HE/6
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 parse_nested_parens(paren_string: str) -> List[int]:
""" Input to this function is a string represented multiple groups for nested parentheses separated by spaces.
For each of the group, output the deepest level of nesting of parentheses.
E.g. (()()) has maximum two levels of nesting while ((())) has three.
>>> parse_nested_parens('(()()) ((())) () ((())()())')
[2, 3, 1, 3]
"""
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 parse_nested_parens(paren_string: str) -> List[int]:
""" Input to this function is a string represented multiple groups for nested parentheses separated by spaces.
For each of the group, output the deepest level of nesting of parentheses.
E.g. (()()) has maximum two levels of nesting while ((())) has three.
>>> parse_nested_parens('(()()) ((())) () ((())()())')
[2, 3, 1, 3]
"""
def parse_paren_group(s):
depth = 0
max_depth = 0
for c in s:
if c == '(':
depth += 1
max_depth = max(depth, max_depth)
else:
depth -= 1
return max_depth
return [parse_paren_group(x) for x in paren_string.split(' ') if x]
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 solves the stated task. It splits the input string by spaces, processes each group independently, and tracks the maximum nesting depth by incrementing on '(' and decrementing on ')'. The logic is sound: max_depth is updated whenever depth increases, capturing the deepest level reached. The solution handles the provided example correctly: '(()())' → 2, '((())) ' → 3, '()' → 1, '((())()())' → 3. The code is idiomatic Python, uses a helper function for clarity, and the `if x` filter correctly handles potential empty strings from consecutive spaces. Edge cases like empty groups and single parentheses are handled correctly.
The solution correctly splits the input string by spaces (filtering empty strings), then for each group tracks depth with a counter, updating max_depth on each '(' increment. This correctly handles the canonical example [2, 3, 1, 3] and edge cases like empty strings between spaces (filtered by `if x`), single-level parentheses, and deeply nested ones. Logic is clean and idiomatic.
The solution correctly computes the maximum depth of nested parentheses for each group in the input string and handles the provided example correctly. However, it does not handle cases where there are unmatched parentheses, which could lead to incorrect depth calculations. Additionally, the function does not check for invalid characters, which could be a potential edge case. Overall, it is mostly correct but has minor issues that could affect its robustness.