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Artificial intelligence

AI can produce checkable proofs; the specification still determines what they establish

New releases from Anthropic, OpenAI and Axiom make AI-generated reasoning more inspectable, while exposing the difference between checking a formal statement and establishing its real-world meaning.

188 words · 1 min

Anthropic’s October 22 collaboration with Theorem reports proofs for selected executable artifacts across 123 open-source libraries.

The guarantees concern modeled RISC-V programs and specified failure conditions, with inputs below 64 MB. They do not certify entire libraries, all memory errors, or the x86 and ARM environments where much of this software actually runs. The public repository currently lists 61 proved entry points in 26 libraries—a released subset of the larger reported effort. [1][2]

OpenAI’s October 26 release takes a related idea into research mathematics: it publishes natural-language arguments and Lean artifacts for claims concerning local smoothing and the Exponential Time Hypothesis. The company is organizing external academic examination, and calls the manuscripts raw research material. Its mathematical output was generated October 18 and formalized October 19; the complexity-theory output dates to October 16–17. Those research dates remain separate from publication. [3][4]

Axiom’s October 26 announcement concerns formalizing an existing mathematical achievement: the classification of finite simple groups. It reports a 24-day effort involving mathematicians, engineers and agent teams, producing about 43.1 million Lean lines. That scale describes the project; it is not an independent measure of correctness or scientific importance. [5]

Take it further

Inspect the released software-proof coverage and assumptions For engineering teams selecting a narrow verification target. The repository lists covered entry points, assumptions and check instructions; the public subset is smaller than the 123-library report.

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Reporting sources

  1. Anthropic · Formal software verification

    October 22, 2026. Author report; modeled executable properties and explicit exclusions.

  2. Theorem · Released OSS Verify proofs

    Live repository inspected October 28: 61 entry points in 26 libraries; Rocq 9.2.0. Artifact scope inspected; proofs not rebuilt.

  3. OpenAI · Academic collaborations and research release

    October 26, 2026. Claims and original output dates distinguished; physics artifacts deferred.

  4. OpenAI math · Formal scope of the ETH claim

    The released formalization’s stated encoding and asymptotic bounds; not an independent proof audit.

  5. Axiom · Formalizing the Enormous Theorem

    October 26, 2026. Author account of Lean formalization and human specification review.

  6. Axiom · CFSG proof map

    Public map and proof-release navigation inspected; no independent rebuild performed.

  7. Theorem · Modeled Linux semantics and limits

    Separate technical artifact checked after the barrier; same project, not independent replication.

Images & figures

  • AI-generated editorial illustration. Precisely interlocking bridge blocks and a measuring square; conceptual editorial illustration of formal dependencies and the specification that gives them meaning.

    Euangelion · Source · Usage terms