Post-Decentralization H; From Linear Scaling to Percolation Transition-A Structural Interpretation of Layer 2 Scalability

Abstract

Layer 2 scaling solutions—including payment-channel-based Lightning Networksand rollup-based off-chain execution environments—are commonly understood aslinear scaling projects for blockchain transaction throughput. This paper proposesan alternative structural interpretation: the emergence of Layer 2 is not a continuous increase in system capacity, but a percolation phase transition that occurswhen the density of off-chain channels or cross-rollup connections crosses a critical threshold. During this phase transition, the system shifts from a fragmentedlocally connected state to a globally routable giant connected state. The paperanalyzes the Lightning Network and the rollup ecosystem as comparative cases.Empirical studies of the Lightning Network show that its scale-free topology forcescritical hub nodes to bear a disproportionate connection load, thereby binding thenetwork’s global connectivity to the survival of a few high-centrality nodes. Therollup ecosystem faces the structural predicament of liquidity fragmentation, and itsevolution toward cross-rollup interoperability likewise exhibits a phase-transitionlogic from quantitative change to qualitative change in network effects. Based onthe above analysis, this paper distills three design principles for Layer 2 scalability:facilitating the institutionalization of cross-domain connections, avoiding overlyhomogenized cognitive convergence, and implementing differentiated verificationrouting among tasks with different security requirements.