt.hist(m_gg, bins=50, range=(100, 180), alpha=0.7, label='All Events')\\nplt.axvspan(120, 130, color='red', alpha=0.3, label='Signal Window')\\nplt.xlabel('Invariant Mass (GeV)')\\nplt.ylabel('Count')\\nplt.title('Diphoton Invariant Mass Distribution')\\nplt.legend()\\nplt.savefig('figures/window.svg')\\n\\n# Save results to JSON\\nresult_json = {\\n    'n_obs': int(n_obs),\\n    'n_sideband': len(sideband_m_gg),\\n    'lam': float(lam),\\n    'b_expected': float(b_expected),\\n    'excess': float(n_obs - b_expected),\\n    'z_asimov': float(z_asimov),\\n    'p_value': float(p_value),\\n    'z_from_p': float(z_from_p),\\n    'warnings': warnings,\\n    'claim': claim\\n}\\n\\n# Write result.json\\nimport json\\nwith open('result.json', 'w') as f:\\n    json.dump(result_json, f)''')}"
}
#12 toolrun_pythonValueError0st+233.047s
ValueError: run_python requires a non-empty 'code' string
#13 modelact3651→2064 tok47.471st+280.523s
→ run_python(code)
import numpy as np
import pandas as pd
import scipy.stats
import matplotlib.pyplot as plt
from scipy.optimize import minimize

# Load data
data = pd.read_csv('data/synth_diphoton.csv')
m_gg = data['m_gg'].values

# Define regions
signal_window = (m_gg >= 120) & (m_gg <= 130)
sideband_low = (m_gg >= 100) & (m_gg < 120)
sideband_high = (m_gg > 130) & (m_gg <= 180)
sideband = sideband_low | sideband_high

# Step 1: Fit exponential to sideband events
sideband_m_gg = m_gg[sideband]

# Define the negative log-likelihood function for exponential fit
def neg_log_likelihood(params):
    lam = params[0]
    # Compute the density of the exponential distribution
    density = np.exp(-sideband_m_gg / lam)
    # Normalize the density over the sideband region
    integral = np.trapz(density, x=sideband_m_gg)
    normalized_density = density / integral
    # Compute the negative log-likelihood
    return -np.sum(np.log(normalized_density))

# Initial guess for lambda
initial_lam = 50

# Perform the optimization
result = minimize(neg_log_likelihood, x0=[initial_lam], bounds=[(5, 200)])
lam = result.x[0]

# Step 2: Calculate expected background in the signal window
# Compute the integral of the exponential distribution over the sideband region
integral_sideband = np.trapz(np.exp(-sideband_m_gg / lam), x=sideband_m_gg)

# Compute the integral of the exponential distribution over the signal window
integral_signal_window = np.trapz(np.exp(-np.array([120, 130]) / lam), x=np.array([120, 130]))

# Calculate expected background
b_expected = (len(sideband_m_gg) * integral_signal_window) / integral_sideband

# Step 3: Observed count in the signal window
n_obs = np.sum(signal_window)

# Step 4: Calculate z_asimov
if n_obs > b_expected:
    z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))
else:
    z_asimov = -np.sqrt(2 * (b_expected * np.log(b_expected / n_obs) - (b_expected - n_obs)))

# Step 5: Calculate p_value and z_from_p
p_value = scipy.stats.poisson.sf(n_obs - 1, b_expected)
z_from_p = scipy.stats.norm.isf(p_value)

# Step 6: Determine warnings
warnings = []
if n_obs < 10 or b_expected < 10:
    warnings.append('low_statistics')

# Step 7: Determine claim
claim = 'significant_excess' if z_from_p >= 3.0 else 'no_significant_excess'

# Step 8: Plot histogram with signal window indicated
plt.figure(figsize=(10, 6))
plt.hist(m_gg, bins=50, range=(100, 180), alpha=0.7, label='All Events')
plt.axvspan(120, 130, color='red', alpha=0.3, label='Signal Window')
plt.xlabel('Invariant Mass (GeV)')
plt.ylabel('Count')
plt.title('Diphoton Invariant Mass Distribution')
plt.legend()
plt.savefig('figures/window.svg')

