Heterogeneous Hegselmann–Krause dynamics: counterexamples to two conjectures and a theorem of Mirtabatabaei and Bullo
A Lean 4 development of the counterexamples of Hegarty, Ognissanti and Wedin (arXiv:2610.03229) to two conjectures and a theorem of Mirtabatabaei and Bullo on heterogeneous Hegselmann–Krause dynamics. n agents with real opinions and positive bounds r_1, ..., r_n update synchronously, x(t+1) = A(x(t)) x(t), where row i of A(y) averages uniformly over the neighbourhood N_i(y): the j with |y_i - y_j| <= r_i in the SBC model (synchronized bounded confidence) and <= r_j in the SBI model (synchronized bounded influence). Conjecture 2.2 says the proximity digraph is constant after a finite time;…
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