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In a frantic and tightly contested bout, the No 4-seeded Nyika did enough to win over one of the five judges on the panel to be on the wrong side of a 4-1 scorecard. Missing out on a spot in the gold medal fight, Nyika automatically claims bronze, as bronze medals are awarded to both semifinal losers in the boxing tournament.
In claiming the bronze, Nyika becomes the fourth New Zealander to claim a boxing medal at the Olympic games, after Ted Morgan (welterweight gold, 1928), Kevin Barry (light heavyweight silver, 1984), and David Tua (heavyweight bronze, 1992).
Speaking to Sky Sport after the bout, Nyika held back tears as he thanked his family and supporters, saying he had "never felt so connected" as he has over the past couple of weeks.
"It might be my last outing on this team at a Games and I'm going to miss it," Nyika said.
"This has been the best two weeks of my life. Just feeling the love from the team, the culture - it's incredible. I'm going to miss it so much.
"This has been an amazing journey. I'm so proud to be representing the best nation in the world. I have so much pride for our culture and I'm never going to forget this time in my life."
Coming into the fight, Gadzhimagomedov had not lost a bout since 2017 and was 1-0 against Nyika, winning their only match-up in 2019 by unanimous decision.
The two highest seeds remaining in the competition put on a terrific showcase for the sport as they traded heavy shots, flaunted their speed, head movement and footwork. Gadzhimagomedov came out the better of the two early.
While having success with his jab, Nyika was a bit loose at times with his overhand left as he looked to make Gadzhimagomedov feel his power. The speedy Russian avoided most of these, although both wore a few power shots in the opening round, with the Russian swaying all but one of the judges in the opening round.
Nyika made adjustments in the second round – after getting touched up a bit early in the round – and landed with more volume in the second round. Gadzhimagomedov read Nyika's entrance into range well and caught him a few times, but resorted to clinching when Nyika got inside the jab, which appeared to have the Kiwi frustrated.
Nyika had a strong second half of the round, but Gadzhimagomedov finished with a flurry in the final 20 seconds and won over four of the five judges again.
Gadzhimagomedov appeared to feel like he had the first two rounds in the bag as he played things rather safe in the final round – fighting behind his jab and trying to clinch whenever Nyika came into a range in which he could utilise his power.
When the final bell sounded, it appeared Nyika knew what was coming on the scorecards as he gave Gadzhimagomedov a nod as they touched gloves.
Nyika won all three rounds on one judge's scorecard, but the other four judges saw it in favour of Gadzhimagomedov.
"It wasn't the result I needed; not quite the performance either, but it's been a tough road getting here and I take no credit away from Muslim...all credit to him."
It was the last bout of Nyika's amateur career, as he now turns his attention to the professional realm.