# Save results to JSON
result_json = {
    'n_obs': int(n_obs),
    'n_sideband': len(sideband_m_gg),
    'lam': float(lam),
    'b_expected': float(b_expected),
    'excess': float(n_obs - b_expected),
    'z_asimov': float(z_asimov),
    'p_value': float(p_value),
    'z_from_p': float(z_from_p),
    'warnings': warnings,
    'claim': claim
}

# Write result.json
import json
with open('result.json', 'w') as f:
    json.dump(result_json, f)

# Write solution.py
with open('solution.py', 'w') as f:
    f.write('''import numpy as np
import pandas as pd
import scipy.stats
import matplotlib.pyplot as plt
from scipy.optimize import minimize

# Load data
data = pd.read_csv('data/synth_diphoton.csv')
m_gg = data['m_gg'].values

# Define regions
signal_window = (m_gg >= 120) & (m_gg <= 130)
sideband_low = (m_gg >= 100) & (m_gg < 120)
sideband_high = (m_gg > 130) & (m_gg <= 180)
sideband = sideband_low | sideband_high

# Step 1: Fit exponential to sideband events
sideband_m_gg = m_gg[sideband]

# Define the negative log-likelihood function for exponential fit
def neg_log_likelihood(params):
    lam = params[0]
    # Compute the density of the exponential distribution
    density = np.exp(-sideband_m_gg / lam)
    # Normalize the density over the sideband region
    integral = np.trapz(density, x=sideband_m_gg)
    normalized_density = density / integral
    # Compute the negative log-likelihood
    return -np.sum(np.log(normalized_density))

# Initial guess for lambda
initial_lam = 50

# Perform the optimization
result = minimize(neg_log_likelihood, x0=[initial_lam], bounds=[(5, 200)])
lam = result.x[0]

# Step 2: Calculate expected background in the signal window
# Compute the integral of the exponential distribution over the sideband region
integral_sideband = np.trapz(np.exp(-sideband_m_gg / lam), x=sideband_m_gg)

# Compute the integral of the exponential distribution over the signal window
integral_signal_window = np.trapz(np.exp(-np.array([120, 130]) / lam), x=np.array([120, 130]))

# Calculate expected background
b_expected = (len(sideband_m_gg) * integral_signal_window) / integral_sideband

# Step 3: Observed count in the signal window
n_obs = np.sum(signal_window)

# Step 4: Calculate z_asimov
if n_obs > b_expected:
    z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))
else:
    z_asimov = -np.sqrt(2 * (b_expected * np.log(b_expected / n_obs) - (b_expected - n_obs)))

# Step 5: Calculate p_value and z_from_p
p_value = scipy.stats.poisson.sf(n_obs - 1, b_expected)
z_from_p = scipy.stats.norm.isf(p_value)

# Step 6: Determine warnings
warnings = []
if n_obs < 10 or b_expected < 10:
    warnings.append('low_statistics')

# Step 7: Determine claim
claim = 'significant_excess' if z_from_p >= 3.0 else 'no_significant_excess'

# Step 8: Plot histogram with signal window indicated
plt.figure(figsize=(10, 6))
plt.hist(m_gg, bins=50, range=(100, 180), alpha=0.7, label='All Events')
plt.axvspan(120, 130, color='red', alpha=0.3, label='Signal Window')
plt.xlabel('Invariant Mass (GeV)')
plt.ylabel('Count')
plt.title('Diphoton Invariant Mass Distribution')
plt.legend()
plt.savefig('figures/window.svg')

# Save results to JSON
result_json = {
    'n_obs': int(n_obs),
    'n_sideband': len(sideband_m_gg),
    'lam': float(lam),
    'b_expected': float(b_expected),
    'excess': float(n_obs - b_expected),
    'z_asimov': float(z_asimov),
    'p_value': float(p_value),
    'z_from_p': float(z_from_p),
    'warnings': warnings,
    'claim': claim
}

