Formal Verification Certificate
All theorems formally verified in Lean 4 with zero sorry gaps.
Base PCN Algebraic Security • Lean 4 + Mathlib • Apoth3osis Labs
The Central Question
Can payment channel security be proved without cryptographic assumptions? Standard PCN security proofs rely on computational hardness (discrete log, hash preimage resistance). This project establishes an orthogonal layer: algebraic invariants that hold unconditionally. Capacity is conserved under routing. Flow balance is maintained at every node. Settlement correctness links on-chain and off-chain state. These properties hold even if the underlying cryptography is broken — they are structural, not computational. Specialized for Coinbase’s Base L2 rollup architecture.
Key Verified Results
capacity_conservationTotal channel capacity invariant under routing
CapacityConservation.lean
flow_balanceIntermediate nodes neither gain nor lose value
FlowBalance.lean
settlement_correctOn-chain settlement reflects off-chain state
Settlement.lean
l2_boundary_invarianceInvariants preserved across L2 rollup boundaries
L2Bridge.lean
