Tonight’s puzzle comes from Hikaru Nakamura vs. Robert Lee Hess, 2012 US Championship in St Louis. GM Robert Hess has just played move 30… Kh8. What did GM Nakamura play for white’s 31st move?

What is white’s best move?
Tonight’s puzzle comes from Hikaru Nakamura vs. Robert Lee Hess, 2012 US Championship in St Louis. GM Robert Hess has just played move 30… Kh8. What did GM Nakamura play for white’s 31st move?
What is white’s best move?
Chris Torres is a nationally renowned scholastic chess coach working in the San Francisco Bay Area. His classes have attracted players of strengths ranging from rank beginners to world champions. A chess professional since 1998, Chris is widely recognized as one of the main driving forces behind the explosion in popularity and sudden rise in quality of scholastic chess in California. Chris Torres served as the President of the Torres Chess and Music Academy from 2005-2020 and currently is recognized as a correspondence chess master with the United States Chess Federation. Since 1998 Chris Torres has taught 6 individual national champions as well as led multiple school teams to win national championship titles. In addition, Chris Torres has directed and taught at 10 different schools which have been California State Champions at chess. In 2011 and 2012, several former and current students of Chris Torres have been selected to represent the United States at the World Youth Chess Championships. Mr. Torres’ hobbies include playing classical guitar and getting his students to appear on the national top 100 chess rating lists. View more posts
I think it might actually be a mate in 9:
1 Rxg7 Kxg7 (Kxg7 forced to prevent Qh7#)
2 Rg3+ Kf7 (2…Kf8 3 Qh7 Qxg2+ 4 Rxg2 Rc7 5 Rg8#, 2…Kh8 3 Qg6 Qxg2+ 4 Rxg2 Rc7 5 Qxe8+ Kh7 6
Qg8#, 2…Kh8 3 Qg6 Qxg2+ 4 Rxg2 Re7 5 Qg8#.)
3 Qf3+ Ke7
4 Rg7+ Kd8
5 Qb7 Qa4 (5…Qxg2+ 6 Kxg2 Re7 7 Qxe7+ Kc8 8 Qb7+ Kd8 9 Qd7#, 5…Qxg2+ 6 Kxg2 Rc7 7 Qxc7# (any other
move that does not protect d7 and is not check is useless, e.g. 5…a4 6 Qd7# ))
6 Qb6+ Kc8 (6…Rc7 7 Qxc7#.)
7 Qxc5+ Qc6
8 Qxc6+ Kb8 (8…Kd8 9 Qc7# or 9 Qd7#.)
9 Qxe8# (or Qb7#)
If you could respond, I would be very grateful. Thank you for the great puzzle!