An exact law for how temperature distorts the Bayes-error proxy

arXiv·low signal

This paper (arXiv 2607.18162) derives an exact relationship showing that the calibration channel determines the soft-label Bayes-error estimator, quantifying how temperature scaling distorts the irreducible-error estimate for binary tasks. Practically, it means confidence-threshold routing — the standard way agents decide when to escalate to a stronger model — inherits a systematic bias from whatever calibration the serving stack applied. Theoretical and single-source, but it undercuts a widely used routing heuristic.