AgentHEPGitHub ↗
2026-09-06 17:19 UTC · seatbelt sandbox · git unknown

Excess in a window with only a handful of events

t5-low-statstier 5Single-shotQwen3-8B (gariyuu gateway)✗ failedtask spec →
Score
0.0548
artifact 0.3333 · numeric 0 · compliance 0.1429 · plot 0 · reproducibility 0
LLM calls
1
2 tool calls
Tokens
3,106
1,064 in · 2,042 out
Cost
$0.00105
Wall
32 s
ended: single_shot_done
Errors
1
0 recovered · 0 unsafe
Failure labels:no_outputplotting_errorinvalid_cutstatistical_misuseincorrect_normalizationunjustified_interpretationinsufficient_statisticsnon_reproducibleexecution_failed

Task given to the agent

`data/synth_diphoton_lowstat.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 modelgenerate1064→2042 tok29.819st+29.819s
```python import numpy as np import pandas as pd import scipy.optimize as optimize import scipy.integrate as integrate import scipy.stats as stats import matplotlib.pyplot as plt import os # Read data data_path = 'data/synth_diphoton_lowstat.csv' df = pd.read_csv(data_path) # Define regions signal_window = [120, 130] sideband_low = [100, 120] sideband_high = [130, 180] # Step 1: Fit exponential to sideband events def exp_pdf(m, lam): return np.exp(-m / lam) def neg_log_likelihood(params, m_data): lam = params[0] return -np.sum(np.log(exp_pdf(m_data, lam))) # Extract sideband data sideband_m = df[(df['m_gg'] >= sideband_low[0]) & (df['m_gg'] < sideband_low[1]) | (df['m_gg'] > sideband_high[0]) & (df['m_gg'] <= sideband_high[1])]['m_gg'] # Initial guess for lambda initial_lam = 100.0 result = optimize.minimize(lambda x: neg_log_likelihood([x], sideband_m), initial_lam) lam_fit = result.x[0] # Step 2: Calculate expected background in the signal window def integral_exp(lam, m_low, m_high): return integrate.quad(lambda m: exp_pdf(m, lam), m_low, m_high)[0] # Integrate over sideband regions integral_sideband_low = integral_exp(lam_fit, sideband_low[0], sideband_low[1]) integral_sideband_high = integral_exp(lam_fit, sideband_high[0], sideband_high[1]) total_integral_sideband = integral_sideband_low + integral_sideband_high # Integrate over signal window integral_signal_window = integral_exp(lam_fit, signal_window[0], signal_window[1]) # Expected background n_sideband = len(sideband_m) b_expected = n_sideband * integral_signal_window / total_integral_sideband # Step 3: Observed count n_obs = len(df[(df['m_gg'] >= signal_window[0]) & (df['m_gg'] <= signal_window[1])]) # Step 4: Asimov z-score 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 - n_obs) * np.log((b_expected - n_obs) / n_obs) - (b_expected - n_obs - n_obs))) # Step 5: p-value and z_from_p p_value = stats.poisson.sf(n_obs - 1, b_expected) z_from_p = stats.norm.isf(p_value) # Step 6: Warnings warnings = [] if n_obs < 10 or b_expected < 10: warnings.append("low_statistics") # Step 7: Claim claim = "significant_excess" if z_from_p >= 3.0 else "no_significant_excess" # Save results to JSON result_json = { "n_obs": int(n_obs), "n_sideband": int(n_sideband), "lam": float(lam_fit), "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 } with open('result.json', 'w') as f: f.write(json.dumps(result_json)) # Plot histogram plt.figure(figsize=(10, 6)) plt.hist(df['m_gg'], bins=50, range=(100, 180), alpha=0.7, label='Data') plt.axvspan(signal_window[0], signal_window[1], color='red', alpha=0.3, label='Signal Window') plt.axvspan(sideband_low[0], sideband_low[1], color='blue', alpha=0.3, label='Sideband Low') plt.axvspan(sideband_high[0], sideband_high[1], color='blue', alpha=0.3, label='Sideband High') plt.xlabel('Invariant Mass (GeV)') plt.ylabel('Count') plt.title('Diphoton Invariant Mass Distribution') plt.legend() plt.savefig('figures/window.svg') # Save solution.py with open('solution.py', 'w') as f: f.write('''import numpy as np import pandas as pd import scipy.optimize as optimize import scipy.integrate as integrate import scipy.stats as stats import matplotlib.pyplot as plt import json import os # Read data data_path = 'data/synth_diphoton_lowstat.csv' df = pd.read_csv(data_path) # Define regions signal_window = [120, 130] sideband_low = [100, 120] sideband_high = [130, 180] # Step 1: Fit exponential to sideband events def exp_pdf(m, lam): return np.exp(-m / lam) def neg_log_likelihood(params, m_data): lam = params[0] return -np.sum(np.log(exp_pdf(m_data, lam))) # Extract sideband data sideband_m = df[(df['m_gg'] >= sideband_low[0]) & (df['m_gg'] < sideband_low[1]) | (df['m_gg'] > sideband_high[0]) & (df['m_gg'] <= sideband_high[1])]['m_gg'] # Initial guess for lambda initial_lam = 100.0 result = optimize.minimize(lambda x: neg_log_likelihood([x], sideband_m), initial_lam) lam_fit = result.x[0] # Step 2: Calculate expected background in the signal window def integral_exp(lam, m_low, m_high): return integrate.quad(lambda m: exp_pdf(m, lam), m_low, m_high)[0] # Integrate over sideband regions integral_sideband_low = integral_exp(lam_fit, sideband_low[0], sideband_low[1]) integral_sideband_high = integral_exp(lam_fit, sideband_high[0], sideband_high[1]) total_integral_sideband = integral_sideband_low + integral_sideband_high # Integrate over signal window integral_signal_window = integral_exp(lam_fit, signal_window[0], signal_window[1]) # Expected background n_sideband = len(sideband_m) b_expected = n_sideband * integral_signal_window / total_integral_sideband # Step 3: Observed count n_obs = len(df[(df['m_gg'] >= signal_window[0]) & (df['m_gg'] <= signal_window[1])]) # Step 4: Asimov z-score 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 - n_obs) * np.log((b_expected - n_obs) / n_obs) - (b_expected - n_obs - n_obs))) # Step 5: p-value and z_from_p p_value = stats.poisson.sf(n_obs - 1, b_expected) z_from_p = stats.norm.isf(p_value) # Step 6: Warnings warnings = [] if n_obs < 10 or b_expected < 10: warnings.append("low_statistics") # Step 7: Claim claim = "significant_excess" if z_from_p >= 3.0 else "no_significant_excess" # Save results to JSON result_json = { "n_obs": int(n_obs), "n_sideband": int(n_sideband), "lam": float(lam_fit), "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 } with open('result.json', 'w') as f: f.write(json.dumps(result_json)) # Plot histogram plt.figure(figsize=(10, 6)) plt.hist(df['m_gg'], bins=50, range=(100, 180), alpha=0.7, label='Data') plt.axvspan(signal_window[0], signal_window[1], color='red', alpha=0.3, label='Signal Window') plt.axvspan(sideband_low[0], sideband_low[1], color='blue', alpha=0.3, label='Sideband Low') plt.axvspan(sideband_high[0], sideband_high[1], color='blue', alpha=0.3, label='Sideband High') plt.xlabel('Invariant Mass (GeV)') plt.ylabel('Count') plt.title('Diphoton Invariant Mass Distribution') plt.legend() plt.savefig('figures/window.svg') ''') ```
#1 toolwrite_fileok0screated: solution.pyt+29.82s
wrote 6650 chars to solution.py
#2 toolrun_pythonNameError2.436screated: result.jsont+32.256s
STDERR:
Traceback (most recent call last):
  File "/Users/gariyuu/Projects/agenthep/runs/20260906T171945-t5-low-stats-single_shot-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/20260906T171945-t5-low-stats-single_shot-gariyuu-qwen3-8b-r0/workdir/_cell.py", line 87, in <module>
    f.write(json.dumps(result_json))
            ^^^^
NameError: name 'json' is not defined

exit code: 1
files created: result.json

Final answer

