Please don't let this be an LLM. Please don't let this be an LLM. It's the only comment here that is worth responding to.
What I really appreciate about Rene’s work is that it pushes Lightning Network discussion into a more rigorous mathematical space. Too often, conversations get trapped in either anecdotal experience or surface-level technical chatter without probing the structural limitations in detail. By framing payments as shifts in wealth distribution across a constrained topology, Rene is essentially giving us a mental model for why certain payments fail before they even have a chance to propagate. That is a more fundamental insight than simply observing failed transactions in the wild.
Absolutely agree.
The point about multi-party channels is particularly important. If you care about Lightning reliability you cannot just tune fees or routing algorithms in isolation. You have to reconsider the architecture itself. Multi-party channels are not just a scaling trick; they alter the feasible state space of the network and that directly changes the economic behavior of participants.
Agree again. But I would go further and say multi-party channels are the only effective mitigation he offers in the paper. The other two (batch settlement and taming depletion) do not solve the bottleneck problem. Section 5.2 proves that for sparse two-party networks, the expected cut size scales with the average channel capacity. So if you want to increase network throughput without changing the protocol, increase the average channel size. While this is mathematically true, it is operationally useless.
That said, the critique about endogeneity of topology is spot on. In the real world channels do not exist in a vacuum. Operators will strategically open and close them in response to routing opportunities and this dynamic element needs to be incorporated into modeling if the ultimate goal is predicting reliability. In economics we often deal with systems where network formation is itself part of the equilibrium and Lightning is no different.
From the paper:
"Given the current incentives in the network, depletion is an emergent phenomenon even in a circular economy when all payments are net-zero. The existence of infeasible payments and depletion are consequences of the geometry of cuts and cycles under the given current protocol design. They are neither software bugs nor necessarily the consequence of poor node operator behavior."
Translation: Economically rational operator behavior will not fix depletion nor infeasible payments. See also
Aside: I would consider it a software bug. Surely LL intended to design a scalable offchain protocol.
If Rene’s framework could be expanded to include adaptive topology, it would bridge the gap between theoretical feasibility and the evolving reality of Lightning.
From the paper: "every infeasible payment needs at least one on-chain transaction to change the topology of the network"
Your line of reasoning sidesteps the real issue that topology changes are a response to infeasible payments i.e. not a solution. When payments are infeasible, the network is forced to adapt its topology. This behavior can be framed as self-repair, but it can just as accurately be described as damage caused by misaligned incentives. Wouldn't the more meaningful goal be to reduce the rate of infeasible payments?
Please don't let this be an LLM. Please don't let this be an LLM. It's the only comment here that is worth responding to.
Absolutely agree.
Agree again. But I would go further and say multi-party channels are the only effective mitigation he offers in the paper. The other two (batch settlement and taming depletion) do not solve the bottleneck problem. Section 5.2 proves that for sparse two-party networks, the expected cut size scales with the average channel capacity. So if you want to increase network throughput without changing the protocol, increase the average channel size. While this is mathematically true, it is operationally useless.
From the paper:
"Given the current incentives in the network, depletion is an emergent phenomenon even in a circular economy when all payments are net-zero. The existence of infeasible payments and depletion are consequences of the geometry of cuts and cycles under the given current protocol design. They are neither software bugs nor necessarily the consequence of poor node operator behavior."
Translation: Economically rational operator behavior will not fix depletion nor infeasible payments. See also
Aside: I would consider it a software bug. Surely LL intended to design a scalable offchain protocol.
From the paper: "every infeasible payment needs at least one on-chain transaction to change the topology of the network"
Your line of reasoning sidesteps the real issue that topology changes are a response to infeasible payments i.e. not a solution. When payments are infeasible, the network is forced to adapt its topology. This behavior can be framed as self-repair, but it can just as accurately be described as damage caused by misaligned incentives. Wouldn't the more meaningful goal be to reduce the rate of infeasible payments?