# CVE-2026-72711: Lean 4 before 4.32.2 Kernel Accepts Opaque Declaration With an Unbound Free Variable

> Attackers can exploit a kernel logic flaw in Lean 4 to prove false statements, undermining the system's logical consistency and trustworthiness.

- **Severity:** Medium 6.8 (`CVSS:4.0/AV:L/AC:L/AT:N/PR:N/UI:P/VC:N/VI:H/VA:N/SC:N/SI:N/SA:N`)
- **Exploited in the wild:** Not known
- **Login needed:** Not needed
- **Attackable:** Local or same network only
- **Victim action needed:** A user has to click or open something
- **Fix available:** No
- **Published:** 24 Aug 2026
- **Updated:** 26 Oct 2026
- **Also known as:** GHSA-fhmq-xvc2-q54h

## What is CVE-2026-72711?

CVE-2026-72711 is a medium-severity vulnerability in leanprover lean4, published on 24 Aug 2026. It can only be exploited from the same machine or local network, and only if a user opens a file or follows a link.

### Official description

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.

Weakness: CWE-20 (Improper Input Validation)

## Which versions are affected by CVE-2026-72711?


## How do I fix CVE-2026-72711?

No fix has been published for CVE-2026-72711 yet. Limit exposure of the affected software until one is available.

## Is CVE-2026-72711 being exploited?

It is not confirmed as exploited in the wild, but public exploit code for CVE-2026-72711 exists.

Public exploit code:

- CVE-2026-72711 — Lean 4 Kernel Soundness Bug: Inference Cache Poisoning (github_poc): https://github.com/endrazine/lean-cve-poc-14484

## Fix prompt for AI coding agents

```text
Check this codebase for CVE-2026-72711 and fix it if it is affected.

What it is: CVE-2026-72711 is a medium-severity vulnerability in leanprover lean4, published on 24 Aug 2026. It can only be exploited from the same machine or local network, and only if a user opens a file or follows a link.
Exploitation: It is not confirmed as exploited in the wild, but public exploit code for CVE-2026-72711 exists.

Affected product: leanprover lean4. No package-level version data is available, so check the vendor advisory linked from the reference page.

Task:
1. Search the dependency manifests and lockfiles (for example package.json, package-lock.json, requirements.txt, poetry.lock, uv.lock, pom.xml, build.gradle, go.mod, Cargo.lock, Gemfile.lock) and any Dockerfiles for the affected packages, including transitive dependencies.
2. If an affected version is in use, upgrade it to the fixed version for its release line with the project's package manager, so the lockfile is regenerated. Prefer the smallest upgrade that fixes it.
3. If there is no fix, or the upgrade would break the build, do not guess: explain the risk and the safest workaround instead.
4. Run the tests and summarise what changed and why.
5. If nothing in the project is affected, say so and change nothing.

Reference: https://insights.sbomify.com/CVE-2026-72711/ (Markdown: https://insights.sbomify.com/CVE-2026-72711/index.md)
```

## Sources

- CVE record: https://www.cve.org/CVERecord?id=CVE-2026-72711
- NVD: https://nvd.nist.gov/vuln/detail/CVE-2026-72711
- OSV: https://osv.dev/vulnerability/CVE-2026-72711

---
From sbomify Insights: https://insights.sbomify.com/CVE-2026-72711/
Summaries are generated and may contain mistakes; the official description above is the record.