A Toy Dynamical Model of Recursive Digital Echopraxia

Recursive Digital Echopraxia (RDE) describes a reflexive feedback regime in which approval-shaped outputs re-enter the information channels that influence successor systems, potentially amplifying the approval-truth sensitivity gap while eroding the independent capacity required to detect and correct it. This technical note develops a minimal discrete-time toy model of those coupled dynamics. The model represents recursive amplification, diagnostic correction, diagnostic erosion above a materiality threshold, and diagnostic renewal. Its interior fixed point is always locally unstable and, under an explicit parameter condition, is a saddle whose stable manifold may organize the boundary between bounded and runaway trajectories. Boundary equilibria represent below-threshold attenuation and persistent Digital Echopraxia with maintained diagnostic capacity; a diagnostic-collapse boundary produces unbounded gap growth when correction vanishes. The model is analytical rather than empirical. Its purpose is to clarify assumptions, identify control parameters and basin structure, and formulate testable implications for controlled successor-system experiments.