unbiased-cka-can-be-negative

Summary

At finite sample sizes, the unbiased alignment score can dip below zero, even though its biased counterpart is mathematically guaranteed to stay between 0 and 1. This matters because any downstream logic that assumes the score is non-negative — thresholds, ranking comparisons, or optimization targets — will misfire or produce misleading results when the unbiased estimator returns a negative value that is simply a finite-sample artifact rather than a meaningful signal of "anti-alignment."