Once the Door Swings Shut

Building on an existing account of how a dictator-to-be converts a society’s collective belief system from a normal to an artificial infosphere, the paper formalizes the mechanism as a onedimensional dynamical system with cubic nonlinearity. The paper proves two results. Proposition 1 classifies the full parameter space into exactly three qualitative regimes (guaranteed capture, guaranteed failure, and a bistable transitional regime) by explicit linearization at each equilibrium, and identifies the two bifurcation values that separate them. Proposition 2 shows that these bifurcation values are asymmetric: the capacity level required to initiate capture is strictly greater than the capacity level required to reverse an already-captured society: a hysteresis theorem giving precise mathematical meaning to the earlier claim that “reinforced loops of acceptance” make a distorted collective mindset resistant to reversal even after the conditions that created it have partly receded.