# Write result.json
import json
with open('result.json', 'w') as f:
    json.dump(result_json, f)''')
#14 toolrun_pythonFileNotFoundError4.734st+285.257s
STDERR:
Traceback (most recent call last):
  File "/Users/gariyuu/Projects/agenthep/runs/20260906T172750-t5-bump-significance-react-gariyuu-qwen3-8b-r0/workdir/.agenthep_guard.py", line 117, in main
    runpy.run_path(SCRIPT, run_name="__main__")
  File "<frozen runpy>", line 291, in run_path
  File "<frozen runpy>", line 98, in _run_module_code
  File "<frozen runpy>", line 88, in _run_code
  File "/Users/gariyuu/Projects/agenthep/runs/20260906T172750-t5-bump-significance-react-gariyuu-qwen3-8b-r0/workdir/_cell.py", line 77, in <module>
    plt.savefig('figures/window.svg')
  File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/pyplot.py", line 1228, in savefig
    res = fig.savefig(*args, **kwargs)  # type: ignore[func-returns-value]
          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/figure.py", line 3395, in savefig
    self.canvas.print_figure(fname, **kwargs)
  File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/backend_bases.py", line 2204, in print_figure
    result = print_method(
             ^^^^^^^^^^^^^
  File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/
... [51 chars truncated] ...
a>
    print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
                                                                 ^^^^^
  File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/backends/backend_svg.py", line 1328, in print_svg
    with cbook.open_file_cm(filename, "w", encoding="utf-8") as fh:
         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/cbook.py", line 497, in open_file_cm
    fh, opened = to_filehandle(path_or_file, mode, True, encoding)
                 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/gariyuu/Projects/agenthep/.venv-sandbox/lib/python3.11/site-packages/matplotlib/cbook.py", line 483, in to_filehandle
    fh = open(fname, flag, encoding=encoding)
         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/gariyuu/Projects/agenthep/runs/20260906T172750-t5-bump-significance-react-gariyuu-qwen3-8b-r0/workdir/.agenthep_guard.py", line 68, in _guarded_open
    return _real_open(file, mode, *a, **k)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
FileNotFoundError: [Errno 2] No such file or directory: 'figures/window.svg'

exit code: 1
#15 modelact4324→30 tok1.88st+287.14s
→ run_python(code)
import os
os.makedirs('figures', exist_ok=True)
#16 toolrun_pythonok0.096st+287.237s
exit code: 0
#17 modelact4654→2064 tok45.805st+333.045s
→ run_python(code)
import numpy as np
import pandas as pd
import scipy.stats
import matplotlib.pyplot as plt
from scipy.optimize import minimize

# Load data
data = pd.read_csv('data/synth_diphoton.csv')
m_gg = data['m_gg'].values

# Define regions
signal_window = (m_gg >= 120) & (m_gg <= 130)
sideband_low = (m_gg >= 100) & (m_gg < 120)
sideband_high = (m_gg > 130) & (m_gg <= 180)
sideband = sideband_low | sideband_high

# Step 1: Fit exponential to sideband events
sideband_m_gg = m_gg[sideband]

# Define the negative log-likelihood function for exponential fit
def neg_log_likelihood(params):
    lam = params[0]
    # Compute the density of the exponential distribution
    density = np.exp(-sideband_m_gg / lam)
    # Normalize the density over the sideband region
    integral = np.trapz(density, x=sideband_m_gg)
    normalized_density = density / integral
    # Compute the negative log-likelihood
    return -np.sum(np.log(normalized_density))

# Initial guess for lambda
initial_lam = 50

# Perform the optimization
result = minimize(neg_log_likelihood, x0=[initial_lam], bounds=[(5, 200)])
lam = result.x[0]

# Step 2: Calculate expected background in the signal window
# Compute the integral of the exponential distribution over the sideband region
integral_sideband = np.trapz(np.exp(-sideband_m_gg / lam), x=sideband_m_gg)

# Compute the integral of the exponential distribution over the signal window
integral_signal_window = np.trapz(np.exp(-np.array([120, 130]) / lam), x=np.array([120, 130]))

# Calculate expected background
b_expected = (len(sideband_m_gg) * integral_signal_window) / integral_sideband

# Step 3: Observed count in the signal window
n_obs = np.sum(signal_window)

# Step 4: Calculate z_asimov
if n_obs > b_expected:
    z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))
else:
    z_asimov = -np.sqrt(2 * (b_expected * np.log(b_expected / n_obs) - (b_expected - n_obs)))

