HE/15
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 string_sequence(n: int) -> str:
""" Return a string containing space-delimited numbers starting from 0 upto n inclusive.
>>> string_sequence(0)
'0'
>>> string_sequence(5)
'0 1 2 3 4 5'
"""
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 string_sequence(n: int) -> str:
""" Return a string containing space-delimited numbers starting from 0 upto n inclusive.
>>> string_sequence(0)
'0'
>>> string_sequence(5)
'0 1 2 3 4 5'
"""
return ' '.join([str(x) for x in range(n + 1)])
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 `range(n + 1)` to generate numbers from 0 to n inclusive, converts each to a string, and joins them with spaces. The logic is sound: `range(n + 1)` produces [0, 1, ..., n], the list comprehension converts each to string, and `' '.join()` produces the space-delimited output. Both provided examples pass: `string_sequence(0)` returns '0' and `string_sequence(5)` returns '0 1 2 3 4 5'. Edge cases are handled correctly: negative n would produce an empty range (empty string), and large n would work as expected. The code is idiomatic Python and clear.
The solution correctly generates a space-delimited string of numbers from 0 to n inclusive using `range(n + 1)` and `' '.join(...)`. It handles the edge case of n=0 (returns '0') and the general case (e.g., n=5 returns '0 1 2 3 4 5'). The implementation is idiomatic, clear, and efficient.
The solution correctly implements the task by generating a space-delimited string of numbers from 0 to n inclusive. It passes the provided examples and handles edge cases, such as n = 0, correctly. The code is clear and idiomatic, using a list comprehension and the join method effectively.