The Price of Self-Calibration: Exact Evidence Budgets and Manufactured Blind Sets in Adaptive Monitoring

Abdou-Raouf Atarmla

Self-calibrating monitors adapt their threshold online to guarantee a prescribed long-run false-alarm rate under arbitrary drift. We compute the price of that guarantee, stating every law with its exact domain of validity. First, the guarantee is an accounting identity, insensitive to what the monitor is meant to detect. Two evidence identities make the cost exact for the online quantile tracker: a persistent step of height $δ$ yields excess alarm mass within one alarm of $δ/η$, and exactly $δ/η$ pathwise when $δ$ is a lattice multiple of the gain $η$; a ramp of slope $c$ yields a stationary excess rate of exactly $c/η$, independent of accumulated size, up to a boundary $c=η(1-α)$ coinciding with the alarm-rate cap. Second, the certificate's own fluctuation obeys an exact law: the windowed alarm rate has standard deviation of order $1/L$, not the binomial $1/\sqrt{L}$, since the windowed mass telescopes to a difference of a tight internal state; the closed-form constant is validated with no fitted parameter. Detectors calibrated on the binomial scale are miscalibrated by $\sqrt{η\varphi(q_0)L}$, and correct calibration turns detection windows from quadratic to linear in the…