The internal version of the new Astra model from OpenAI has received ten important results in mathematics. The developers described these achievements as significant progress in high-dimensional geometry and coding theory. The company has released a voluminous paper with detailed analyses explaining the reasoning behind the neural network. The researchers also published a special repository with formalizations of all proofs in the Lean 4 language. The mathematical arguments were completely generated by the internal version of the system, working without direct human intervention. People only prepared the final manuscripts together with the neural network, passing them on to the scientific community. Representatives of OpenAI emphasized the importance of honest attribution, describing the process of obtaining intellectual results. Attributing authorship to a human would distort the real contribution of AI developing modern science. The total amount of calculations to find solutions would cost about two thousand dollars. This assessment does not include a follow-up check performed by the mathematical community.

One of the stated results directly concerns the problem of quantum parallel repeatability. This concept describes the change in the probability of success when running an interactive game multiple times. The neural network has proven exponential repeatability for arbitrary finite quantum games with two participants. This result may be important for the development of new cryptographic protocols. Another achievement relates to the difficult task of finding the nearest lattice vector. The model obtained a stronger result on the complexity of the approximate solution of this problem. OpenAI calls the successful construction of a non-technological group the main achievement of the publication. Among other results, improved estimates for packing balls in high dimensions were noted. The researchers also introduced new lower bounds in arithmetic circuit complexity. The company announced that it had found a counterexample to the well-known Conn rigidity hypothesis.

Formalizing proofs in Lean language significantly reduces the risk of common logical gaps. The published code can be easily assembled and verified by machine methods. However, automatic verification is absolutely no substitute for a full-fledged scientific examination. Mathematicians have yet to assess the accuracy of matching formal statements to the original problems. OpenAI directly referred to the Leiden Declaration approved by the International Mathematical Union. This document calls for maintaining transparent attribution when using AI in research. The Company assumes full responsibility for the correctness of the published materials. At the same time, the mathematical arguments themselves are attributed to the system, not to people. The publication The Quantum Insider noted the absence of a date for the public launch of the Astra model. The developers have not yet provided the neural network for independent testing by external experts.