HE/11
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 string_xor(a: str, b: str) -> str:
""" Input are two strings a and b consisting only of 1s and 0s.
Perform binary XOR on these inputs and return result also as a string.
>>> string_xor('010', '110')
'100'
"""
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 string_xor(a: str, b: str) -> str:
""" Input are two strings a and b consisting only of 1s and 0s.
Perform binary XOR on these inputs and return result also as a string.
>>> string_xor('010', '110')
'100'
"""
def xor(i, j):
if i == j:
return '0'
else:
return '1'
return ''.join(xor(x, y) for x, y in zip(a, b))
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 XOR logic for the canonical example ('010' XOR '110' = '100'). However, it has a critical flaw: it uses `zip(a, b)` which silently truncates to the shorter string when inputs have different lengths. For example, string_xor('1', '101') would return '1' instead of raising an error or handling the mismatch. The task states inputs are "two strings" performing XOR, which typically assumes equal length. The solution fails on this plausible edge case of mismatched input lengths. The XOR logic itself is sound, but the incomplete handling of input validation is a significant bug that would surface on realistic input variations.
The solution correctly implements XOR for equal-length strings and passes the canonical example ('010' XOR '110' = '100'). The inner `xor` function correctly returns '0' when characters are equal and '1' otherwise, which is valid XOR logic for binary strings. However, it uses `zip(a, b)` which silently truncates to the shorter string if inputs have different lengths — this could be considered a bug for unequal-length inputs, though the task description doesn't explicitly address that edge case. The solution is clean and idiomatic for the stated constraints.
The solution correctly implements the binary XOR operation for two strings of '0's and '1's, passing the provided example and handling edge cases such as different lengths of input strings. The code is clear and idiomatic, using a helper function for clarity.