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OpenAI: For this release, we are publishing our results in a GitHub code repository, along with paper revisions and citation guidelines. For future result releases, we commit to further improving paper quality, refining literature citations, mathematical exposition, and the presentation of results to facilitate understanding by the academic community. The repository provides a large amount of proof formalization code completed in the Lean language. To ensure scientific transparency and openness, the repository also discloses more process details of this research: including 10 model reasoning summaries, estimates of computational resource consumption benchmarked against ChatGPT Pro compute, and statistics on the problems the model attempted to solve. The average compute consumed per result is roughly equivalent to the compute required for three hours of deep thinking by ChatGPT Pro.