Self-Poisoning in Adaptive Out-of-Distribution Detection: A Sharp-Threshold Theory and Certified Label-Free Calibration

arXiv:2607.21673v1 Announce Type: cross Abstract: Test-time adaptive out-of-distribution (OOD) detectors update a memory bank from the unlabelled stream. We show this adaptation obeys a provable dynamical law. Modelling bank impurity as a generalized P\'olya urn, we prove almost-sure convergence to a mean-field equilibrium whose slope acts as a reproduction number. Below one, impurity stays benign. Above one, the bank is fully poisoned and the detector collapses. The measured admission kernel is affine ($R^2 \ge 0.996$) with slope just below one in every encoder family (a protocol signature),