HE/13
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 greatest_common_divisor(a: int, b: int) -> int:
""" Return a greatest common divisor of two integers a and b
>>> greatest_common_divisor(3, 5)
1
>>> greatest_common_divisor(25, 15)
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 greatest_common_divisor(a: int, b: int) -> int:
""" Return a greatest common divisor of two integers a and b
>>> greatest_common_divisor(3, 5)
1
>>> greatest_common_divisor(25, 15)
5
"""
while b:
a, b = b, a % b
return a
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 implements Euclid's algorithm correctly and passes the provided examples (gcd(3,5)=1 and gcd(25,15)=5). The logic is sound: it repeatedly replaces (a,b) with (b, a%b) until b becomes 0, then returns a. However, there are notable edge cases not handled: (1) negative inputs—the algorithm will return a negative GCD if either input is negative, but mathematical convention defines GCD as non-negative; (2) zero inputs—gcd(0,0) returns 0 (mathematically undefined), and gcd(n,0) correctly returns |n| only if n≥0. The code is idiomatic and efficient (O(log min(a,b))), but the lack of handling for negative numbers is a real limitation that would fail on realistic inputs like gcd(-25, 15) or gcd(25, -15).
The solution implements the Euclidean algorithm correctly. It passes both provided examples (gcd(3,5)=1, gcd(25,15)=5). It also handles edge cases: gcd(0,0) returns 0 (conventional), gcd(n,0) returns n, gcd(0,n) returns n. The algorithm is the standard, idiomatic, and efficient approach for computing GCD in Python.
The candidate solution correctly implements the Euclidean algorithm to find the greatest common divisor (GCD) of two integers. It passes the provided test cases and handles edge cases, such as when one of the integers is zero. The code is clear and idiomatic.