Two processes that answer different questions
Lean proof verification asks whether an encoded proposition follows within a formal environment and trust base. Mathematical peer review asks experts to critically assess a submitted work for an editorial venue. Peer review may consider significance, exposition, originality and mathematical reasoning, but its exact process varies; it should not be assumed to include code execution, axiom inspection or kernel replay.
| Process | Main question | Typical evidence | Boundary |
|---|---|---|---|
| Lean kernel checking | Does this proof term have the claimed formal type? | Source, declarations, imports, proof term and kernel acceptance | Does not establish that the type matches the paper’s intended claim. |
| Independent Lean artifact audit | Can the exact target be rebuilt, inspected and replayed, and what does it correspond to? | Frozen versions, build logs, theorem identity, axiom closure, replay and correspondence analysis | Limited to accepted scope, artifacts and checks actually performed. |
| Mathematical peer review | Should this submission be accepted, revised or rejected under a venue’s standards? | Expert reading, referee reports, author revisions and editorial judgment | Process varies and does not automatically include formal or computational verification. |
Where they overlap
Both can challenge definitions, assumptions and conclusions. A careful referee may find a formalization mismatch; a formal audit may identify an unsupported informal consequence. Neither label tells you which checks actually occurred. The record must do that.
When to commission both
Use both when a central theorem has a formal artifact and the broader paper also depends on novelty, mathematical interpretation, exposition or consequences outside that artifact. Formal verification can provide unusually precise evidence for a target; peer review can assess the larger scholarly contribution. The two records should cross-reference the same version and preserve disagreements.
Sources and further reading
- Lean Reference: Validating a Lean Proof
- ICMJE: Responsibilities in the submission and peer-review process
- American Mathematical Society: Communications of the AMS review description
Authorship and relationship disclosure
Original article author and publisher: Haivian Technology, a brand of Qonduit Limited, New Zealand. This is AI-assisted company editorial work. Haivian sells research-audit services and publishes the Validation Journal under common organizational control. “Third-party” describes Haivian’s relationship to a research producer only where Haivian did not produce the audited research; it does not mean external journal peer review, institutional accreditation or independent human-expert certification.
Scope, source versions and trust assumptions determine every finding. An optional audit-to-publication pathway is separately assessed and does not guarantee publication or a favourable result.