HE/1
This is one (task, candidate response) pair flowing through the full PANOPTES pipeline. Each section below is a stage of the analysis: the task itself, the candidate solution being evaluated, every judge's score + rationale, the sampling-pass dispersion that captures within-judge noise, and the uncertainty-quantification metrics computed on top.
The function signature + docstring presented to both the model under test and to every judge.
from typing import List
def separate_paren_groups(paren_string: str) -> List[str]:
""" Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
separate those group into separate strings and return the list of those.
Separate groups are balanced (each open brace is properly closed) and not nested within each other
Ignore any spaces in the input string.
>>> separate_paren_groups('( ) (( )) (( )( ))')
['()', '(())', '(()())']
"""
The full solution every judge is grading. For these runs the candidate is the reference solution prepended with the task signature so it parses as a complete program.
from typing import List
def separate_paren_groups(paren_string: str) -> List[str]:
""" Input to this function is a string containing multiple groups of nested parentheses. Your goal is to
separate those group into separate strings and return the list of those.
Separate groups are balanced (each open brace is properly closed) and not nested within each other
Ignore any spaces in the input string.
>>> separate_paren_groups('( ) (( )) (( )( ))')
['()', '(())', '(()())']
"""
result = []
current_string = []
current_depth = 0
for c in paren_string:
if c == '(':
current_depth += 1
current_string.append(c)
elif c == ')':
current_depth -= 1
current_string.append(c)
if current_depth == 0:
result.append(''.join(current_string))
current_string.clear()
return result
One call per judge at temperature=0. This is the "best single guess" each judge has. Disagreement here is structural. The judges literally see this candidate differently.
n draws per judge at temperature=1. Dots are individual draws; vertical bar is the mean; shaded band is ±1σ. Wide band = the judge is uncertain even with itself; narrow band = it's consistent.
Three statistical methods computed on top of the raw scores above. Each one tells you something different about how much to trust the headline number.
How to read these: self-consistency = does the judge agree with itself when resampled? Narrower CI means more consistent. Semantic entropy = do the judge's rationales cluster into one meaning, or several? Higher entropy means the judge is internally conflicted about why. Decomposition = how much of the total variance comes from within-judge sampling noise (aleatoric, hard to fix) vs between-judge disagreement (epistemic, fixable by calling more judges).
The natural-language explanation each judge gave alongside its score. These are produced via tool-use structured output, so the score and the rationale are guaranteed to come from the same forward pass.
The solution correctly implements the required functionality. It uses a depth-tracking approach to identify balanced parenthesis groups: incrementing depth on '(', decrementing on ')', and appending a complete group to the result when depth returns to 0. The solution properly ignores spaces by only processing '(' and ')' characters. Testing against the provided example: '( ) (( )) (( )( ))' correctly produces ['()', '(())', '(()())']. The logic handles edge cases well: empty input returns [], single groups work correctly, and multiple groups are properly separated. The code is idiomatic, clear, and efficient with O(n) time complexity.
The solution correctly tracks depth with a counter, accumulates characters into a current group, and appends the completed group when depth returns to 0. Spaces are implicitly ignored (neither `(` nor `)` branch handles spaces, so they're skipped). The canonical example `'( ) (( )) (( )( ))'` produces `['()', '(())', '(()())']` as expected. Edge cases like empty string return `[]`, single group works, and deeply nested groups work correctly. The implementation is clean and idiomatic.
The solution correctly separates groups of parentheses and handles the provided example. However, it does not account for ignoring spaces in the input string, which could lead to incorrect results if spaces are present. This is a minor issue, but it affects the overall correctness.