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In the nearly four years since the Sochi Olympics, U.S. skaters earned world championships medals and topped Grand Prix series events. Even captured world junior titles.

But this week, two months before PyeongChang, could come the most prestigious victory for a U.S. skater since Meryl Davis and Charlie White became the first U.S. Olympic ice dance champions.

This week is the Grand Prix Final, the second-biggest annual competition after the world championships. It’s also the most exclusive, taking the top six per discipline from the fall Grand Prix series.

And it’s the single biggest indicator of Olympic medal prospects among all pre-PyeongChang competitions this season.

There are six total U.S. entries at the Final in Nagoya, Japan, matching the nation’s biggest-ever contingent — three each in the men’s event and ice dance.

A preview of all four disciplines:

GRAND PRIX FINAL: TV Schedule | Entries/Rankings

MEN

U.S. champion Nathan Chen is the only undefeated male skater in the world this season. He enters Nagoya as a co-favorite at worst with world silver medalist Shoma Uno of Japan.

The world’s other top men’s skaters — world gold and bronze medalists Yuzuru Hanyu and Jin Boyang and two-time world champion Javier Fernandez — aren’t in Nagoya this week. Each dealt with illness or injury this fall but is expected to be fine for the Olympics, where they should join Chen and Uno as the medal favorites.

The absences would take some of the prestige out of a Chen win this week. But beating Uno — the highest-scoring man this season — and wiping away the memory of an error-filled Skate America free skate would be very beneficial.

The last U.S. singles skater to win the Grand Prix Final was Alissa Czisny in 2010. The last U.S. man, Evan Lysacek in 2009 en route to Olympic gold.

Chen and Uno are joined in Nagoya but the 2015 and 2016 U.S. champions — Jason Brown and Adam Rippon — and Russians Mikhail Kolyada and Sergei Voronov.

For Brown and Rippon, just getting to the Grand Prix Final boosts their resumes to be chosen by a committee for the three-man Olympic team following nationals in one month. Though Brown didn’t qualify for the Final outright. He got in with Jin’s withdrawal last week.

WOMEN

The winner here will likely not become the Olympic favorite.

That’s because Russian Yevgenia Medvedeva, undefeated for two years, is out with a broken foot (but expected back if not for the Russian Championships, then definitely the European Championships in January).

In her absence, training partner Alina Zagitova, the 15-year-old world junior champion, enters with the best credentials this season — aside from Medvedeva, the only woman to win both Grand Prix starts plus highest score in the world.

The most likely challengers are Olympic bronze medalist Carolina Kostner, runner-up to Medvedeva in her two Grand Prix starts, and Canadian Kaetlyn Osmond and Japanese Satoko Miyahara, past world silver medalists.

No American in the field for a second straight year.

ICE DANCE

The Grand Prix season brought a change. France’s Gabriella Papadakis and Guillaume Cizeron, the world champions in 2015 and 2016, posted the two highest scores of all time in their two Grand Prix starts.

They broke the world record held by Canadians Tessa Virtue and Scott Moir, who won all three of their head-to-heads with the French last season, including at the world championships.

This will be their first head-to-head this season. It will determine the Olympic favorite.

Nobody else has been within five points of the French or Canadians this season, a clear dividing line in dance rankings.

The favorites to join them on the podium have to be U.S. champions Maia Shibutani and Alex Shibutani, who did just that at last season’s Grand Prix Final and worlds.

In winning Skate America, the Shibutanis posted the second-highest U.S. score under an eight-year system. It trailed only Davis and White from the Sochi Olympics.

Joining the Shibutanis at the Grand Prix Final for a third straight year are U.S. silver and bronze medalists Madison Chock and Evan Bates and Madison Hubbell and Zachary Donohue. Chock and Bates haven’t beaten the Shibutanis since the 2015 Grand Prix Final, and Hubbell and Donohue never have.

Those three couples are overwhelming favorites to make up the U.S. Olympic ice dance contingent named after nationals.

PAIRS

An event that looked wide open after last year’s Grand Prix Final has since been dominated by Chinese Sui Wenjing and Han Cong. They are the biggest favorites in this week’s field.

Sui and Han are undefeated since returning from Sui’s ankle and foot surgeries in February, including leading the world rankings by 10 points this season.

Their primary competition this week may be the world-record score of 237.71 set by Sochi Olympic champions Tatyana Volosozhar and Maksim Trankov, who are no longer active. Sui and Han put up a personal-best 234.53 last time out.

A few teams are jockeying to be the primary challenger.

Russians Yevgenia Tarasova and Vladimir Morozov rank No. 2 in the world this season by total score and also won both of their Grand Prix starts.

Germans Aljona Savchenko and Bruno Massot, the world silver medalists, won the most recent Grand Prix, Skate America, with a personal-best free skate.

Canadians Meagan Duhamel and Eric Radford and Russians Ksenia Stolbova and Fedor Klimov each have season’s best scores within 2.03 points of Tarasova and Morozov.

MORE: Figure skating season broadcast schedule