Coalescing Force of Group Pressure: Consensus in Nonlinear Opinion Dynamics

The paper’s Theorem 1 states exactly the three claims (divergent sum of p*(t) implies consensus; uniform lower bound implies exponential contraction; p*(t0)=1 implies termination) and proves them via (i) nested convex hulls, (ii) the one-step diameter contraction R(t+1) ≤ (1−p*(t))R(t), and (iii) a compactness/intersection argument; the candidate solution follows the same structure and inequalities, adding only a brief justification that diam(conv S)=diam(S). These steps and conclusions coincide with the paper’s Steps 1–3 and Theorem 1 statements.