I’ve read anywhere from 5 times the normal shelf life… to indefinitly. Amaranth seems to have a normal shelf life of 2 years, so freezing should extend that to 10+ years. I think the range has more to do with the type of freezer and how dry the seeds are. The seeds need to be very dry. One test is to bend the seed. If dry, it should snap. Obviously that test wouldn’t work with the tiny, roundish amarath seed. Commercial seed packs, will probably work much better than seed you save, as they dry their seed properly. You also want to make sure the seed is airtight so that you don’t deal with condensation. I have some small mylar pouches that I use for seed. I’ll add a dessicant and then heat seal the pouch to ensure it is airtight. Another option is just to grow some amaranth each year & save the seed heads. That way you always have a ready supply of seed. The plants are so decorative, you could just plant them in a regular flower bed. The video below, with the giant amaranth, shows you how to dry the seed. In my case, I just chop off the tops of a few plants & hang them in my upper barn. After a few weeks, if you rub the dried flowers, the seeds just falls off. If you are just doing this to get the seed, there is no need to clean the seed of chaff. Just collect it, put in an airtight container & store in a cool spot. I built a prepper closet in my upper barn, that is very well insulated and has a wall mounted air conditioner. That room stays dry & no warmer than 65. I feel that helps my bulk seed and other items last much longer. It can get hot here in Mississippi. But small seed like amaranth goes in the freezer.