Measured or Real? When Model-Derived Measurements Can Be Corrected or Compared

arXiv:2610.38015v1 Announce Type: new Abstract: Numbers computed from trained models, such as an example's difficulty or a model's benchmark lead, change with seed and prompt. We ask when such measurements can be corrected or compared. Noise shrinks correlations, and the textbook correction divides by the square root of two estimated reliabilities. On two CIFAR-100 difficulty scores, it returned correlations above one in 70 of 100 classes. We prove that its mean squared error is infinite even when the correlation and the reliabilities use separate seeds. Our rule corrects only when both reliabilities pass a significance test, then divides by their upper confidence bounds. Its output is always bounded, and its coverage guarantees assume Gaussian noise.