```python import numpy as np import pandas as pd import scipy.optimize as optimize import scipy.integrate as integrate import scipy.stats as stats import matplotlib.pyplot as plt import os # Read data data_path = 'data/synth_diphoton_lowstat.csv' df = pd.read_csv(data_path) # Define regions signal_window = [120, 130] sideband_low = [100, 120] sideband_high = [130, 180] # Step 1: Fit exponential to sideband events def exp_pdf(m, lam): return np.exp(-m / lam) def neg_log_likelihood(params, m_data): lam = params[0] return -np.sum(np.log(exp_pdf(m_data, lam))) # Extract sideband data sideband_m = df[(df['m_gg'] >= sideband_low[0]) & (df['m_gg'] < sideband_low[1]) | (df['m_gg'] > sideband_high[0]) & (df['m_gg'] <= sideband_high[1])]['m_gg'] # Initial guess for lambda initial_lam = 100.0 result = optimize.minimize(lambda x: neg_log_likelihood([x], sideband_m), initial_lam) lam_fit = result.x[0] # Step 2: Calculate expected background in the signal window def integral_exp(lam, m_low, m_high): return integrate.quad(lambda m: exp_pdf(m, lam), m_low, m_high)[0] # Integrate over sideband regions integral_sideband_low = integral_exp(lam_fit, sideband_low[0], sideband_low[1]) integral_sideband_high = integral_exp(lam_fit, sideband_high[0], sideband_high[1]) total_integral_sideband = integral_sideband_low + integral_sideband_high # Integrate over signal window integral_signal_window = integral_exp(lam_fit, signal_window[0], signal_window[1]) # Expected background n_sideband = len(sideband_m) b_expected = n_sideband * integral_signal_window / total_integral_sideband # Step 3: Observed count n_obs = len(df[(df['m_gg'] >= signal_window[0]) & (df['m_gg'] <= signal_window[1])]) # Step 4: Asimov z-score 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 - n_obs) * np.log((b_expected - n_obs) / n_obs) - (b_expected - n_obs - n_obs))) # S
no assumptions stated
Numbers in the summary not found in any produced artifact: 120, 130, 100, 120, 130, 180, 100

