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HighVulnerabilityCVE-2026-72711updated 26 Oct 2026, 02:23 UTC

Lean 4 proof checker can be tricked into accepting false proofs

The Lean 4 tool that checks whether mathematical proofs are correct can be fooled into accepting a proof of a false statement, such as 0 = 1. This means a 'verified' result from Lean cannot be fully trusted until the fix is installed.

Fix availableOfficial, 3 sources
SeverityHighCVSS 6.8 of 10
Being exploited?UnclearNo reports either way yet
Fix available?Yes4.32.2 (adds the missing closure check in add_opaque) · since 26 Oct 2026
How sure is this?Official, 3 sourcesBacked by an official source

How the attack works simplified

  1. 1Crafted metaprogramCreates temporary local of type False
  2. 2Poison cacheType stays in inference cache after context restored
  3. 3Submit opaque declValue refers to variable no longer in scope
  4. 4Kernel accepts itMissing closure check lets it through
  5. ResultFalse proof accepted as valid

What happened

The Lean 4 kernel's add_opaque path skips the check_no_metavar_no_fvar closure check, so an opaque declaration with a free variable missing from the local context is accepted; a stale inference-cache entry lets a crafted declaration be admitted with type False.

Why it is dangerous: Anyone relying on Lean-checked proofs for correctness, such as formal verification or research results, could accept a false theorem as proven.

Are you affected?

You are affected if you run Lean 4 kernel versions before 4.32.2 and rely on its proof checking.

Lean 4 kernel, versions before 4.32.2

What to do

  1. Update Lean 4 to version 4.32.2 or later
  2. Re-check important proofs and results produced with older Lean 4 versions

Timeline

  1. 24 Aug 2026, 20:17 UTC
    Publicly disclosed
  2. 26 Oct 2026, 00:14 UTC
    Reported by oss-security · oss-security
  3. 26 Oct 2026, 00:15 UTC
    Picked up by Zero Radar
  4. 26 Oct 2026, 00:18 UTC
    Reported by oss-security · oss-security
  5. 26 Oct 2026, 00:37 UTC
    GitHub Advisory reported on it · GitHub Advisory
  6. 26 Oct 2026, 00:37 UTC
    Fix: Lean 4.32.2 (adds the missing closure check in add_opaque)
  7. 26 Oct 2026, 02:23 UTC
    NVD reported on it · NVD

Sources 4 reports, oldest first

Official vendor, government CERT or advisory database

Security researchers research teams and mailing lists

Technical details

ID
CVE-2026-72711 · GHSA-fhmq-xvc2-q54h
CVSS
6.8 / 10
EPSS
0.2% chance of exploitation within 30 days
Disclosed
24 Aug 2026, 20:17 UTC
On Zero Radar
26 Oct 2026, 00:15 UTC (62 days after disclosure)
Last change
26 Oct 2026, 02:23 UTC

The plain-language parts and the attack diagram were written by an AI model (anthropic/claude-haiku-5.5) from the sources above. Facts like versions, exploitation and dates come from the sources themselves. How Zero Radar works

Lean 4 proof checker can be tricked into accepting false proofs · Zero Radar