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Nov 20, 2025
Lighting on Bitcoin Photo by: Decrypt
Bitcoin researcher René Pickhardt has published a new paper that introduces a key idea about how the Lightning Network scales. The paper presents a simple equation:
S = ζ / ρ
This means that Lightning’s off‑chain payment capacity (S) depends on how many transactions can fit on‑chain (ζ), divided by how often payments fail (ρ). If failures are frequent, the system relies more on Bitcoin’s base layer, which is limited. So, unless payment failures are rare, Lightning’s ability to scale stays tightly capped by how much Bitcoin can handle on-chain.
Payment “failures” here include any situation where a payment can’t be completed because the path doesn’t have enough funds, or the channels are unbalanced. When that happens, a transaction often needs to go on‑chain to fix it, consuming block space and time.
This is where the paper makes an important point: today’s Lightning uses mostly two-party channels — one user connected to another. But Pickhardt argues that multiparty setups like channel factories or coinpools can help significantly. These let more users share liquidity across fewer on‑chain transactions, making the network more connected and resilient.
In simple terms, multiparty channels reduce the chance that a payment will fail, meaning fewer trips to the blockchain and more scalability. Developers have discussed these tools as helpful features, but this paper suggests they may be fundamental building blocks if Lightning is to grow and support more users reliably.
This shifts the focus from just improving routing or balancing to thinking more deeply about Lightning’s structure. If the Bitcoin base layer is scarce, then reducing payment failures through smarter channel design becomes the key to true scalability.