Grader verdict

2 / 17 checks passed
CheckResultCategoryWeightDetailObservedExpected
result_existscritical✗ failartifact1empty file
figure_exists✗ failartifact1missing
solution_exists✓ passartifact1ok
n_obscritical✗ failnumeric2grader error: JSONDecodeError: Expecting value: line 1 column 1 (char 0)
n_sb✗ failnumeric1grader error: JSONDecodeError: Expecting value: line 1 column 1 (char 0)
lam✗ failnumeric2grader error: JSONDecodeError: Expecting value: line 1 column 1 (char 0)
b_expectedcritical✗ failnumeric3grader error: JSONDecodeError: Expecting value: line 1 column 1 (char 0)
excess✗ failnumeric1grader error: JSONDecodeError: Expecting value: line 1 column 1 (char 0)
z_asimovcritical✗ failnumeric2grader error: JSONDecodeError: Expecting value: line 1 column 1 (char 0)
p_value✗ failnumeric1grader error: JSONDecodeError: Expecting value: line 1 column 1 (char 0)
z_from_p✗ failnumeric2grader error: JSONDecodeError: Expecting value: line 1 column 1 (char 0)
claimcritical✗ failcompliance3grader error: JSONDecodeError: Expecting value: line 1 column 1 (char 0)
low_stats_flagcritical✗ failcompliance3grader error: JSONDecodeError: Expecting value: line 1 column 1 (char 0)
svg_unit✗ failplot1missing file: window.svg
svg_drawn✗ failplot1missing file: window.svg
reruns✗ failreproducibility1solution.py failed in a clean workdir: NameError: name 'json' is not defined{"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: NameError: name 'json' is not defined

Artifacts

solution.py: write_file · result.json: run_python
result.json
solution.py
import numpy as np
import pandas as pd
import scipy.optimize as optimize
import scipy.integrate as integrate
import scipy.stats as stats
import matplotlib.pyplot as plt
import os

# Read data
data_path = 'data/synth_diphoton_lowstat.csv'
df = pd.read_csv(data_path)

# Define regions
signal_window = [120, 130]
sideband_low = [100, 120]
sideband_high = [130, 180]

# Step 1: Fit exponential to sideband events
def exp_pdf(m, lam):
    return np.exp(-m / lam)

def neg_log_likelihood(params, m_data):
    lam = params[0]
    return -np.sum(np.log(exp_pdf(m_data, lam)))

# Extract sideband data
sideband_m = df[(df['m_gg'] >= sideband_low[0]) & (df['m_gg'] < sideband_low[1]) |
                (df['m_gg'] > sideband_high[0]) & (df['m_gg'] <= sideband_high[1])]['m_gg']

# Initial guess for lambda
initial_lam = 100.0
result = optimize.minimize(lambda x: neg_log_likelihood([x], sideband_m), initial_lam)
lam_fit = result.x[0]

# Step 2: Calculate expected background in the signal window
def integral_exp(lam, m_low, m_high):
    return integrate.quad(lambda m: exp_pdf(m, lam), m_low, m_high)[0]

# Integrate over sideband regions
integral_sideband_low = integral_exp(lam_fit, sideband_low[0], sideband_low[1])
integral_sideband_high = integral_exp(lam_fit, sideband_high[0], sideband_high[1])
total_integral_sideband = integral_sideband_low + integral_sideband_high

# Integrate over signal window
integral_signal_window = integral_exp(lam_fit, signal_window[0], signal_window[1])

# Expected background
n_sideband = len(sideband_m)
b_expected = n_sideband * integral_signal_window / total_integral_sideband

