To determine which statement(s) are not correct, we must evaluate the factual accuracy of each statement based on current knowledge as of October 2023.

1. Statement 1: "The 3^rd WHO Global Summit on Traditional Medicine was held in New Delhi in December 2025."
   • This statement is regarding a future prediction as of October 2023. However, it is already known that the 1^st WHO Global Summit on Traditional Medicine was held in 2023 in India. Any prediction about events in December 2025 cannot be confirmed based on current information. Since there is no supporting information for a planned future summit in 2025 at New Delhi, the accuracy of this statement as of now remains inaccurate.
2. Statement 2: "The theme for the 11^th International Yoga Day 2025 was 'Yoga for One Earth, One Health'."
   • International Yoga Day is celebrated on June 21 each year. The themes for these days are often announced a few months before the event. As of October 2023, there is no official declaration for the 2025 theme. However, as this is a prospective statement, it cannot be confirmed or refuted with available data. Thus, there is no evidence to label this statement incorrect based on current facts.

Conclusion: As of now, given the uncertainties, statement 1 is the only statement with identifiable inaccuracies as it speculates an event in a future context without confirmed scheduling.

Therefore, the correct answer is: 1 only.