What the reference describes.
Lean is a proof assistant and a functional programming language. It is based on the calculus of constructions with inductive types (specifically, the Calculus of Inductive Constructions), the foundational type theory developed with the Coq theorem prover, which was renamed to Rocq in 2024. It is a free and open-source software project hosted on GitHub. Development is currently supported by the nonprofit Lean Focused Research Organization (FRO).
What the process still cannot guarantee.
The presence of Lean code can be mistaken for an independent certification of the intended mathematics.
That is a design criticism of how this research operation may be used, not a claim that the encyclopedia endorses the limitation. In this domain, the general redesign question is: mathematical, computational and semantic validation are separated into independent trust layers.
Replace the mechanism.
Pin exact statements, packages, kernel trust and informal-to-formal correspondence checks.
Implementation requires a typed scientific claim, explicit operational definitions, controlled access to evidence, an immutable record of relevant transformations, and independent checking appropriate to the kind of assertion. An AI-generated interpretation without those checks would reproduce the underlying failure at greater speed.
What would demonstrate improvement?
Audit theorem statements for changed quantifiers and hidden added hypotheses.
Compare with a defined baseline under matched resources, keep evaluation cases independent of the system under test, and measure both false alarms and undetected errors. Publish any negative or inconclusive result as part of the same investigation record.
Continue across concepts.
Each related title has its own revision-specific Wikipedia source and a separate critical dossier. Crosslinks are exploratory; they do not imply the encyclopedia articles support the proposed replacement.
No single authority.
The reference article establishes the historical and methodological subject under examination. The proposed criticism and replacement must earn their own support through reproducible tests and independent validation. Record disagreements instead of silently overwriting them.
Current Wikipedia article ↗ · Exact reference revision ↗ · Complete source ledger ↗