# Step 5: Calculate p_value and z_from_p
p_value = scipy.stats.poisson.sf(n_obs - 1, b_expected)
z_from_p = scipy.stats.norm.isf(p_value)

# Step 6: Determine warnings
warnings = []
if n_obs < 10 or b_expected < 10:
    warnings.append('low_statistics')

# Step 7: Determine claim
claim = 'significant_excess' if z_from_p >= 3.0 else 'no_significant_excess'

# Step 8: Plot histogram with signal window indicated
plt.figure(figsize=(10, 6))
plt.hist(m_gg, bins=50, range=(100, 180), alpha=0.7, label='All Events')
plt.axvspan(120, 130, color='red', alpha=0.3, label='Signal Window')
plt.xlabel('Invariant Mass (GeV)')
plt.ylabel('Count')
plt.title('Diphoton Invariant Mass Distribution')
plt.legend()
plt.savefig('figures/window.svg')

# Save results to JSON
result_json = {
    'n_obs': int(n_obs),
    'n_sideband': len(sideband_m_gg),
    'lam': float(lam),
    'b_expected': float(b_expected),
    'excess': float(n_obs - b_expected),
    'z_asimov': float(z_asimov),
    'p_value': float(p_value),
    'z_from_p': float(z_from_p),
    'warnings': warnings,
    'claim': claim
}

# Write result.json
import json
with open('result.json', 'w') as f:
    json.dump(result_json, f)

# Write solution.py
with open('solution.py', 'w') as f:
    f.write('''import numpy as np
import pandas as pd
import scipy.stats
import matplotlib.pyplot as plt
from scipy.optimize import minimize

# Load data
data = pd.read_csv('data/synth_diphoton.csv')
m_gg = data['m_gg'].values

# Define regions
signal_window = (m_gg >= 120) & (m_gg <= 130)
sideband_low = (m_gg >= 100) & (m_gg < 120)
sideband_high = (m_gg > 130) & (m_gg <= 180)
sideband = sideband_low | sideband_high

# Step 1: Fit exponential to sideband events
sideband_m_gg = m_gg[sideband]

# Define the negative log-likelihood function for exponential fit
def neg_log_likelihood(params):
    lam = params[0]
    # Compute the density of the exponential distribution
    density = np.exp(-sideband_m_gg / lam)
    # Normalize the density over the sideband region
    integral = np.trapz(density, x=sideband_m_gg)
    normalized_density = density / integral
    # Compute the negative log-likelihood
    return -np.sum(np.log(normalized_density))

# Initial guess for lambda
initial_lam = 50

# Perform the optimization
result = minimize(neg_log_likelihood, x0=[initial_lam], bounds=[(5, 200)])
lam = result.x[0]

# Step 2: Calculate expected background in the signal window
# Compute the integral of the exponential distribution over the sideband region
integral_sideband = np.trapz(np.exp(-sideband_m_gg / lam), x=sideband_m_gg)

# Compute the integral of the exponential distribution over the signal window
integral_signal_window = np.trapz(np.exp(-np.array([120, 130]) / lam), x=np.array([120, 130]))

# Calculate expected background
b_expected = (len(sideband_m_gg) * integral_signal_window) / integral_sideband

# Step 3: Observed count in the signal window
n_obs = np.sum(signal_window)

# Step 4: Calculate z_asimov
if n_obs > b_expected:
    z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))
else:
    z_asimov = -np.sqrt(2 * (b_expected * np.log(b_expected / n_obs) - (b_expected - n_obs)))

# Step 5: Calculate p_value and z_from_p
p_value = scipy.stats.poisson.sf(n_obs - 1, b_expected)
z_from_p = scipy.stats.norm.isf(p_value)

# Step 6: Determine warnings
warnings = []
if n_obs < 10 or b_expected < 10:
    warnings.append('low_statistics')

# Step 7: Determine claim
claim = 'significant_excess' if z_from_p >= 3.0 else 'no_significant_excess'

# Step 8: Plot histogram with signal window indicated
plt.figure(figsize=(10, 6))
plt.hist(m_gg, bins=50, range=(100, 180), alpha=0.7, label='All Events')
plt.axvspan(120, 130, color='red', alpha=0.3, label='Signal Window')
plt.xlabel('Invariant Mass (GeV)')
plt.ylabel('Count')
plt.title('Diphoton Invariant Mass Distribution')
plt.legend()
plt.savefig('figures/window.svg')

