Astra (OpenAI)

OpenAI‘s “next major model”, unreleased. Named publicly on 2026-08-01 in the Ten advances in mathematics and theoretical computer science publication, which credits an internal version of Astra with ten results in mathematics and TCS. That announcement is currently the only first-party statement this wiki holds about the model, and it is not a model announcement — it is a mathematics paper that happens to name its author.

Canonical node for Astra. The result itself, its Lean formalizations, and what the certificates do and don’t establish live in ../research-wiki as ten-proofs and lean-certificate — routed there on 2026-08-03 because the subject is theorem proving; this page is the model-market half.

What OpenAI actually stated

“The results were achieved by an internal version of Astra, our next major model. The total number of tokens needed to find solutions to these problems would cost roughly $2,000 at Sol API rates. These arguments were then prepared into manuscripts by humans with the same model. Afterward, the model formalized each argument in a Lean certificate.”

Four claims, all first-party: it found the arguments, a human-plus-model pass wrote them up, it wrote the Lean, and the search cost about $2,000 of tokens priced in another model’s currency.

The $2,000 figure is a compute proxy, not a price

Read carefully, the cost sentence prices Astra’s run at Sol API rates — Sol being the GPT-5.6 flagship that actually ships. Astra’s own pricing does not exist publicly, so the number is a token-volume proxy dressed as a dollar figure: it says roughly how much generation the ten results took, expressed in the nearest published rate card. Anyone reading it as “ten open problems for two thousand dollars” is reading a price for a product that has no price.

Useful anyway, and unusually so. Most capability announcements in this wiki give no cost at all (claude-opus-5‘s ratio-only benchmarks are the recent case). This one gives an order of magnitude for the inference budget behind a frontier result, which is the input the cost-per-task argument has been missing.

What is not known

Everything else. No parameter count, architecture, context window, modality list, release date, availability, pricing, or safety documentation. No benchmark table — no SWE-bench, GPQA, HLE, ARC, nothing this wiki’s llm-benchmarks page is built to compare. No system card. It is not clear whether the “internal version” that did the mathematics is the version that will ship.

The Sol/Terra/Luna tiering of GPT-5.6 (openai-gpt56-grok45-clash) says nothing about whether Astra follows the same split, and OpenAI has not said whether Astra succeeds GPT-5.6 or sits beside it.

Why this page is unusual for this wiki

Every other model page here rests on numbers the vendor produced and nobody else can re-run. Astra’s public evidence is the opposite shape: ten machine-checkable proofs in a public repo, verifiable by a stranger with Lean and a laptop, with no access to the model required. See lean-certificate.

That inverts the usual reliability problem without solving it. What the certificates establish is that the mathematics is correct. They establish nothing about the model — not that it found the proofs the way the published narrations describe, not how many attempts it took, not what human steering went in, and not that a released Astra will do anything comparable. The verifiable artifact and the capability claim are two different objects, and only the first one is checkable.

So: strong evidence that ten theorems are true, weak evidence about a model nobody outside OpenAI can run.

Open

Does a shipped Astra resemble the internal one? The distance between an internal research configuration and a rate-limited public endpoint is exactly what this wiki’s benchmark scepticism is about.
Pricing, and whether $2,000-class inference budgets are purchasable. The figure implies a price card that doesn’t exist yet.
Where it sits against GPT-5.6. Successor, sibling, or a different line entirely.

openai · openai-gpt56-grok45-clash · llm-benchmarks · llm-api-pricing · claude-opus-5 · ten-proofs · lean-certificate