The bearings you referenced are pretty heavy duty units (they're on my 5200# axle, and are also used on 6000# ones as well.)
I'd be surprised if it wasn't a 1" nut, but hey, you have the part. The popular sizes here seem to be 1" x 14tpi, and 3/4" x 16tpi. There is also a nut normally used on idler hubs that they list as 13/16" fine thread (no idea on the thread pitch, and it appears to be a standard nut, not castellated.)
Hope this helps;
jky
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