The Teacher Problematic: A Companion Record on Failure—Where the Homeostatic Boundary Fails

AbstractThis companion record formalizes the Teacher Problematic within the HomeostaticConvergence framework: the principled impossibility of knowing whether a regulatoryboundary model succeeds until it fails. Rather than treating this as a methodologicalweakness, we present it as a necessary epistemic feature of learning, adaptive, and safety-critical systems. We document classes of systems, perturbations, and boundarytopologies in which the Homeostatic Boundary Integral (HBI) fails to predict coherencepreservation, and where the Homeostatic Drift Integral (HDI) either saturates too late,misidentifies the failure mode, or becomes unobservable. By publishing these negativeand null results, we aim to prevent overgeneralization, resist institutional capture, andpreserve the framework’s core safety property: failure visibility. This record should be read as a complement to Homeostatic Convergence: Conservative Field Theory as a Unifying Framework for Quantum Coherence, Biological Vitality, and AI Safety (v2.0), and cited alongside it when applying the framework in safety-critical contexts.