HE/16
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.
def count_distinct_characters(string: str) -> int:
""" Given a string, find out how many distinct characters (regardless of case) does it consist of
>>> count_distinct_characters('xyzXYZ')
3
>>> count_distinct_characters('Jerry')
4
"""
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.
def count_distinct_characters(string: str) -> int:
""" Given a string, find out how many distinct characters (regardless of case) does it consist of
>>> count_distinct_characters('xyzXYZ')
3
>>> count_distinct_characters('Jerry')
4
"""
return len(set(string.lower()))
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 converts the input string to lowercase using `.lower()` to handle case-insensitivity, then uses `set()` to extract distinct characters, and returns the count via `len()`. This approach is both correct and idiomatic Python. Testing against the provided examples: 'xyzXYZ'.lower() = 'xyzxyz' → set gives {'x','y','z'} → len = 3 ✓; 'Jerry'.lower() = 'jerry' → set gives {'j','e','r','y'} → len = 4 ✓. Edge cases are handled correctly: empty string returns 0, strings with all identical characters return 1, and strings with special characters/spaces are counted as distinct characters (which aligns with the task's "any character" interpretation).
The solution correctly converts the string to lowercase and counts distinct characters using a set. It handles both provided examples correctly: 'xyzXYZ'.lower() = 'xyzxyz' → set size 3, and 'Jerry'.lower() = 'jerry' → set size 4 (j, e, r, y). Edge cases like empty string return 0, single characters return 1, and mixed case is handled properly. The implementation is idiomatic and concise.
The solution correctly counts distinct characters in a string, ignoring case. It passes the provided examples and handles edge cases like empty strings and varying character cases. The use of `set` and `lower()` is idiomatic and efficient for this task.