CVE-2026-72711: The Lean 4 kernel does not check that the body of an opaque declaration is closed.

The Lean 4 kernel does not check that the body of an opaque declaration is closed.

The Lean 4 kernel does not check that the body of an opaque declaration is closed. environment::add_opaque omits the check_no_metavar_no_fvar call that the definition and theorem paths perform, so a value containing a free variable that is absent from the local context is not rejected outright. A metaprogram can first cause the kernel to create a temporary local of type False and record its type in the type checker's inference cache, then restore the local context while that cache entry persists on the same type checker instance, and finally submit an opaque declaration whose value is the now-unbound variable. The cache lookup answers before the branch that would test membership of the local context, so the kernel infers the cached type and admits an opaque constant of type False, from which any proposition follows. The declaration is accepted through the ordinary checked path at maximum kernel checking, without sorry, unsafeCast, debug.skipKernelTC, addDeclWithoutChecking, foreign code or a modified .olean file, and the result carries no axioms. Fixed in 4.32.2 by adding the missing closure check.

Description from the National Vulnerability Database, published by VulnCheck

What it means for a small business

If your business uses lean4, install the vendor's update. If you're not sure whether you use it, ask whoever manages your computers.

How likely is an attack? The Exploit Prediction Scoring System, run by FIRST (the global association of security response teams), puts the odds of this one being exploited in the next 30 days at 0.18%, higher than 7% of CVEs. That’s low, but low isn’t zero, and the odds jump the day someone publishes an exploit. Scored October 29, 2026, updated daily.

Check your own setup

Website check: reads what your site runs from the outside (WordPress version, plugins it can see, old server software) and matches it against this database.
Server check: what your web server says about itself, and whether that version has known flaws.

Sources

Part of the Huttenlocher Technologies vulnerability database, refreshed twice a day from CISA and the NVD. The title, category and plain-language guidance are ours; check the linked record before acting on a detail. This is general guidance, not a review of your systems.

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