PCN Feasibility
Machine-checked Lean 4 formalization of Pickhardt's payment channel network feasibility theory. Wealth constraints, cut capacity bounds, Hall completeness for multi-path payments, rebalancing invariance, and EVM seam for on-chain settlement. 42 modules, 0 sorry.
Formal Verification Certificate
Every theorem in this project has been machine-checked by the Lean 4 kernel. No axiom is assumed without proof. No gap exists in the verification chain.
PCN Feasibility • Lean 4 + Mathlib • Apoth3osis Labs
Key Mathematics
Wealth Feasibility
Lean: node_wealth, wealth_feasible
Cut Capacity
Lean: cutCapacity, cut_completeness
Rebalancing Invariance
Lean: rebalancing_invariance, total_capacity
Paper ↔ Proof Correspondence
| Claim | Theorem | Status |
|---|---|---|
| Wealth feasibility: sender has sufficient capacity | wealth_feasible | ✓ |
| Cut capacity bounds maximum flow | cutCapacity | ✓ |
| Total capacity invariant under rebalancing | rebalancing_invariance | ✓ |
| Hall condition for complete feasibility | hall_completeness | ✓ |
| Cut completeness characterization | cut_completeness | ✓ |
| EVM seam: on-chain settlement correctness | seam_theorem | ✓ |
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