We do have a few problems, though, mainly because the Indians will want to buy it.
One: if Checkmate is stealthy enough to counter the F-35, it'll pose a major threat to the J-20. The J-20 will have to rely on laser pods to gain a decisive advantage.
Two: if Checkmate isn't stealthy enough to counter the F-35, the J-20s will only have trouble if the Indians have them in massive numbers, but Checkmate won't allow the Russians to counter the F-35.
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One other way to think of it is that the J-20 and Su-57 were intended to counter the F-22, but the F-35 has significant advantages over the F-22 in certain realms (stealth, sensors, strike). Stuff like Checkmate (and perhaps the FC-31) are intended to counter the F-35. The FC-31 though, in being twin-engined, seems to be intended at a purely qualititative as opposed to quantitative counter to the F-35. Checkmate might be both, but it all depends on Russian stealth design and Russian sensors. If the Russians can't get Checkmate stealthy enough and have sufficient sensor quality, it's just skeet.
On the other hand, the fact that the Russians aren't hobbled by engines like the Chinese are mean that they can get a design like this out early. If you look at the scale of the aircraft, there is a strong chance that this is powered by a Russian upgrade of their RD-33s, not a single Item 30. It's tiny.