CVE-2026-72844: CVE-2026-72844: The Lean 4 kernel does not verify that the structure named in a projection expression matc…

What it is

The Lean 4 kernel does not verify that the structure named in a projection expression matches the type of the value being projected, and environment::add_inductive in src/kernel/inductive.cpp did not type check the nested inductive applications that are replaced by auxiliary types, so their parametric arguments escaped checking. A metaprogram running in the Lean process can register an ill-typed nested inductive whose constructor applies a .proj C 0 projection to a value of the unrelated type W, and the kernel admits the declaration through the ordinary checked addDecl path at maximum kernel checking, without sorry, unsafeCast, debug.skipKernelTC, addDeclWithoutChecking, FFI, or a modified .olean file. The result is a type confusion yielding a proof of False that carries no axioms, from which any proposition can be derived. The published proof of concept additionally pads two expressions until their hashes and approximate depths collide, which defeats kernel caching; that is the technique used to reach the flaw, not its cause. Exploitation requires running a metaprogram in-process, for example by building a project or importing a malicious Lake dependency.

Exploitation evidence

First exploit evidence seen: 2026-08-20 (earliest date across the sources below).

Exploited in the wild

No source on this site lists in-the-wild exploitation yet (CISA KEV, VulnCheck KEV).

Public exploit code

GitHub proof-of-concept repositories

1 public repositories from 1 accounts, first seen 2026-08-20. Most starred: endrazine/lean-cve-poc (26 stars), view repository.

Verify before running: public PoCs can be malicious. Read the code and only run it in an isolated lab. A PoC means exploit code is public, not that this CVE is exploited in the wild.

Sources: nomi-sec/PoC-in-GitHub.

How to fix it

Fixed versions

NVD does not list a fixed version for this CVE. Use the vendor advisory below.

Derived from the NVD CPE configuration (versionEndExcluding / versionEndIncluding). Always confirm with the vendor advisory.

Vendor advisories and patches

No vendor-tagged reference yet; see the full reference list.

MITRE ATT&CK mitigations for this chain

• M1050 Exploit Protection (for T1203) : Security applications that look for behavior used during exploitation such as Windows Defender Exploit Guard (WDEG) and the Enhanced Mitigation Experience Toolkit (EMET) can be used to mitigate some exploitation behavior. Control flow integrity checking is another way to potentially identify and stop a software exploi
• M1051 Update Software (for T1203) : Perform regular software updates to mitigate exploitation risk. Keeping software up-to-date with the latest security patches helps prevent adversaries from exploiting known vulnerabilities in client software, reducing the risk of successful attacks.
• M1048 Application Isolation and Sandboxing (for T1203) : Browser sandboxes can be used to mitigate some of the impact of exploitation, but sandbox escapes may still exist. Other types of virtualization and application microsegmentation may also mitigate the impact of client-side exploitation. Risks of additional exploits and weaknesses in those systems may still exist.

Detection Generic guidance

• Execution: Watch for the service process spawning shells or script interpreters (cmd.exe, powershell, sh, bash, python) via EDR process-tree rules.

Response checklist Generic guidance

1. Inventory: find every instance of the affected product and version (include internet-facing and forgotten ones).
2. Patch or mitigate per the vendor advisory; if you cannot patch, remove internet exposure or apply the vendor workaround.
3. Assume compromise if the system was exposed before patching: hunt for the indicators in the advisory and review logs back to the disclosure date.
4. Rotate credentials and secrets stored on or used by the affected system if compromise cannot be ruled out.