OpenAI's efforts fell short of several high-profile objectives by the end of September. A court appeal by the Trump administration to overturn an Anthropic injunction was rejected, and a reported breakthrough on the hodge problem Did not materialize.

OpenAI had been targeting a second Millennium Prize solution before the end of September. The deadline passed without an announcement, confirming that no additional Prize was secured. The company's research teams continued work, but the expected public disclosure Did not occur.

The United States Patent and trademark Office denied OpenAI's request to register "GPT" as a trademark. The decision left the branding unprotected under U.S. trademark law. Meanwhile, financial data showed the firm's valuation remained below $975 billion at the close of September.

The Trump administration sought to reverse a federal injunction against Anthropic, an AI competitor, on appeal. The appellate court upheld the injunction, ending the administration's effort to overturn it.

Speculation had suggested OpenAI might have solved the so-called hodge problem. By the end of September, no solution had been reported, confirming the problem remained unsolved. The research community therefore continued to explore the issue without a breakthrough from OpenAI.