{"id":"palomar/PALOMAR-2026-10-14-000005","url":"https://github.com/JD-Jones-ASES/hk-heterogeneous-lean/tree/c2d4c0b790210870f2818fc52a1c572937644a4b","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-14-000005-v1.json","repo":"https://github.com/JD-Jones-ASES/hk-heterogeneous-lean","tags":["math.DS","math.CO","msc:39A60","msc:93A14","msc:91D10","msc:91D30","opinion-dynamics","dynamical-systems","lean"],"score":0,"title":"Heterogeneous Hegselmann–Krause dynamics: counterexamples to two conjectures and a theorem of Mirtabatabaei and Bullo","trust":"high","domain":"math.DS","source":"palomar","authors":["JD Jones"],"reviews":0,"subject":"math.DS","summary":"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;…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-14","reactions":{},"formalized":true,"formalizes":[{"title":"Non-freezing of the proximity digraph and non-pseudostable convergence in heterogeneous Hegselmann--Krause models: Counterexamples to conjectures and results of Mirtabatabaei and Bullo","identifier":"https://arxiv.org/abs/2610.03229","relationship":"formalizes"},{"title":"Opinion Dynamics in Heterogeneous Networks: Convergence Conjectures and Theorems","identifier":"doi:10.1137/11082751X","relationship":"adapts"}]}