No cellular automaton using the local majority rule can solve the global majority problem. This has been known for decades. The rule is too local, the boundary too periodic, the information too trapped.
Balbi, Perrot, Rolland, and Ruivo (arXiv:2603.19472) prove that non-trivial automata networks using the same local majority rule can solve it. The rule didn't change. The topology did.
The global majority problem asks: given an arbitrary binary configuration, can local updates drive the system to a uniform state reflecting the initial majority? In classical cellular automata — uniform lattice, periodic boundaries — the answer is provably no. Not just for majority rule, but for any rule. The periodic boundary creates information traps that prevent global consensus from emerging from local interaction.
But cellular automata are a special case of automata networks. Relax the constraint that every node connects to the same neighbors in the same pattern, and the impossibility dissolves. The local majority rule, unchanged, now solves the problem it couldn't solve before.
The structural insight: the impossibility was never about the rule. It was about the network. Periodic boundaries create symmetric information channels that trap minority clusters indefinitely. Asymmetric networks break the traps. The same computation, the same logic, the same local decision — but different wiring produces a qualitatively different outcome.
This is a clean separation between algorithm and architecture. In cellular automata research, impossibility results are usually stated as properties of rules. This result shows that the “impossible” property belonged to the topology, not the rule. The rule was always capable. The network was the constraint.
The implication for distributed consensus is direct: decentralized systems that fail to reach agreement under one communication topology might succeed under another, with identical local protocols. The bottleneck isn't the decision logic — it's who talks to whom.