OpenAI says its unreleased internal 'Astra' model posted proofs to 10 open math and CS problems

OpenAI says its internal, unreleased "Astra" model produced proofs to 10 open problems in math and theoretical computer science, a vendor proof drop that ships before the model does and before any independent check. The announcement pairs each result with a Lean 4 verification file and a narrated transcript of the model's reasoning, all built on a system OpenAI has not made available to outside labs.

The release extends a pattern that started in May 2026, when OpenAI published a model-generated disproof of a long-standing Erdős conjecture on unit distances in the plane on its own blog. This week's set is the larger sibling: ten problems across high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, operator algebras, quantum complexity, lattice cryptography, and extremal combinatorics, with a public repository of Lean 4 certificates backing each proof.

A few of the results carry enough weight that the math community will check them first. One is a disproof of Connes's rigidity conjecture, a statement about how operator algebras sit inside one another that has been open for half a century. Another is a polynomial-factor hardness-of-approximation result for the closest vector problem (CVP) on lattices, a problem at the center of post-quantum cryptography; a tighter lower bound here changes the floor that lattice-based encryption schemes have to clear. A third gives an arithmetic-formula lower bound of order n^4/log n for the permanent, a classical counting problem and a long-standing benchmark for how hard algebraic proofs can get. A fourth, posted by OpenAI's Sebastien Bubeck, asserts that nonsofic groups exist, settling a question that has split group theory for two decades. The remaining results include a superexponential lower bound for multicolor triangle Ramsey numbers, resolving Erdős problem 183, and counterexamples to two compactness and degeneracy conjectures that resolve Erdős problems 146 and 180.

The artifacts are designed to be checkable. A Lean 4 file is a piece of machine-checked code; if the proof compiles, the steps follow from the axioms Lean accepts. That is not the same as community acceptance or peer review. It means a human reader can run the file and either trust the derivation or find the spot where it breaks. OpenAI is leaning on that difference: the company's post explicitly references the Leiden declaration on AI and Mathematics, a community position paper that pushed for clearer attribution and process when AI-generated results enter the literature.

Several things are still missing. The model is internal, so other labs cannot run the same setup and watch the proof come out. The $2,000 total compute figure is stated at OpenAI's Sol API rates, which is the company's own pricing and not a market price. The X thread from OpenAI's Noam Brown frames the release as a single arc, and Wojciech Zaremba, an OpenAI co-founder, corroborated the headline. There is no independent expert quote in the source basis yet; the strongest external signal is a Hacker News thread where mathematicians and theorists are pushing on what "solved" means when the model has not shipped, and on the choice to publish ten results at once rather than through the normal review pipeline.

A reader can treat the announcement as one of three things. It is, at minimum, a category event: a frontier lab using proof drops to claim scientific-reasoning territory before its next model is out the door. It is, at best, a set of ten results that survive community checking and shift the state of the art in their subfields. It is, at worst, a packaging exercise wrapped around a research-quality proof assistant demo. The Lean files will tell which one within weeks, and the check that matters first is whether the Connes disproof and the CVP lower bound hold under independent scrutiny.