Apoth3osis
<_RESEARCH/PROJECTS

Base PCN Algebraic Security

VERIFIED0 SORRY5 MENTAT CERTSLean 4 + Mathlib
>_VERIFICATION.SEAL
FORMALLY VERIFIED • LEAN 4 • MACHINE-CHECKED • APOTH3OSIS¬QED0 SORRY

Formal Verification Certificate

All theorems formally verified in Lean 4 with zero sorry gaps.

0 SORRY

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_conservation

Total channel capacity invariant under routing

CapacityConservation.lean

flow_balance

Intermediate nodes neither gain nor lose value

FlowBalance.lean

settlement_correct

On-chain settlement reflects off-chain state

Settlement.lean

l2_boundary_invariance

Invariants preserved across L2 rollup boundaries

L2Bridge.lean