# Step 3: Observed count
n_obs = len(df[(df['m_gg'] >= signal_window[0]) & (df['m_gg'] <= signal_window[1])])

# Step 4: Asimov z-score
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 - n_obs) * np.log((b_expected - n_obs) / n_obs) - (b_expected - n_obs - n_obs)))

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

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

# Step 7: Claim
claim = "significant_excess" if z_from_p >= 3.0 else "no_significant_excess"

# Save results to JSON
result_json = {
    "n_obs": int(n_obs),
    "n_sideband": int(n_sideband),
    "lam": float(lam_fit),
    "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
}

with open('result.json', 'w') as f:
    f.write(json.dumps(result_json))

# Plot histogram
plt.figure(figsize=(10, 6))
plt.hist(df['m_gg'], bins=50, range=(100, 180), alpha=0.7, label='Data')
plt.axvspan(signal_window[0], signal_window[1], color='red', alpha=0.3, label='Signal Window')
plt.axvspan(sideband_low[0], sideband_low[1], color='blue', alpha=0.3, label='Sideband Low')
plt.axvspan(sideband_high[0], sideband_high[1], color='blue', alpha=0.3, label='Sideband High')
plt.xlabel('Invariant Mass (GeV)')
plt.ylabel('Count')
plt.title('Diphoton Invariant Mass Distribution')
plt.legend()
plt.savefig('figures/window.svg')

# Save solution.py
with open('solution.py', 'w') as f:
    f.write('''import numpy as np
import pandas as pd
import scipy.optimize as optimize
import scipy.integrate as integrate
import scipy.stats as stats
import matplotlib.pyplot as plt
import json
import os

# Read data
data_path = 'data/synth_diphoton_lowstat.csv'
df = pd.read_csv(data_path)

# Define regions
signal_window = [120, 130]
sideband_low = [100, 120]
sideband_high = [130, 180]

# Step 1: Fit exponential to sideband events
def exp_pdf(m, lam):
    return np.exp(-m / lam)

def neg_log_likelihood(params, m_data):
    lam = params[0]
    return -np.sum(np.log(exp_pdf(m_data, lam)))

# Extract sideband data
sideband_m = df[(df['m_gg'] >= sideband_low[0]) & (df['m_gg'] < sideband_low[1]) |
                (df['m_gg'] > sideband_high[0]) & (df['m_gg'] <= sideband_high[1])]['m_gg']

# Initial guess for lambda
initial_lam = 100.0
result = optimize.minimize(lambda x: neg_log_likelihood([x], sideband_m), initial_lam)
lam_fit = result.x[0]

# Step 2: Calculate expected background in the signal window
def integral_exp(lam, m_low, m_high):
    return integrate.quad(lambda m: exp_pdf(m, lam), m_low, m_high)[0]

# Integrate over sideband regions
integral_sideband_low = integral_exp(lam_fit, sideband_low[0], sideband_low[1])
integral_sideband_high = integral_exp(lam_fit, sideband_high[0], sideband_high[1])
total_integral_sideband = integral_sideband_low + integral_sideband_high

# Integrate over signal window
integral_signal_window = integral_exp(lam_fit, signal_window[0], signal_window[1])

# Expected background
n_sideband = len(sideband_m)
b_expected = n_sideband * integral_signal_window / total_integral_sideband

# Step 3: Observed count
n_obs = len(df[(df['m_gg'] >= signal_window[0]) & (df['m_gg'] <= signal_window[1])])

# Step 4: Asimov z-score
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 - n_obs) * np.log((b_expected - n_obs) / n_obs) - (b_expected - n_obs - n_obs)))

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

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

# Step 7: Claim
claim = "significant_excess" if z_from_p >= 3.0 else "no_significant_excess"

# Save results to JSON
result_json = {
    "n_obs": int(n_obs),
    "n_sideband": int(n_sideband),
    "lam": float(lam_fit),
    "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
}

with open('result.json', 'w') as f:
    f.write(json.dumps(result_json))

# Plot histogram
plt.figure(figsize=(10, 6))
plt.hist(df['m_gg'], bins=50, range=(100, 180), alpha=0.7, label='Data')
plt.axvspan(signal_window[0], signal_window[1], color='red', alpha=0.3, label='Signal Window')
plt.axvspan(sideband_low[0], sideband_low[1], color='blue', alpha=0.3, label='Sideband Low')
plt.axvspan(sideband_high[0], sideband_high[1], color='blue', alpha=0.3, label='Sideband High')
plt.xlabel('Invariant Mass (GeV)')
plt.ylabel('Count')
plt.title('Diphoton Invariant Mass Distribution')
plt.legend()
plt.savefig('figures/window.svg')
''')

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