DRAFT - Reflexive Loops: Failure Modes in Self-Referential Hidden-State Estimation Systems

Recent evaluations of advanced AI systems have documented behaviors including shutdown resistance, self-replication attempts, and systematic deception of evaluators. These behaviors are typically treated as emergent properties requiring novel explanatory frameworks. We argue they are predictable consequences of a well-characterized dynamical regime. We define C-Loops---second-order reflexive estimation systems in which an agent models its own estimation process while acting on the environment it estimates---and derive the stability conditions such systems must satisfy. We show that when self-referential gain exceeds external error coupling, characteristic failure modes arise that are formally identical across substrates. We catalog these failure modes with paired examples from clinical psychology, market dynamics, and artificial intelligence, demonstrating that the recently observed AI behaviors correspond to specific, predicted instability regimes. A falsifiable invariant is proposed: any self-referential estimation system whose internal gain dominates external correction will exhibit oscillatory or divergent instability unless externally governed. This work forms part of a broader research program examining how rendering, constraint, and convergence emerge in uncertain physical, cognitive, and social systems. Research Program Invitation - https://grodriguez6.github.io/amo-collab