A lot of multi-syllable -ion words will be tossed around following the United States' return to the top of the Olympic podium in women's soccer after a 1-0 win over Brazil on Saturday at the Parc des Princes.

Redemption will be one. Vindication another. Reclamation, too. All fit in their own way, but aren't perfect.

We'll proffer restoration. In just a few months on the job, Emma Hayes has restored the USWNT by underlining the program's swagger with respect and discipline.

The most-celebrated program in the game has won gold for the first time since 2012, and their fifth Olympic gold medal in eight tries does indeed feel restorative.

Think about it this way: Gold, silver, gold, gold, gold, quarterfinals, bronze, gold.

And while there's little-to-no chance the USWNT will continue to win major trophies at its previous rate, there's more reason for hope in the team's power than there has been at any point since their last World Cup win.

Emma Hayes was hired from Chelsea in November and given the freedom to finish her season with the Women's Super League club, a show of respect and maybe a bit of desperation from U.S. Soccer.

The last boss was hired with the seeming endorsement of if not outright selection by the star players of the last generation. He won 79% of his matches as USWNT boss but the team did poorly in major tournaments and seemed to lack ideas other than "be better than the other team." It sounds uninspired and it looked that way, too.

Hayes' hire screamed change with purpose — not just for the sake of change. Her reputation in Europe is nearly spotless and she spent a decade in the United States burnishing her coaching credentials before going to Chelsea. Her journey in the U.S. after playing at Arsenal's academy saw her truly put in grunt work and rapidly rise from the college to pro level here. So she knew the culture but didn't have to cater to any parts of it that would get in the way of her imprint.

And how about her response when Mike Tirico asked her what turned the program around so quickly?

"Just love," Hayes said. "I come from a place of wanting players to enjoy themselves. I've been at a club at 12 years and I've had huge success but I was desperate to do it for this country. It's not every day you win a gold medal."

Why did she want to win in the United States?

I love America," Hayes said, continuing to speak through tears. "It made me, and I always say that.

So it's not a surprise that this team bought into the idea of Hayes, but it's still very impressive that the coach was able to make bold and correct choices while limited to a slim 18-player roster, moving away from living legends in some cases in order to make this first major tournament her tournament.

Her tournament was awesome. And so we go back to those syllables.

Redemption. Nine of these players were on the last U.S. Olympic team, while more were at the side's worst ever World Cup finish in 2023. And while it's no shame to lose a major tournament given the quality of teams around the world, the performances of that team were not at that level. For some of these players, especially Alyssa Naeher and Crystal Dunn, they've re-stamped their living legend passports with primary driver status. The tears streaming down the face of Lindsey Horan and pals after the final whistle were that of release.

Vindication. Many players including Dunn, Naomi Girma and Trinity Rodman have been on USWNT teams but forced to wait their turn at major tournaments. And Hayes drew ire from some corners when she left Alex Morgan off this Olympic roster.

Reclamation. The Yanks are back on top after just 10 games under Hayes. Nine wins, one draw, and zero minutes trailing to an opponent. It's possible Hayes doesn't know her best team yet — the midfield is still a huge question mark — and she's got a gold medal. This team went to extra time twice in two matches leading up to this game. They were going against an in-form side buzzing to give Marta — its (and maybe any nation's) best ever player — a first gold medal. They stood firm. 

Restoration. This win puts the U.S. at the top. There's no guarantee for future success, of course, but Hayes' team has just shown just so much. Her game-controlling center back Girma just turned 24. Korbin Albert's 20. The members of "Triple Espresso" are 26, 23, and 22. And Lily Yohannes (17), Catarina Macario (24), and other young pieces may well slot into this unit for the 2027 World Cup in Brazil.

Swanson missed the last World Cup through a devasting late injury, Rodman was barely used, and Smith often left on an island. They could conceivably be the stars in attack for five more years but will also have to fight for their places in the squad.

Julie Foudy and then Jon Champion said, "We're back, baby" at the end of the NBC broadcast of the gold medal game.

Sure feels that way.