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As part of model development, we evaluate our models on open research problems. We expanded these evaluations after performance on our existing mathematical evaluations saturated. Some outputs build upon earlier results produced by the models.

Bend offers the feel and features of expressive languages like Python and Haskell. This includes fast object allocations, full support for higher-order functions with closures, unrestricted recursion, and even continuations.

Open Ontologies is written in Rust. It ships as one binary.

Conditional integer multiplication: kappa > 2^-15. Community proofs, exact certificates and reproducible audits; assumes the OpenAI #109 framework.

Z3 is a theorem prover from Microsoft Research. It is licensed under the MIT license. Windows binary distributions include C++ runtime redistributables

lean). The argument is that of Frey, Serre, Ribet, Wiles and Taylor-Wiles. md names each step and the Lean theorem that carries it, and the html/ folder presents the whole proof as web pages you can browse offline (see "Reading the proof in a browser" below).

Coding agents now write faster than people can understand what they wrote (Geoffrey Litt, Understanding is the new bottleneck). This repository is for writing, for one reader, only what that reader does not already know, with claims and figures checked by tools.

0-rc2, Mathlib, and Lake. With elan installed, fetch the mathlib cache and build the formalizations with:

This project has not provided a description yet.

Choir aims to spread the cost of a large formalization. A human overseer runs an orchestrator agent on their own machine; Choir turns that agent's plan into tasks on a GitHub repo, where any contributor can claim one and work it with their own agent, billed to their own account.