Opinion Flow Concentration: The Phase-Transition Dynamics of Continuation Flows on Topic Paths in the Social Field

Drawing on sedimentation field dynamics, this paper redefines public opinion from an aggregation of views to a phase-transition structure of continuation flows on topic paths within the social field. The central claim is that when the opinion flow concentration intensity (OpinionFlow) of a topic path exceeds the critical threshold θ_opinion, a positive feedback mechanism is triggered and continuation flows accelerate their convergence to form a self-organizing opinion structure; θ_opinion ∝ φ_{F_S} / K_{F_S}, so in solidified social fields the concentration threshold is lower and public opinion more easily erupts. The paper derives the complete dynamic equation for concentration (incorporating the concentration seed Seed, saturation constraint, and threshold-activated suppression effect), identifies three forms of concentration (event-driven, accumulative, suppression-induced), and establishes three theorems: (1) Opinion Concentration Formation Tendency Theorem — under conditions of Familiarity asymmetry and non-zero Seed, the system systematically tends toward concentration formation; (2) Concentration Argument-Resistance Theorem — a single individual field’s logical argument cannot break an established concentration; an alternative topic requires Shock exceeding T_replace(T) to trigger genuine topic replacement; (3) Suppression Rebound Theorem — suppression below the replacement threshold triggers rejection and concentration returns in stronger form after suppression (the dynamical formalization of the Streisand Effect). The fundamental path to changing public opinion is not providing better arguments but changing the social field’s structural parameters or introducing a new topic event exceeding the replacement threshold.