The Autonomy of the Lightning Network: A Mathematical and Economic Proof of Structural Decoupling from BTC

Abstract

This paper presents a formal analysis of the Lightning Network as a monetary system structurally diverging from Bitcoin's base-layer settlement model. We demonstrate that under increasing transaction demand, BTC transaction fees rise superlinearly due to throughput constraints, while Lightning Network routing costs approach a bounded asymptote. Using mathematical modeling, game-theoretic proofs, and complexity analysis, we show that Lightning enables indefinite off-chain operation via the emergence of liquidity hub oligopolies. These hubs exhibit properties of unregulated financial intermediaries, including rent extraction, opacity, and systemic fragility. Strategic agent models show that channel closure becomes economically infeasible, and routing problems approach hardness limits in P-Space complexity. We conclude that Lightning does not merely extend Bitcoin, but constitutes a synthetic financial system with shadowbank characteristics, lacking reserve discipline, transparency, or enforceable settlement guarantees.