2025/10/24 by Aghanya, Nnamdi Daniel, Leemans, Romain
#03B70 #05C20 #68Q85 #91D30 #C.2.4 #Distributed #F.4.1 #FOS: Computer and information sciences #G.2.2 #Parallel #Social and Information Networks (cs.SI) #and Cluster Computing (cs.DC)
paper · doi:10.48550/arxiv.2510.21950
We study Heaven-Hell dynamics, a model for network consensus. A known result establishes an exact one-step convergence threshold for systems with a single uniform hub: the per-node inbound hub weight W suffices if and only if W >= maxrest, the maximum non-hub inbound mass. We develop scale laws and operational refinements that make this threshold robust to tie-breaking policies, node-specific tolerances, targeted seeding, multiple hubs, and asynchronous updates. Our contributions include a conservation-law perspective, parameterized tie policies, tighter pointwise bounds improving on classical worst-case guarantees, one-pass fairness for asynchronous updates, and sufficient conditions for seeded convergence. All proofs are mechanized in Coq, with experiments on rings, grids, scale-free graphs, and heterogeneous weighted graphs validating tightness and gap closures