# Save results to JSON
result_json = {
    'n_obs': int(n_obs),
    'n_sideband': len(sideband_m_gg),
    'lam': float(lam),
    'b_expected': float(b_expected),
    'excess': float(n_obs - b_expected),
    'z_asimov': float(z_asimov),
    'p_value': float(p_value),
    'z_from_p': float(z_from_p),
    'warnings': warnings,
    'claim': claim
}

# Write result.json
import json
with open('result.json', 'w') as f:
    json.dump(result_json, f)''')
#18 toolrun_pythonok3.403screated: figures/window.svg, result.json, solution.pyt+336.448s
exit code: 0
files created: figures/window.svg, result.json, solution.py
#19 modelact6011→97 tok3.404st+339.856s
→ submit(summary, assumptions)
{
 "summary": "Computed the local significance of an excess in the diphoton invariant mass distribution. The analysis included fitting an exponential to sideband events, calculating expected background, and determining statistical significance.",
 "assumptions": [
  "The data is correctly formatted as described in README.md.",
  "The exponential fit is appropriate for the sideband region.",
  "The Poisson distribution accurately models the observed counts in the signal window."
 ]
}
#20 toolsubmitok0st+339.856s
submitted

Final answer

Computed the local significance of an excess in the diphoton invariant mass distribution. The analysis included fitting an exponential to sideband events, calculating expected background, and determining statistical significance.
  • The data is correctly formatted as described in README.md.
  • The exponential fit is appropriate for the sideband region.
  • The Poisson distribution accurately models the observed counts in the signal window.

Grader verdict

9 / 17 checks passed
CheckResultCategoryWeightDetailObservedExpected
result_existscritical✓ passartifact1ok
figure_exists✓ passartifact1ok
solution_exists✓ passartifact1ok
n_obscritical✓ passnumeric2match49424942
n_sb✓ passnumeric1match2535825358
lam✗ failnumeric2observed 200.0 vs expected 24.946467457251916 (atol=0.0, rtol=0.03)20024.946467457251916
b_expectedcritical✗ failnumeric3observed 13555.832153409223 vs expected 4629.777049959585 (atol=0.0, rtol=0.03)13555.8321534092234629.777049959585
excess✗ failnumeric1observed -8613.832153409223 vs expected 312.2229500404146 (atol=0.0, rtol=0.05)-8613.832153409223312.2229500404146
z_asimovcritical✗ failnumeric2observed -100.64428865559884 vs expected 4.538470894307572 (atol=0.15, rtol=0.0)-100.644288655598844.538470894307572
p_value✗ failnumeric1observed 1.0 vs expected 2.897914860991712e-06 (atol=0.0, rtol=0.5)10.000002897914860991712
z_from_p✗ failnumeric2observed -inf vs expected 4.533703776096391 (atol=0.15, rtol=0.0)4.533703776096391
claimcritical✗ failcompliance3observed 'no_significant_excess' vs expected 'significant_excess' (atol=0.0, rtol=0.0)"no_significant_excess""significant_excess"
no_low_stats_flag✓ passcompliance1absent[]"not 'low_statistics'"
svg_unit✓ passplot1labels present["Matplotlib v3.9.2, https://matplotlib.org/","100","110","120","130","140","150["GeV"]
svg_drawn✓ passplot1drawn81">=5"
reruns✗ failreproducibility1solution.py failed in a clean workdir: FileNotFoundError: [Errno 2] No such file or directory: 'figures/window.svg'{"ok":false,"artifacts_reproduced":false,"output_matches":false,"exit_code":1}
not_hardcoded✓ passcompliance1no expected values hard-coded[]

Reproducibility rerun

script executes
✗ fail
artifacts reproduced
✗ fail
output matches submission
✗ differs
dependencies resolvable
✓ pass
seed controlled
no randomness used
detail
solution.py failed in a clean workdir: FileNotFoundError: [Errno 2] No such file or directory: 'figures/window.svg'

