Resolution is based on the chatbot arena LLM leaderboard (https://lmarena.ai), specifically the company with the highest Text Arena score in the Math category.
In the case of a tie, all companies tied for 1st place resolve to equal probability, such that they sum to 100%.
Ranking as of Aug 19, 2025:

See also:
Which company has best AI model end of 2025? (Chatbot Arena Leaderboard)
/Bayesian/which-company-has-the-best-ai-model
/Bayesian/who-will-have-the-best-texttoimage-SO0uN6suuS
/Bayesian/who-will-have-the-best-texttovideo-AtZ0CdIc8Z
/Bayesian/which-company-has-best-ai-computer
/Bayesian/which-company-has-best-vision-ai-en
/Bayesian/which-company-has-best-search-ai-mo
Update 2025-12-05 (PST) (AI summary of creator comment): The market will resolve based on the Chatbot Arena Leaderboard with style control ON.
@traders Some trader asked me whether style control is on or off for this market. I'll go with the option used in the screenshot in the question description, which is style control on.