Capital

Full mesh, sweet spot

Crypto is global, so the default is 0% intra-hub — every payment can leave the hub. Raise intra-hub % to model regionalization: local traffic stays on the spoke book, and the sweet spot moves to fewer, larger hubs.

Customers (P)10.0BSpoke / customer (S)$3,000Mesh / link (M)$1.0MIntra-hub %0% intra

R* routers: 5K
Capital / router at R*: $11.0B
Customers / router: 1.8M
Inter-hub fraction α: 100%
Total system capital: $46.8T

Spoke = PS / R
Inter-hub spoke = αPS / R
Mesh = RM
Total = PS/R + RM
R* = √(αPS/M)

α = 1 − intra% · R* = √(αPS / M) · αPS/R = RM at R*

Each hub keeps spoke channels to its customers and a payment channel to every other hub. At 0% intra, α = 100% and spoke = mesh at R*. Intra-hub payments never hit the mesh — only the remainder (α) does. The receiving hub deposits 3N on hop 2, so a payment cannot exceed one third of the link. Larger than that is done on-chain.