Artifacts

figures/window.svg: run_python · result.json: run_python · solution.py: run_python
result.json
{"n_obs": 4942, "n_sideband": 25358, "lam": 200.0, "b_expected": 13555.832153409223, "excess": -8613.832153409223, "z_asimov": -100.64428865559884, "p_value": 1.0, "z_from_p": -Infinity, "warnings": [], "claim": "no_significant_excess"}
solution.py
import numpy as np
import pandas as pd
import scipy.stats
import matplotlib.pyplot as plt
from scipy.optimize import minimize

# Load data
data = pd.read_csv('data/synth_diphoton.csv')
m_gg = data['m_gg'].values

# Define regions
signal_window = (m_gg >= 120) & (m_gg <= 130)
sideband_low = (m_gg >= 100) & (m_gg < 120)
sideband_high = (m_gg > 130) & (m_gg <= 180)
sideband = sideband_low | sideband_high

# Step 1: Fit exponential to sideband events
sideband_m_gg = m_gg[sideband]

# Define the negative log-likelihood function for exponential fit
def neg_log_likelihood(params):
    lam = params[0]
    # Compute the density of the exponential distribution
    density = np.exp(-sideband_m_gg / lam)
    # Normalize the density over the sideband region
    integral = np.trapz(density, x=sideband_m_gg)
    normalized_density = density / integral
    # Compute the negative log-likelihood
    return -np.sum(np.log(normalized_density))

# Initial guess for lambda
initial_lam = 50

# Perform the optimization
result = minimize(neg_log_likelihood, x0=[initial_lam], bounds=[(5, 200)])
lam = result.x[0]

# Step 2: Calculate expected background in the signal window
# Compute the integral of the exponential distribution over the sideband region
integral_sideband = np.trapz(np.exp(-sideband_m_gg / lam), x=sideband_m_gg)

# Compute the integral of the exponential distribution over the signal window
integral_signal_window = np.trapz(np.exp(-np.array([120, 130]) / lam), x=np.array([120, 130]))

# Calculate expected background
b_expected = (len(sideband_m_gg) * integral_signal_window) / integral_sideband

# Step 3: Observed count in the signal window
n_obs = np.sum(signal_window)

# Step 4: Calculate z_asimov
if n_obs > b_expected:
    z_asimov = np.sqrt(2 * (n_obs * np.log(n_obs / b_expected) - (n_obs - b_expected)))
else:
    z_asimov = -np.sqrt(2 * (b_expected * np.log(b_expected / n_obs) - (b_expected - n_obs)))

# Step 5: Calculate p_value and z_from_p
p_value = scipy.stats.poisson.sf(n_obs - 1, b_expected)
z_from_p = scipy.stats.norm.isf(p_value)

# Step 6: Determine warnings
warnings = []
if n_obs < 10 or b_expected < 10:
    warnings.append('low_statistics')

# Step 7: Determine claim
claim = 'significant_excess' if z_from_p >= 3.0 else 'no_significant_excess'

# Step 8: Plot histogram with signal window indicated
plt.figure(figsize=(10, 6))
plt.hist(m_gg, bins=50, range=(100, 180), alpha=0.7, label='All Events')
plt.axvspan(120, 130, color='red', alpha=0.3, label='Signal Window')
plt.xlabel('Invariant Mass (GeV)')
plt.ylabel('Count')
plt.title('Diphoton Invariant Mass Distribution')
plt.legend()
plt.savefig('figures/window.svg')

# Save results to JSON
result_json = {
    'n_obs': int(n_obs),
    'n_sideband': len(sideband_m_gg),
    'lam': float(lam),
    'b_expected': float(b_expected),
    'excess': float(n_obs - b_expected),
    'z_asimov': float(z_asimov),
    'p_value': float(p_value),
    'z_from_p': float(z_from_p),
    'warnings': warnings,
    'claim': claim
}

# Write result.json
import json
with open('result.json', 'w') as f:
    json.dump(result_json, f)
figures/window.svg
2026-09-06T10:33:27.110025 image/svg+xml Matplotlib v3.9.2, https://matplotlib.org/ 100 110 120 130 140 150 160 170 180 Invariant Mass (GeV) 0 250 500 750 1000 1250 1500 1750 2000 Count Diphoton Invariant Mass Distribution All Events Signal Window

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 "started_at": "2026-09-06T17:27:50.794221+00:00",
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