
“Program testing can be used to show the presence of bugs, but never to show their absence.”
Edsger W. Dijkstra, Notes on Structured Programming, 1970
Zero-knowledge systems and blockchain cryptographic protocols increasingly operate as production financial and computational infrastructure. Correctness failures can have significant security and financial consequences.
The team applies hard formal methods, protocol modeling, and interactive theorem proving to provide strong correctness assurances for production cryptographic systems. The team works closely with the Ethereum Foundation Protocol Cluster to secure the cryptographic foundations of the L1 proving transition.
The work spans across zk proof systems, zkVMs, protocol verification, execution semantics, and verification infrastructure for production blockchain systems.
Formal verification uses machine-checked proofs to demonstrate that systems behave according to formally specified correctness properties.
Subtle implementation errors, invalid constraints, verifier inconsistencies, or protocol-level failures may not be discoverable through conventional testing or security review alone.
Formal verification complements audits, testing, and security engineering by providing stronger assurances for systems where correctness requirements are unusually high.
Zero-knowledge systems
Cryptographic protocols
Blockchain execution environments
Distributed systems
The team works in established proof tooling and builds its own where the ecosystem has none.
Lean
Halo2
Plonky3
Circom
EVM / Yul
CLAP
CertiPlonk
Halva
Surveyor
ArkLib
Bluebell
The work spans zero-knowledge systems, cryptographic infrastructure, blockchain protocols, and execution environments.
Formal verification of zk proof systems, verifiers, and their implementations, including theFRI formalization in ArkLib and ongoing work toward STIR/WHIR.
Verification of circuit correctness and proving-system behavior across Halo2 and Plonky3, including CLAP, a Lean-based compiler carrying correctness assurances from source specifications to generated constraints.
Mathematical modeling and verification of blockchain protocols and distributed systems.
Reusable verification infrastructure, formal semantics, and theorem-proving tooling for Ethereum and zk systems.
Formal reasoning about smart contract execution behavior for systems requiring stronger correctness assurances. Built on the team's executable EVM and Yul semantics in Lean, the same reference model used for execution-level verification.
A significant portion of the work focuses on reusable verification infrastructure rather than one-off engagements. The team is building formal methods infrastructure for Ethereum and the broader ecosystem.
Every engagement is shaped around the specific properties, assumptions, and threat models of the target system. There is no template. The team works directly with each client to identify the correctness and security properties that matter most, then scopes a verification effort to those failure modes.
The methodology favors the strongest available techniques over the most convenient ones. Specifications are derived from deep technical discussions with teams rather than informal documentation.
The objective is a machine-checked proof, not confidence accumulated from test cases.
Representative verification work across zk systems, execution environments, protocol verification, and formal methods infrastructure.
First formal proof of honesty for a production zk verifier implementation using EasyCrypt.
EasyCrypt
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zkSync
Verification work across zkVM systems including SP1, Pico, and OpenVM.
Succinct
•
Brevis
•
Axiom
Formal semantics of the EVM and Yul in Lean for the Cancun hard fork, passing 99.99% of official Cancun execution tests.
Ethereum Foundation
•
ArkLib
•
Yul
First executable model of the FRI protocol in Lean, with formalization of STIR and WHIR in progress. Building formally verified implementations of these key cryptographic protocols to secure Ethereum during the L1 proving transition.
Ethereum Foundation
•
ArkLib
•
Axiom
Framework for extracting and formally verifying Plonky3 zk constraints in Lean without modifying developer workflows.
Plonky3
•
Lean
Lean-based infrastructure for verifying Halo2 circuits used in production zk systems.
Halo2
Lean-based zk circuit compiler carrying correctness assurances from source-level specificationsthrough generated constraint systems.
Aptos
•
Lean
•
zkDSLs
Formal verification of key security and correctness properties for the INTMAX2 protocol.
INTMAX
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Distributed Protocols
Formal verification is typically applied when systems require stronger correctness assurances than testing or audits alone can provide.
zk proof systems & zkVMs
Blockchain protocols
Cryptographic infrastructure
Execution environments
High-value smart contract systems
Systems secure significant value
Protocol correctness is foundational
Cryptographic assumptions are critical
Infrastructure dependencies expand
Failures are difficult to detect through testing alone
Formal verification research and infrastructure development across Ethereum and zk ecosystems.
Reusable zk verification infrastructure
zkVM verification systems
zk proof-system verification
Post-quantum cryptography
Probabilistic program logics
Contributions also include formalization efforts related to post-quantum cryptography and emerging cryptographic standards.
How formal verification differs from an audit, what it proves, and what an engagement produces.